Daily Papers

Self-supervised learning (SSL) has been extensively explored in recent years. Particularly, generative SSL has seen emerging success in natural language processing and other AI fields, such as the wide adoption of BERT and GPT. Despite this, contrastive learning-which heavily relies on structural data augmentation and complicated training strategies-has been the dominant approach in graph SSL, while the progress of generative SSL on graphs, especially graph autoencoders (GAEs), has thus far not reached the potential as promised in other fields. In this paper, we identify and examine the issues that negatively impact the development of GAEs, including their reconstruction objective, training robustness, and error metric. We present a masked graph autoencoder GraphMAE that mitigates these issues for generative self-supervised graph pretraining. Instead of reconstructing graph structures, we propose to focus on feature reconstruction with both a masking strategy and scaled cosine error that benefit the robust training of GraphMAE. We conduct extensive experiments on 21 public datasets for three different graph learning tasks. The results manifest that GraphMAE-a simple graph autoencoder with careful designs-can consistently generate outperformance over both contrastive and generative state-of-the-art baselines. This study provides an understanding of graph autoencoders and demonstrates the potential of generative self-supervised pre-training on graphs.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

A deep hashing model typically has two main learning objectives: to make the learned binary hash codes discriminative and to minimize a quantization error. With further constraints such as bit balance and code orthogonality, it is not uncommon for existing models to employ a large number (>4) of losses. This leads to difficulties in model training and subsequently impedes their effectiveness. In this work, we propose a novel deep hashing model with only a single learning objective. Specifically, we show that maximizing the cosine similarity between the continuous codes and their corresponding binary orthogonal codes can ensure both hash code discriminativeness and quantization error minimization. Further, with this learning objective, code balancing can be achieved by simply using a Batch Normalization (BN) layer and multi-label classification is also straightforward with label smoothing. The result is an one-loss deep hashing model that removes all the hassles of tuning the weights of various losses. Importantly, extensive experiments show that our model is highly effective, outperforming the state-of-the-art multi-loss hashing models on three large-scale instance retrieval benchmarks, often by significant margins. Code is available at https://github.com/kamwoh/orthohash

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

Quantization has emerged as a standard technique for accelerating inference for generative models by enabling faster low-precision computations and reduced memory transfers. Recently, GPU accelerators have added first-class support for microscaling Block Floating Point (BFP) formats. Standard BFP algorithms use a fixed scale based on the maximum magnitude of the block. We observe that this scale choice can be suboptimal with respect to quantization errors. In this work, we propose ScaleSearch, an alternative strategy for selecting these scale factors: using a fine-grained search leveraging the mantissa bits in microscaling formats to minimize the quantization error for the given distribution. ScaleSearch can be integrated with existing quantization methods such as Post Training Quantization and low-precision attention, and is shown to improve their performance. Additionally, we introduce ScaleSearchAttention, an accelerated NVFP4-based attention algorithm, which uses ScaleSearch and adapted prior techniques to ensure near-0 performance loss for causal language modeling. Experiments show that ScaleSearch reduces quantization error by 27% for NVFP4 and improves language model PTQ by up to 15 points for MATH500 (Qwen3-8B), while ScaleSearchAttention improves Wikitext-2 PPL by upto 0.77 points for Llama 3.1 70B. The proposed methods closely match baseline performance while providing quantization accuracy improvements.

Requirement traceability is the process of identifying the inter-dependencies between requirements. It poses a significant challenge when conducted manually, especially when dealing with requirements at various levels of abstraction. In this work, we propose a novel approach to automate the task of linking high-level business requirements with more technical system requirements. The proposed approach begins by representing each requirement using a Bag of-Words (BOW) model combined with the Term Frequency-Inverse Document Frequency (TF-IDF) scoring function. Then, we suggested an enhanced cosine similarity that uses recent advances in word embedding representation to correct traditional cosine similarity function limitations. To evaluate the effectiveness of our approach, we conducted experiments on three well-known datasets: COEST, WARC(NFR), and WARC(FRS). The results demonstrate that our approach significantly improves efficiency compared to existing methods. We achieved better results with an increase of approximately 18.4% in one of the datasets, as measured by the F2 score.

Large language models (LLMs) demand substantial computational and memory resources, creating deployment challenges. Quantization-aware training (QAT) addresses these challenges by reducing model precision while maintaining performance. However, the scaling behavior of QAT, especially at 4-bit precision (W4A4), is not well understood. Existing QAT scaling laws often ignore key factors such as the number of training tokens and quantization granularity, which limits their applicability. This paper proposes a unified scaling law for QAT that models quantization error as a function of model size, training data volume, and quantization group size. Through 268 QAT experiments, we show that quantization error decreases as model size increases, but rises with more training tokens and coarser quantization granularity. To identify the sources of W4A4 quantization error, we decompose it into weight and activation components. Both components follow the overall trend of W4A4 quantization error, but with different sensitivities. Specifically, weight quantization error increases more rapidly with more training tokens. Further analysis shows that the activation quantization error in the FC2 layer, caused by outliers, is the primary bottleneck of W4A4 QAT quantization error. By applying mixed-precision quantization to address this bottleneck, we demonstrate that weight and activation quantization errors can converge to similar levels. Additionally, with more training data, weight quantization error eventually exceeds activation quantization error, suggesting that reducing weight quantization error is also important in such scenarios. These findings offer key insights for improving QAT research and development.

Recent research has generated hope that inference scaling could allow weaker language models to match or exceed the accuracy of stronger models, such as by repeatedly sampling solutions to a coding problem until it passes unit tests. The central thesis of this paper is that there is no free lunch for inference scaling: indefinite accuracy improvement through resampling can only be realized if the "verifier" (in this case, a set of unit tests) is perfect. When the verifier is imperfect, as it almost always is in domains such as reasoning or coding (for example, unit tests have imperfect coverage), there is a nonzero probability of false positives: incorrect solutions that pass the verifier. Resampling cannot decrease this probability, so it imposes an upper bound to the accuracy of resampling-based inference scaling even with an infinite compute budget. We find that there is a very strong correlation between the model's single-sample accuracy (i.e. accuracy without unit tests) and its false positive rate on coding benchmarks HumanEval and MBPP, whose unit tests have limited coverage. Therefore, no amount of inference scaling of weaker models can enable them to match the single-sample accuracy of a sufficiently strong model (Fig. 1a). When we consider that false positives have a negative utility compared to abstaining from producing a solution, it bends the inference scaling curve further downward. Empirically, we find that the optimal number of samples can be less than 10 under realistic assumptions (Fig. 1b). Finally, we show that beyond accuracy, false positives may have other undesirable qualities, such as poor adherence to coding style conventions.

Large Reasoning Models (LRMs) have shown impressive capabilities in complex problem-solving, often benefiting from training on difficult mathematical problems that stimulate intricate reasoning. Recent efforts have explored automated synthesis of mathematical problems by prompting proprietary models or large-scale open-source models from seed data or inherent mathematical concepts. However, scaling up these methods remains challenging due to their high computational/API cost, complexity of prompting, and limited difficulty level of the generated problems. To overcome these limitations, we propose ScaleDiff, a simple yet effective pipeline designed to scale the creation of difficult problems. We efficiently identify difficult problems from existing datasets with only a single forward pass using an adaptive thinking model, which can perceive problem difficulty and automatically switch between "Thinking" and "NoThinking" modes. We then train a specialized difficult problem generator (DiffGen-8B) on this filtered difficult data, which can produce new difficult problems in large scale, eliminating the need for complex, per-instance prompting and its associated high API costs. Fine-tuning Qwen2.5-Math-7B-Instruct on the ScaleDiff-Math dataset yields a substantial performance increase of 11.3% compared to the original dataset and achieves a 65.9% average accuracy on AIME'24, AIME'25, HMMT-Feb'25, BRUMO'25, and MATH500, outperforming recent strong LRMs like OpenThinker3. Notably, this performance is achieved using the cost-efficient Qwen3-8B model as a teacher, demonstrating that our pipeline can effectively transfer advanced reasoning capabilities without relying on larger, more expensive teacher models. Furthermore, we observe a clear scaling phenomenon in model performance on difficult benchmarks as the quantity of difficult problems increases. Code: https://github.com/QizhiPei/ScaleDiff.

Applications such as weather forecasting and personalized medicine demand models that output calibrated probability estimates---those representative of the true likelihood of a prediction. Most models are not calibrated out of the box but are recalibrated by post-processing model outputs. We find in this work that popular recalibration methods like Platt scaling and temperature scaling are (i) less calibrated than reported, and (ii) current techniques cannot estimate how miscalibrated they are. An alternative method, histogram binning, has measurable calibration error but is sample inefficient---it requires O(B/ε^2) samples, compared to O(1/ε^2) for scaling methods, where B is the number of distinct probabilities the model can output. To get the best of both worlds, we introduce the scaling-binning calibrator, which first fits a parametric function to reduce variance and then bins the function values to actually ensure calibration. This requires only O(1/ε^2 + B) samples. Next, we show that we can estimate a model's calibration error more accurately using an estimator from the meteorological community---or equivalently measure its calibration error with fewer samples (O(B) instead of O(B)). We validate our approach with multiclass calibration experiments on CIFAR-10 and ImageNet, where we obtain a 35% lower calibration error than histogram binning and, unlike scaling methods, guarantees on true calibration. In these experiments, we also estimate the calibration error and ECE more accurately than the commonly used plugin estimators. We implement all these methods in a Python library: https://pypi.org/project/uncertainty-calibration

Scaling up the size of vision models has been the de facto standard to obtain more powerful visual representations. In this work, we discuss the point beyond which larger vision models are not necessary. First, we demonstrate the power of Scaling on Scales (S^2), whereby a pre-trained and frozen smaller vision model (e.g., ViT-B or ViT-L), run over multiple image scales, can outperform larger models (e.g., ViT-H or ViT-G) on classification, segmentation, depth estimation, Multimodal LLM (MLLM) benchmarks, and robotic manipulation. Notably, S^2 achieves state-of-the-art performance in detailed understanding of MLLM on the V* benchmark, surpassing models such as GPT-4V. We examine the conditions under which S^2 is a preferred scaling approach compared to scaling on model size. While larger models have the advantage of better generalization on hard examples, we show that features of larger vision models can be well approximated by those of multi-scale smaller models. This suggests most, if not all, of the representations learned by current large pre-trained models can also be obtained from multi-scale smaller models. Our results show that a multi-scale smaller model has comparable learning capacity to a larger model, and pre-training smaller models with S^2 can match or even exceed the advantage of larger models. We release a Python package that can apply S^2 on any vision model with one line of code: https://github.com/bfshi/scaling_on_scales.

Widely observed neural scaling laws, in which error falls off as a power of the training set size, model size, or both, have driven substantial performance improvements in deep learning. However, these improvements through scaling alone require considerable costs in compute and energy. Here we focus on the scaling of error with dataset size and show how in theory we can break beyond power law scaling and potentially even reduce it to exponential scaling instead if we have access to a high-quality data pruning metric that ranks the order in which training examples should be discarded to achieve any pruned dataset size. We then test this improved scaling prediction with pruned dataset size empirically, and indeed observe better than power law scaling in practice on ResNets trained on CIFAR-10, SVHN, and ImageNet. Next, given the importance of finding high-quality pruning metrics, we perform the first large-scale benchmarking study of ten different data pruning metrics on ImageNet. We find most existing high performing metrics scale poorly to ImageNet, while the best are computationally intensive and require labels for every image. We therefore developed a new simple, cheap and scalable self-supervised pruning metric that demonstrates comparable performance to the best supervised metrics. Overall, our work suggests that the discovery of good data-pruning metrics may provide a viable path forward to substantially improved neural scaling laws, thereby reducing the resource costs of modern deep learning.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

In this work, we aim to discretize the high-dimensional visual representations to bridge the gap with language models - a non-trivial challenge, as existing quantization methods suffer from codebook collapse, failing to scale while preserving semantic coherence. We identify the root cause as metric mismatch: standard Euclidean codebook objectives are fundamentally misaligned with the anisotropic geometry of representation space, leading to codebook embeddings with high-variance magnitude scales and uneven angular distributions that hinder scalability. To address this, we propose Hyper-Spherical Quantization (HSQ), which decouples semantic content from feature magnitude via angular routing, preventing code assignment from being dominated by scale rather than meaning. The resulting discrete Representation Autoencoder (dRAE) achieves high-fidelity reconstruction while preserving semantic integrity and supporting scalable codebook budget. Extensive experiments demonstrate consistent performance gains as the vocabulary size scales to 131{,}072, along with 100\% codebook utilization, simplified training pipeline, and strong performance across understanding and generation tasks.

We present unit scaling, a paradigm for designing deep learning models that simplifies the use of low-precision number formats. Training in FP16 or the recently proposed FP8 formats offers substantial efficiency gains, but can lack sufficient range for out-of-the-box training. Unit scaling addresses this by introducing a principled approach to model numerics: seeking unit variance of all weights, activations and gradients at initialisation. Unlike alternative methods, this approach neither requires multiple training runs to find a suitable scale nor has significant computational overhead. We demonstrate the efficacy of unit scaling across a range of models and optimisers. We further show that existing models can be adapted to be unit-scaled, training BERT-Large in FP16 and then FP8 with no degradation in accuracy.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

As large language models have grown larger, interest has grown in low-precision numerical formats such as NVFP4 as a way to improve speed and reduce memory usage. However, quantizing models to NVFP4 remains difficult as the lack of precision generally degrades model performance. In this work, we address this issue with Four Over Six (4/6), a modification to the block-scaled NVFP4 quantization algorithm that yields reduced quantization error. Unlike integer formats, floating point formats have non-uniform step sizes which create larger quantization error on larger values. 4/6 takes advantage of this by adaptively scaling some blocks to smaller FP4 values, making the distribution of representable values more uniform and reducing quantization error for near-maximal values. We show that 4/6 can be implemented efficiently on NVIDIA Blackwell GPUs, resulting in performance gains during both pre-training and inference with minimal computational overhead. In pre-training experiments with the Nemotron 3 Nano 30B-A3B model architecture, we find that 4/6 brings training loss closer to BF16 compared to models trained with current state-of-the-art NVFP4 training recipes. Our code is available at http://github.com/mit-han-lab/fouroversix.

We estimate ([M/H], [alpha/M]) for 48 million giants and dwarfs in low-dust extinction regions from the Gaia DR3 XP spectra by using tree-based machine-learning models trained on APOGEE DR17 and metal-poor star sample from Li et al. The root mean square error of our estimation is 0.0890 dex for [M/H] and 0.0436 dex for [alpha/M], when we evaluate our models on the test data that are not used in training the models. Because the training data is dominated by giants, our estimation is most reliable for giants. The high-[alpha/M] stars and low-[alpha/M] stars selected by our ([M/H], [alpha/M]) show different kinematical properties for giants and low-temperature dwarfs. We further investigate how our machine-learning models extract information on ([M/H], [alpha/M]). Intriguingly, we find that our models seem to extract information on [alpha/M] from Na D lines (589 nm) and Mg I line (516 nm). This result is understandable given the observed correlation between Na and Mg abundances in the literature. The catalog of ([M/H], [alpha/M]) as well as their associated uncertainties are publicly available online.

In embedding-based retrieval, Approximate Nearest Neighbor (ANN) search enables efficient retrieval of similar items from large-scale datasets. While maximizing recall of relevant items is usually the goal of retrieval systems, a low precision may lead to a poor search experience. Unlike lexical retrieval, which inherently limits the size of the retrieved set through keyword matching, dense retrieval via ANN search has no natural cutoff. Moreover, the cosine similarity scores of embedding vectors are often optimized via contrastive or ranking losses, which make them difficult to interpret. Consequently, relying on top-K or cosine-similarity cutoff is often insufficient to filter out irrelevant results effectively. This issue is prominent in product search, where the number of relevant products is often small. This paper introduces a novel relevance filtering component (called "Cosine Adapter") for embedding-based retrieval to address this challenge. Our approach maps raw cosine similarity scores to interpretable scores using a query-dependent mapping function. We then apply a global threshold on the mapped scores to filter out irrelevant results. We are able to significantly increase the precision of the retrieved set, at the expense of a small loss of recall. The effectiveness of our approach is demonstrated through experiments on both public MS MARCO dataset and internal Walmart product search data. Furthermore, online A/B testing on the Walmart site validates the practical value of our approach in real-world e-commerce settings.

Test-time scaling is a powerful approach to obtain better reasoning in large language models, but it becomes memory-bottlenecked during long-horizon decoding, as the KV-cache grows. KV-cache quantization can help improve this, but current methods are evaluated under prefill-like settings and errors behave differently under autoregressive decoding. We show that in the latter regime, quantization errors accumulate across timesteps, driven primarily by incorrect token scales. We introduce KVarN, a calibration-free KV-cache quantizer that applies a Hadamard rotation followed by a dual-scaling variance normalization across both axes of the K and V matrices. We find that this combination fixes outlying token-scale errors and substantially reduces error accumulation over existing baselines. KVarN establishes a new state-of-theart for KV-cache quantization on generative benchmarks, including MATH500, AIME24 and HumanEval, at 2-bit precision. A vLLM implementation of the KVarN method is available at https://github.com/huawei-csl/KVarN

This work presents the first quantitative study of alignment errors between small uncrewed aerial systems (sUAS) geospatial imagery and a priori building polygons and finds that alignment errors are non-uniform and irregular. The work also introduces a publicly available dataset of imagery, building polygons, and human-generated and curated adjustments that can be used to evaluate existing strategies for aligning building polygons with sUAS imagery. There are no efforts that have aligned pre-existing spatial data with sUAS imagery, and thus, there is no clear state of practice. However, this effort and analysis show that the translational alignment errors present in this type of data, averaging 82px and an intersection over the union of 0.65, which would induce further errors and biases in downstream machine learning systems unless addressed. This study identifies and analyzes the translational alignment errors of 21,619 building polygons in fifty-one orthomosaic images, covering 16787.2 Acres (26.23 square miles), constructed from sUAS raw imagery from nine wide-area disasters (Hurricane Ian, Hurricane Harvey, Hurricane Michael, Hurricane Ida, Hurricane Idalia, Hurricane Laura, the Mayfield Tornado, the Musset Bayou Fire, and the Kilauea Eruption). The analysis finds no uniformity among the angle and distance metrics of the building polygon alignments as they present an average degree variance of 0.4 and an average pixel distance variance of 0.45. This work alerts the sUAS community to the problem of spatial alignment and that a simple linear transform, often used to align satellite imagery, will not be sufficient to align spatial data in sUAS orthomosaic imagery.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

In this work we analyze strategies for convolutional neural network scaling; that is, the process of scaling a base convolutional network to endow it with greater computational complexity and consequently representational power. Example scaling strategies may include increasing model width, depth, resolution, etc. While various scaling strategies exist, their tradeoffs are not fully understood. Existing analysis typically focuses on the interplay of accuracy and flops (floating point operations). Yet, as we demonstrate, various scaling strategies affect model parameters, activations, and consequently actual runtime quite differently. In our experiments we show the surprising result that numerous scaling strategies yield networks with similar accuracy but with widely varying properties. This leads us to propose a simple fast compound scaling strategy that encourages primarily scaling model width, while scaling depth and resolution to a lesser extent. Unlike currently popular scaling strategies, which result in about O(s) increase in model activation w.r.t. scaling flops by a factor of s, the proposed fast compound scaling results in close to O(s) increase in activations, while achieving excellent accuracy. This leads to comparable speedups on modern memory-limited hardware (e.g., GPU, TPU). More generally, we hope this work provides a framework for analyzing and selecting scaling strategies under various computational constraints.

We present an online post-hoc calibration method, called Online Platt Scaling (OPS), which combines the Platt scaling technique with online logistic regression. We demonstrate that OPS smoothly adapts between i.i.d. and non-i.i.d. settings with distribution drift. Further, in scenarios where the best Platt scaling model is itself miscalibrated, we enhance OPS by incorporating a recently developed technique called calibeating to make it more robust. Theoretically, our resulting OPS+calibeating method is guaranteed to be calibrated for adversarial outcome sequences. Empirically, it is effective on a range of synthetic and real-world datasets, with and without distribution drifts, achieving superior performance without hyperparameter tuning. Finally, we extend all OPS ideas to the beta scaling method.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting into improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. The high-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of real data sets exhibit advantages of the proposed methods.

Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length n summation, the worst-case error of SR grows as n with high probability, unlike for standard modes, like round-to-nearest (RN), which grows as n. For this reason, the former is increasingly employed in large-scale, low-precision computations as an RN alternative. Additionally, SR alleviates stagnation, whereby relatively small summands are completely rounded off and do not contribute to the sum. We provide an update to [Croci et al., Roy. Soc. Open Sci. 9.3 (2022), pp. 1-25], a survey which discusses the development and use of SR between 1949 and 2022, citing over 100 references. Since then, there has been a surge of new research, and this update covers almost four years of further progress in applying, analysing, and implementing SR. Our main focus is limited-precision stochastic rounding, a new variant that fixes the precision of the random numbers used. We provide insights into industrial and numerical analysis activities surrounding SR, highlighting the next possible steps in making this rounding mode more widely available in hardware.

Kaplan et al. and Hoffmann et al. developed influential scaling laws for the optimal model size as a function of the compute budget, but these laws yield substantially different predictions. We explain the discrepancy by reproducing the Kaplan scaling law on two datasets (OpenWebText2 and RefinedWeb) and identifying three factors causing the difference: last layer computational cost, warmup duration, and scale-dependent optimizer tuning. With these factors corrected, we obtain excellent agreement with the Hoffmann et al. (i.e., "Chinchilla") scaling law. Counter to a hypothesis of Hoffmann et al., we find that careful learning rate decay is not essential for the validity of their scaling law. As a secondary result, we derive scaling laws for the optimal learning rate and batch size, finding that tuning the AdamW beta_2 parameter is essential at lower batch sizes.

Large, pretrained models are commonly finetuned with imagery that is heavily augmented to mimic different conditions and scales, with the resulting models used for various tasks with imagery from a range of spatial scales. Such models overlook scale-specific information in the data for scale-dependent domains, such as remote sensing. In this paper, we present Scale-MAE, a pretraining method that explicitly learns relationships between data at different, known scales throughout the pretraining process. Scale-MAE pretrains a network by masking an input image at a known input scale, where the area of the Earth covered by the image determines the scale of the ViT positional encoding, not the image resolution. Scale-MAE encodes the masked image with a standard ViT backbone, and then decodes the masked image through a bandpass filter to reconstruct low/high frequency images at lower/higher scales. We find that tasking the network with reconstructing both low/high frequency images leads to robust multiscale representations for remote sensing imagery. Scale-MAE achieves an average of a 2.4 - 5.6% non-parametric kNN classification improvement across eight remote sensing datasets compared to current state-of-the-art and obtains a 0.9 mIoU to 1.7 mIoU improvement on the SpaceNet building segmentation transfer task for a range of evaluation scales.

Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create high-quality mathematical reasoning data using frontier LLMs (e.g., {\tt GPT-3.5}). Inspired by the cognitive mechanism in human mathematical learning, it first extracts topics and knowledge points from seed math questions and then build a concept graph, which is subsequently used to generate new math questions. MathScale exhibits effective scalability along the size axis of the math dataset that we generate. As a result, we create a mathematical reasoning dataset (MathScaleQA) containing two million math question-answer pairs. To evaluate mathematical reasoning abilities of LLMs comprehensively, we construct {\sc MwpBench}, a benchmark of Math Word Problems, which is a collection of ten datasets (including GSM8K and MATH) covering K-12, college, and competition level math problems. We apply MathScaleQA to fine-tune open-source LLMs (e.g., LLaMA-2 and Mistral), resulting in significantly improved capabilities in mathematical reasoning. Evaluated on {\sc MwpBench}, MathScale-7B achieves state-of-the-art performance across all datasets, surpassing its best peers of equivalent size by 42.9\% in micro average accuracy and 43.7\% in macro average accuracy, respectively.

Recent advances in large language models (LLMs) highlight a strong connection between intelligence and compression. Learned image compression, a fundamental task in modern data compression, has made significant progress in recent years. However, current models remain limited in scale, restricting their representation capacity, and how scaling model size influences compression performance remains unexplored. In this work, we present a pioneering study on scaling up learned image compression models and revealing the performance trends through scaling laws. Using the recent state-of-the-art HPCM model as baseline, we scale model parameters from 68.5 millions to 1 billion and fit power-law relations between test loss and key scaling variables, including model size and optimal training compute. The results reveal a scaling trend, enabling extrapolation to larger scale models. Experimental results demonstrate that the scaled-up HPCM-1B model achieves state-of-the-art rate-distortion performance. We hope this work inspires future exploration of large-scale compression models and deeper investigations into the connection between compression and intelligence.

Low-precision training is considered an effective strategy for reducing both training and downstream inference costs. Previous scaling laws for precision mainly focus on integer quantization, which pay less attention to the constituents in floating-point quantization and thus cannot well fit the LLM losses in this scenario. In contrast, while floating-point quantization training is more commonly implemented in production, the research on it has been relatively superficial. In this paper, we thoroughly explore the effects of floating-point quantization targets, exponent bits, mantissa bits, and the calculation granularity of the scaling factor in floating-point quantization training performance of LLM models. While presenting an accurate floating-point quantization unified scaling law, we also provide valuable suggestions for the community: (1) Exponent bits contribute slightly more to the model performance than mantissa bits. We provide the optimal exponent-mantissa bit ratio for different bit numbers, which is available for future reference by hardware manufacturers; (2) We discover the formation of the critical data size in low-precision LLM training. Too much training data exceeding the critical data size will inversely bring in degradation of LLM performance; (3) The optimal floating-point quantization precision is directly proportional to the computational power, but within a wide computational power range, we estimate that the best cost-performance precision lies between 4-8 bits.

This paper asks whether current self-supervised learning methods, if sufficiently scaled up, would be able to reach human-level visual object recognition capabilities with the same type and amount of visual experience humans learn from. Previous work on this question only considered the scaling of data size. Here, we consider the simultaneous scaling of data size, model size, and image resolution. We perform a scaling experiment with vision transformers up to 633M parameters in size (ViT-H/14) trained with up to 5K hours of human-like video data (long, continuous, mostly egocentric videos) with image resolutions of up to 476x476 pixels. The efficiency of masked autoencoders (MAEs) as a self-supervised learning algorithm makes it possible to run this scaling experiment on an unassuming academic budget. We find that it is feasible to reach human-level object recognition capacity at sub-human scales of model size, data size, and image size, if these factors are scaled up simultaneously. To give a concrete example, we estimate that a 2.5B parameter ViT model trained with 20K hours (2.3 years) of human-like video data with a spatial resolution of 952x952 pixels should be able to reach roughly human-level accuracy on ImageNet. Human-level competence is thus achievable for a fundamental perceptual capability from human-like perceptual experience (human-like in both amount and type) with extremely generic learning algorithms and architectures and without any substantive inductive biases.

Chinchilla Approach 2 is among the most widely used methods for fitting neural scaling laws. Its parabolic approximation introduces systematic biases in compute-optimal allocation estimates, even on noise-free synthetic data. Applied to published Llama 3 IsoFLOP data at open frontier compute scales, these biases imply a parameter underallocation corresponding to 6.5% of the 3.8times10^{25} FLOP training budget and \1.4M (90% CI: 412K-\2.9M) in unnecessary compute at 50% H100 MFU. Simulated multimodal model misallocations show even greater opportunity costs due to higher loss surface asymmetry. Three sources of this error are examined: IsoFLOP sampling grid width (Taylor approximation accuracy), uncentered IsoFLOP sampling, and loss surface asymmetry (α\neq β$). Chinchilla Approach 3 largely eliminates these biases but is often regarded as less data-efficient, numerically unstable, prone to local minima, and harder to implement. Each concern is shown to be unfounded or addressable, especially when the partially linear structure of the objective is exploited via Variable Projection, enabling unbiased inference on all five loss surface parameters through a two-dimensional optimization that is well-conditioned, analytically differentiable, and amenable to dense, or even exhaustive, grid search. It may serve as a more convenient replacement for Approach 2 or a more scalable alternative for adaptations of Approach 3 to richer scaling law formulations.

Neural scaling laws approximate a language model's loss as a power-law function of parameter count N and token count D. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed tokens-per-parameter (TPP) ratio k and set D = kN. We show that this collinear design, combined with the empirically common near-equality of the exponents governing N and D, induces an inherent ill-conditioning in the Gauss-Newton least-squares problem: the condition number of the design grows as the inverse square of the gap between the N and D-exponents. The scale coefficients become practically unidentifiable, with confidence intervals inflating by an order of magnitude or more, yielding a ``sloppy'' model whose extrapolations degrade sharply off the training ray. We prove this for four scaling-law formalisms and derive a closed-form TPP-diversity threshold that is necessary and sufficient for well-conditioned estimation. Empirically, non-collinear designs outperform collinear ones on held-out splits with a 97.3\% win rate across four laws, five corpora, multiple floating point precision modes. We further show the degeneracy is rooted in Jacobian geometry and is not an artifact of the loss function: any smooth estimation objective whose curvature involves the Jacobian inherits the same ill-conditioning.

NVFP4 has grown increasingly popular as a 4-bit format for quantizing large language models due to its hardware support and its ability to retain useful information with relatively few bits per parameter. However, the format is not without limitations: recent work has shown that NVFP4 suffers from its error distribution, resulting in large amounts of quantization error on near-maximal values in each group of 16 values. In this work, we leverage this insight to design new Adaptive Block-Scaled Data Types that can adapt to the distribution of their input values. For four-bit quantization, our proposed IF4 (Int/Float 4) data type selects between FP4 and INT4 representations for each group of 16 values, which are then scaled by an E4M3 scale factor as is done with NVFP4. The selected data type is denoted using the scale factor's sign bit, which is currently unused in NVFP4, and we apply the same insight to design formats for other bit-widths, including IF3 and IF6. When used to quantize language models, we find that IF4 outperforms existing 4-bit block-scaled formats, achieving lower loss during quantized training and achieving higher accuracy on many tasks in post-training quantization. We additionally design and evaluate an IF4 Multiply-Accumulate (MAC) unit to demonstrate that IF4 can be implemented efficiently in next-generation hardware accelerators. Our code is available at https://github.com/mit-han-lab/fouroversix.

This work presents Switti, a scale-wise transformer for text-to-image generation. Starting from existing next-scale prediction AR models, we first explore them for T2I generation and propose architectural modifications to improve their convergence and overall performance. We then observe that self-attention maps of our pretrained scale-wise AR model exhibit weak dependence on preceding scales. Based on this insight, we propose a non-AR counterpart facilitating {sim}11% faster sampling and lower memory usage while also achieving slightly better generation quality.Furthermore, we reveal that classifier-free guidance at high-resolution scales is often unnecessary and can even degrade performance. %may be not only unnecessary but potentially detrimental. By disabling guidance at these scales, we achieve an additional sampling acceleration of {sim}20% and improve the generation of fine-grained details. Extensive human preference studies and automated evaluations show that Switti outperforms existing T2I AR models and competes with state-of-the-art T2I diffusion models while being up to 7{times} faster.

Low-precision number formats are widely used in modern machine learning systems due to their efficiency. Accurate direction representation is key to the accuracy of vector operations. This work precisely explores the extent to which the direction of a vector can be represented by selecting its scalar elements from a common finite alphabet of a given size. This is standard practice in machine learning, where low-precision significands may be narrow-width floating-point or integer values. A geometric framework is introduced for analyzing the directional coverage of such product-structured codes. This work analytically quantifies the suboptimality gap between such product-structured codes and spherical codes for the vector as a whole, in both low and asymptotically high dimensions. Furthermore, within the product code class, it is proven that the standard formats of two's complement, fixed-point, and floating-point are suboptimal, again with quantified gap, pointing to the potential to develop new scalar number formats. Such scalar alphabets are numerically optimized across multiple block dimensions for directional coverage, including the dimension used in NVIDIA's NVFP4 format. Experimental results are presented comparing the performance of standard formats and the optimized alphabet. We find that for four bits, NVIDIA's choice of E2M1 closely approximates the optimized alphabet, providing a geometric explanation for its strong performance in low-precision machine learning workloads and an analytical understanding of the link between that superiority and block size. We provide open-source formal proofs in Lean for the theorems in this work, along with the experimental code and the optimized alphabets obtained.

Weight oscillation is an undesirable side effect of quantization-aware training, in which quantized weights frequently jump between two quantized levels, resulting in training instability and a sub-optimal final model. We discover that the learnable scaling factor, a widely-used de facto setting in quantization aggravates weight oscillation. In this study, we investigate the connection between the learnable scaling factor and quantized weight oscillation and use ViT as a case driver to illustrate the findings and remedies. In addition, we also found that the interdependence between quantized weights in query and key of a self-attention layer makes ViT vulnerable to oscillation. We, therefore, propose three techniques accordingly: statistical weight quantization (rm StatsQ) to improve quantization robustness compared to the prevalent learnable-scale-based method; confidence-guided annealing (rm CGA) that freezes the weights with high confidence and calms the oscillating weights; and query-key reparameterization (rm QKR) to resolve the query-key intertwined oscillation and mitigate the resulting gradient misestimation. Extensive experiments demonstrate that these proposed techniques successfully abate weight oscillation and consistently achieve substantial accuracy improvement on ImageNet. Specifically, our 2-bit DeiT-T/DeiT-S algorithms outperform the previous state-of-the-art by 9.8% and 7.7%, respectively. Code and models are available at: https://github.com/nbasyl/OFQ.

FP8 formats are gaining popularity to boost the computational efficiency for training and inference of large deep learning models. Their main challenge is that a careful choice of scaling is needed to prevent degradation due to the reduced dynamic range compared to higher-precision formats. Although there exists ample literature about selecting such scalings for INT formats, this critical aspect has yet to be addressed for FP8. This paper presents a methodology to select the scalings for FP8 linear layers, based on dynamically updating per-tensor scales for the weights, gradients and activations. We apply this methodology to train and validate large language models of the type of GPT and Llama 2 using FP8, for model sizes ranging from 111M to 70B. To facilitate the understanding of the FP8 dynamics, our results are accompanied by plots of the per-tensor scale distribution for weights, activations and gradients during both training and inference.

Linear probes are widely used in interpretability research and often compared by cosine similarity. The Mahalanobis cosine similarity (MCS) between two directions, which reweights the inner product by test data covariance, is a natural task-aware refinement. Ying et al. (2026) report that a probe's MCS to a reference probe trained on the out-of-distribution (OOD) data near-perfectly linearly predicts the probe's OOD AUROC (R^2 = 0.98). Here, we extend this empirical finding across models, layers, and concept domains, and prove this general phenomenon in closed form: For balanced classes whose projections are Gaussian, OOD AUROC and MCS to the reference probe are linear because both are sigmoid-shaped functions of the probe's signal-to-noise ratio (SNR) on the test data. The theory also predicts when this linearity fails, which we verify empirically. MCS offers a theoretically grounded and empirically effective alternative to Euclidean cosine similarity for comparing linear probes.

Large Language Model training with 8-bit floating point (FP8) formats promises significant efficiency improvements, but reduced numerical precision makes training challenging. It is currently possible to train in FP8 only if one is willing to tune various hyperparameters, reduce model scale, or accept the overhead of computing dynamic scale factors. We demonstrate simple, scalable FP8 training that requires no dynamic scaling factors or special hyperparameters, even at large model sizes. Our method, munit Scaling (muS), also enables simple hyperparameter transfer across model widths, matched numerics across training and inference, and other desirable properties. munit Scaling is straightforward to implement, consisting of a set of minimal interventions based on a first-principles analysis of common transformer operations. We validate our method by training models from 1B to 13B parameters, performing all hidden linear layer computations in FP8. We achieve quality equal to higher precision baselines while also training up to 33% faster.

The increasing computational demands of foundation models have spurred research into low-precision training, with 4-bit floating-point (FP4) formats emerging as a frontier for maximizing hardware throughput. While numerous techniques have been proposed to stabilize FP4 training, they often present isolated solutions with varying, and not always clear, computational overheads. This paper aims to provide a unified view of the design space of FP4 training. We introduce a comprehensive, quantisation gradient-based framework for microscaling quantization that allows for a theoretical analysis of the computational costs associated with different stabilization methods on both the forward and backward passes. Using a simulator built on this framework, we conduct an extensive empirical study across a wide range of machine learning tasks, including regression, image classification, diffusion models, and language models. By systematically evaluating thousands of combinations of techniques, such as novel gradient approximations, rounding strategies, and scaling methods, we identify which configurations offer the most favourable performance-to-overhead trade-off. We find that the techniques enabling the best trade-off involve carefully combining Hadamard transformations, tensor scaling and stochastic rounding. We further find that using UE5M3 as a scaling factor potentially offers a good compromise between range and precision with manageable computational overhead.

In this work we propose an analytical model that reproduces the core-bounds phase of gravitational waves (GW) of Rapidly Rotating (RR) from Core Collapse Supernovae (CCSNe), as a function of three parameters, the arrival time tau, the ratio of the kinetic and potential energy beta and a phenomenological parameter alpha related to rotation and equation of state (EOS). To validate the model we use 126 waveforms from the Richers catalog Richers_2017 selected with the criteria of exploring a range of rotation profiles, and involving EOS. To quantify the degree of accuracy of the proposed model, with a particular focus on the rotation parameter beta, we show that the average Fitting Factor (FF) between the simulated waveforms with the templates is 94.4\%. In order to estimate the parameters we propose a frequentist matched filtering approach in real interferometric noise which does not require assigning any priors. We use the Matched Filter (MF) technique, where we inject a bank of templates considering simulated colored Gaussian noise and the real noise of O3L1. For example for A300w6.00\_BHBLP at 10Kpc we obtain a standar deviation of sigma = 3.34times 10^{-3} for simulated colored Gaussian noise and sigma= 1.46times 10^{-2} for real noise. On the other hand, from the asymptotic expansion of the variance we obtain the theoretical minimum error for beta at 10 kpc and optimal orientation. The estimation error in this case is from 10^{-2} to 10^{-3} as beta increases. We show that the results of the estimation error of beta for the 3-parameter space (3D) is consistent with the single-parameter space (1D), which allows us to conclude that beta is decoupled from the others two parameters.

Temporal question answering is an established method for evaluating temporal reasoning in large language models. Expected answers are often numeric (e.g., dates or durations), yet model responses are evaluated like regular text with exact match (EM), unable to distinguish small from large errors. In this investigative work, we frame temporal question answering as a numerical estimation task to assess the shortcomings of EM. We introduce TempAnswerQA, a benchmark distilled from Test of Time and TempTabQA, where all questions require a numerical, temporal answer, allowing us to evaluate models beyond EM. We use the forecasting metrics symmetric mean absolute percentage error (sMAPE) and mean absolute scaled error (MASE). With sMAPE, we find that error size and EM are decoupled. Models with low EM still have low sMAPE (both ~20%), and some models have high sMAPE despite high EM. Scaling errors by the deviation of the ground truth data with MASE reshuffles model rankings compared to EM, revealing gaps in models' understanding of temporal domain knowledge, especially when trained with synthetic data. Lastly, the models' most frequent error is to deviate by only pm1 from the ground truth. sMAPE and MASE, unlike EM, adequately weight these errors. Our findings underscore the need for specialised metrics for temporal QA tasks. Code and data are available on https://github.com/aauss/temporal-answer-qa.

This paper describes the design and simulation of an 8-bit dedicated processor for calculating the Sine and Cosine of an Angle using CORDIC Algorithm (COordinate Rotation DIgital Computer), a simple and efficient algorithm to calculate hyperbolic and trigonometric functions. We have proposed a dedicated processor system, modeled by writing appropriate programs in VHDL, for calculating the Sine and Cosine of an angle. System simulation was carried out using ModelSim 6.3f and Xilinx ISE Design Suite 12.3. A maximum frequency of 81.353 MHz was reached with a minimum period of 12.292 ns. 126 (3%) slices were used. This paper attempts to survey the existing CORDIC algorithm with an eye towards implementation in Field Programmable Gate Arrays (FPGAs). A brief description of the theory behind the algorithm and the derivation of the Sine and Cosine of an angle using the CORDIC algorithm has been presented. The system can be implemented using Spartan3 XC3S400 with Xilinx ISE 12.3 and VHDL.

For Image Super-Resolution (SR), it is common to train and evaluate scale-specific models composed of an encoder and upsampler for each targeted scale. Consequently, many SR studies encounter substantial training times and complex deployment requirements. In this paper, we address this limitation by training and evaluating multiple scales simultaneously. Notably, we observe that encoder features are similar across scales and that the Sub-Pixel Convolution (SPConv), widely-used scale-specific upsampler, exhibits strong inter-scale correlations in its functionality. Building on these insights, we propose a multi-scale framework that employs a single encoder in conjunction with Implicit Grid Convolution (IGConv), our novel upsampler, which unifies SPConv across all scales within a single module. Extensive experiments demonstrate that our framework achieves comparable performance to existing fixed-scale methods while reducing the training budget and stored parameters three-fold and maintaining the same latency. Additionally, we propose IGConv^{+} to improve performance further by addressing spectral bias and allowing input-dependent upsampling and ensembled prediction. As a result, ATD-IGConv^{+} achieves a notable 0.21dB improvement in PSNR on Urban100times4, while also reducing the training budget, stored parameters, and inference cost compared to the existing ATD.

Self-supervised learning aims to learn representations from the data itself without explicit manual supervision. Existing efforts ignore a crucial aspect of self-supervised learning - the ability to scale to large amount of data because self-supervision requires no manual labels. In this work, we revisit this principle and scale two popular self-supervised approaches to 100 million images. We show that by scaling on various axes (including data size and problem 'hardness'), one can largely match or even exceed the performance of supervised pre-training on a variety of tasks such as object detection, surface normal estimation (3D) and visual navigation using reinforcement learning. Scaling these methods also provides many interesting insights into the limitations of current self-supervised techniques and evaluations. We conclude that current self-supervised methods are not 'hard' enough to take full advantage of large scale data and do not seem to learn effective high level semantic representations. We also introduce an extensive benchmark across 9 different datasets and tasks. We believe that such a benchmark along with comparable evaluation settings is necessary to make meaningful progress. Code is at: https://github.com/facebookresearch/fair_self_supervision_benchmark.

Reduced numerical precision is a common technique to reduce computational cost in many Deep Neural Networks (DNNs). While it has been observed that DNNs are resilient to small errors and noise, no general result exists that is capable of predicting a given DNN system architecture's sensitivity to reduced precision. In this project, we emulate arbitrary bit-width using a specified floating-point representation with a truncation method, which is applied to the neural network after each batch. We explore the impact of several model parameters on the network's training accuracy and show results on the MNIST dataset. We then present a preliminary theoretical investigation of the error scaling in both forward and backward propagations. We end with a discussion of the implications of these results as well as the potential for generalization to other network architectures.

Scene text detection has seen the emergence of high-performing methods that excel on academic benchmarks. However, these detectors often fail to replicate such success in real-world scenarios. We uncover two key factors contributing to this discrepancy through extensive experiments. First, a Fine-tuning Gap, where models leverage Dataset-Specific Optimization (DSO) paradigm for one domain at the cost of reduced effectiveness in others, leads to inflated performances on academic benchmarks. Second, the suboptimal performance in practical settings is primarily attributed to the long-tailed distribution of texts, where detectors struggle with rare and complex categories as artistic or overlapped text. Given that the DSO paradigm might undermine the generalization ability of models, we advocate for a Joint-Dataset Learning (JDL) protocol to alleviate the Fine-tuning Gap. Additionally, an error analysis is conducted to identify three major categories and 13 subcategories of challenges in long-tailed scene text, upon which we propose a Long-Tailed Benchmark (LTB). LTB facilitates a comprehensive evaluation of ability to handle a diverse range of long-tailed challenges. We further introduce MAEDet, a self-supervised learning-based method, as a strong baseline for LTB. The code is available at https://github.com/pd162/LTB.

This paper studies the error metric selection for long-term memory learning in sequence modelling. We examine the bias towards short-term memory in commonly used errors, including mean absolute/squared error. Our findings show that all temporally positive-weighted errors are biased towards short-term memory in learning linear functionals. To reduce this bias and improve long-term memory learning, we propose the use of a temporally rescaled error. In addition to reducing the bias towards short-term memory, this approach can also alleviate the vanishing gradient issue. We conduct numerical experiments on different long-memory tasks and sequence models to validate our claims. Numerical results confirm the importance of appropriate temporally rescaled error for effective long-term memory learning. To the best of our knowledge, this is the first work that quantitatively analyzes different errors' memory bias towards short-term memory in sequence modelling.

The discrete cosine transform (DCT) is a central tool for image and video coding because it can be related to the Karhunen-Lo\`eve transform (KLT), which is the optimal transform in terms of retained transform coefficients and data decorrelation. In this paper, we introduce 16-, 32-, and 64-point low-complexity DCT approximations by minimizing individually the angle between the rows of the exact DCT matrix and the matrix induced by the approximate transforms. According to some classical figures of merit, the proposed transforms outperformed the approximations for the DCT already known in the literature. Fast algorithms were also developed for the low-complexity transforms, asserting a good balance between the performance and its computational cost. Practical applications in image encoding showed the relevance of the transforms in this context. In fact, the experiments showed that the proposed transforms had better results than the known approximations in the literature for the cases of 16, 32, and 64 blocklength.

There are now several comprehensive web applications, stand-alone computer programs and computer algebra functions that, given a floating point number such as 6.518670730718491, can return concise nonfloat constants such as 3 arctan 2 + ln 9 + 1, that closely approximate the float. Examples include AskConstants, Inverse Symbolic Calculator, the Maple identify function, MESearch, OEIS, RIES, and WolframAlpha. Usefully often such a result is the exact limit as the float is computed with increasing precision. Therefore these program results are candidates for proving an exact result that you could not otherwise compute or conjecture without the program. Moreover, candidates that are not the exact limit can be provable bounds, or convey qualitative insight, or suggest series that they truncate, or provide sufficiently close efficient approximations for subsequent computation. This article describes some of these programs, how they work, and how best to use each of them. Almost everyone who uses or should use mathematical software can benefit from acquaintance with several such programs, because these programs differ in the sets of constants that they can return.

Motivated by recent advances in operational weather forecasting, we study the efficacy of low-precision arithmetic for climate simulations. We develop a framework to measure rounding error in a climate model which provides a stress-test for a low-precision version of the model, and we apply our method to a variety of models including the Lorenz system; a shallow water approximation for flow over a ridge; and a coarse resolution global atmospheric model with simplified parameterisations (SPEEDY). Although double precision (52 significant bits) is standard across operational climate models, in our experiments we find that single precision (23 sbits) is more than enough and that as low as half precision (10 sbits) is often sufficient. For example, SPEEDY can be run with 12 sbits across the entire code with negligible rounding error and this can be lowered to 10 sbits if very minor errors are accepted, amounting to less than 0.1 mm/6hr for the average grid-point precipitation, for example. Our test is based on the Wasserstein metric and this provides stringent non-parametric bounds on rounding error accounting for annual means as well as extreme weather events. In addition, by testing models using both round-to-nearest (RN) and stochastic rounding (SR) we find that SR can mitigate rounding error across a range of applications. Thus our results also provide evidence that SR could be relevant to next-generation climate models. While many studies have shown that low-precision arithmetic can be suitable on short-term weather forecasting timescales, our results give the first evidence that a similar low precision level can be suitable for climate.

In computer vision, models must be able to adapt to changes in image resolution to effectively carry out tasks such as image segmentation; This is known as scale-equivariance. Recent works have made progress in developing scale-equivariant convolutional neural networks, e.g., through weight-sharing and kernel resizing. However, these networks are not truly scale-equivariant in practice. Specifically, they do not consider anti-aliasing as they formulate the down-scaling operation in the continuous domain. To address this shortcoming, we directly formulate down-scaling in the discrete domain with consideration of anti-aliasing. We then propose a novel architecture based on Fourier layers to achieve truly scale-equivariant deep nets, i.e., absolute zero equivariance-error. Following prior works, we test this model on MNIST-scale and STL-10 datasets. Our proposed model achieves competitive classification performance while maintaining zero equivariance-error.

Recent neural network-based language models have benefited greatly from scaling up the size of training datasets and the number of parameters in the models themselves. Scaling can be complicated due to various factors including the need to distribute computation on supercomputer clusters (e.g., TPUs), prevent bottlenecks when infeeding data, and ensure reproducible results. In this work, we present two software libraries that ease these issues: t5x simplifies the process of building and training large language models at scale while maintaining ease of use, and seqio provides a task-based API for simple creation of fast and reproducible training data and evaluation pipelines. These open-source libraries have been used to train models with hundreds of billions of parameters on datasets with multiple terabytes of training data. Along with the libraries, we release configurations and instructions for T5-like encoder-decoder models as well as GPT-like decoder-only architectures. t5x and seqio are open source and available at https://github.com/google-research/t5x and https://github.com/google/seqio, respectively.

Recent 4D Gaussian Splatting (4DGS) methods achieve impressive dynamic scene reconstruction but often rely on piecewise linear velocity approximations and short temporal windows. This disjointed modeling leads to severe temporal fragmentation, forcing primitives to be repeatedly eliminated and regenerated to track complex nonlinear dynamics. This makeshift approximation eliminates the long-term temporal identity of objects and causes an inevitable proliferation of Gaussians, hindering scalability to extended video sequences. To address this, we propose TRiGS, a novel 4D representation that utilizes unified, continuous geometric transformations. By integrating SE(3) transformations, hierarchical Bezier residuals, and learnable local anchors, TRiGS models geometrically consistent rigid motions for individual primitives. This continuous formulation preserves temporal identity and effectively mitigates unbounded memory growth. Extensive experiments demonstrate that TRiGS achieves high fidelity rendering on standard benchmarks while uniquely scaling to extended video sequences (e.g., 600 to 1200 frames) without severe memory bottlenecks, significantly outperforming prior works in temporal stability.

Can scaling transform reasoning? In this work, we explore the untapped potential of scaling Long Chain-of-Thought (Long-CoT) data to 1000k samples, pioneering the development of a slow-thinking model, RedStar. Through extensive experiments with various LLMs and different sizes, we uncover the ingredients for specialization and scale for Long-CoT training. Surprisingly, even smaller models show significant performance gains with limited data, revealing the sample efficiency of Long-CoT and the critical role of sample difficulty in the learning process. Our findings demonstrate that Long-CoT reasoning can be effectively triggered with just a few thousand examples, while larger models achieve unparalleled improvements. We also introduce reinforcement learning (RL)-scale training as a promising direction for advancing slow-thinking systems. RedStar shines across domains: on the MATH-Hard benchmark, RedStar-code-math boosts performance from 66.2\% to 81.6\%, and on the USA Math Olympiad (AIME), it solves 46.7\% of problems using only 21k mixed-code-math datasets. In multimodal tasks like GeoQA and MathVista-GEO, RedStar-Geo achieves competitive results with minimal Long-CoT data, outperforming other slow-thinking systems like QvQ-Preview. Compared to QwQ, RedStar strikes the perfect balance between reasoning and generalizability. Our work highlights that, with careful tuning, scaling Long-CoT can unlock extraordinary reasoning capabilities-even with limited dataset and set a new standard for slow-thinking models across diverse challenges. Our data and models are released at https://huggingface.co/RedStar-Reasoning.

Empirical scaling laws prescribe how to allocate parameters, data, and compute, while maximal-update parameterization (muP) enables learning-rate transfer across widths by equalizing early-time update magnitudes. However, in modern scale-invariant architectures, training quickly enters an optimizer-governed steady state where normalization layers create backward scale sensitivity and the effective learning rate becomes width dependent, degrading muP transfer. We address this by introducing a weight-decay scaling rule for AdamW that preserves sublayer gain across widths. Empirically, the singular-value spectrum of each matrix parameter scales in norm as eta/lambda with an approximately invariant shape; under width scaling d, we observe that the top singular value scales approximately as eta/lambdacdot d^{0.75}. Combining this observation with the muP learning-rate rule eta_2propto d^{-1} for matrix-like parameters implies an empirical weight-decay scaling rule lambda_2propto d that approximately keeps sublayer gains width invariant. Together with vector-like parameters trained at eta_1=Theta_d(1) and lambda_1=0, this yields zero-shot transfer of both learning rate and weight decay from proxy to target widths, removing per-width sweeps. We validate the rule on LLaMA-style Transformers and in a minimal synthetic setting, and we provide a simple diagnostic, matching top singular values, to check sublayer-gain invariance. Our results extend muP beyond the near-init regime by explicitly controlling steady-state scales set by the optimizer, offering a practical recipe for width-robust hyperparameter transfer under AdamW.

Bessel functions are critical in scientific computing for applications such as machine learning, protein structure modeling, and robotics. However, currently, available routines lack precision or fail for certain input ranges, such as when the order v is large, and GPU-specific implementations are limited. We address the precision limitations of current numerical implementations while dramatically improving the runtime. We propose two novel algorithms for computing the logarithm of modified Bessel functions of the first and second kinds by computing intermediate values on a logarithmic scale. Our algorithms are robust and never have issues with underflows or overflows while having relative errors on the order of machine precision, even for inputs where existing libraries fail. In C++/CUDA, our algorithms have median and maximum speedups of 45x and 6150x for GPU and 17x and 3403x for CPU, respectively, over the ranges of inputs and third-party libraries tested. Compared to SciPy, the algorithms have median and maximum speedups of 77x and 300x for GPU and 35x and 98x for CPU, respectively, over the tested inputs. The ability to robustly compute a solution and the low relative errors allow us to fit von Mises-Fisher, vMF, distributions to high-dimensional neural network features. This is, e.g., relevant for uncertainty quantification in metric learning. We obtain image feature data by processing CIFAR10 training images with the convolutional layers of a pre-trained ResNet50. We successfully fit vMF distributions to 2048-, 8192-, and 32768-dimensional image feature data using our algorithms. Our approach provides fast and accurate results while existing implementations in SciPy and mpmath fail to fit successfully. Our approach is readily implementable on GPUs, and we provide a fast open-source implementation alongside this paper.

We present SigmaScale, a method for learning auxiliary scaling matrices S to aid truncated Singular Value Decomposition (SVD) based Large Language Model (LLM) compression. Instead of deriving scaling matrices analytically, SigmaScale optimizes two sets of vectors that define diagonal row and column scaling transformations under an activation-aware compression loss. We show that learned scaling lowers the effective intrinsic rank of weight matrices, as reflected by reductions in effective-rank entropy, and that this reduction is strongly correlated with compression loss. Experiments on Llama 3.1 8B Instruct and Qwen3-8B show that SigmaScale is competitive with closely related state-of-the-art SVD-based compression methods across perplexity and zero-shot benchmarks. By using learned activation-aware transformations, SigmaScale explores a more flexible route to low-rank LLM compression by adapting to the structure of individual model weights. The advantage observed in specific tasks makes our approach a valid option for applications requiring a reduced LLM-inference computing cost.

Network quantization generally converts full-precision weights and/or activations into low-bit fixed-point values in order to accelerate an inference process. Recent approaches to network quantization further discretize the gradients into low-bit fixed-point values, enabling an efficient training. They typically set a quantization interval using a min-max range of the gradients or adjust the interval such that the quantization error for entire gradients is minimized. In this paper, we analyze the quantization error of gradients for the low-bit fixed-point training, and show that lowering the error for large-magnitude gradients boosts the quantization performance significantly. Based on this, we derive an upper bound of quantization error for the large gradients in terms of the quantization interval, and obtain an optimal condition for the interval minimizing the quantization error for large gradients. We also introduce an interval update algorithm that adjusts the quantization interval adaptively to maintain a small quantization error for large gradients. Experimental results demonstrate the effectiveness of our quantization method for various combinations of network architectures and bit-widths on various tasks, including image classification, object detection, and super-resolution.

Low-precision formats such as float8 have been introduced in machine learning accelerated hardware to improve computational efficiency for large language models training and inference. Nevertheless, adoption by the ML community has been slowed down by the complex, and sometimes brittle, techniques required to match higher precision training accuracy. In this work, we present Scalify, a end-to-end scale propagation paradigm for computational graphs, generalizing and formalizing existing tensor scaling methods. Experiment results show that Scalify supports out-of-the-box float8 matrix multiplication and gradients representation, as well as float16 optimizer state storage. Our JAX implementation of Scalify is open-sourced at https://github.com/graphcore-research/jax-scalify

Time series models face significant challenges in scaling to handle large and complex datasets, akin to the scaling achieved by large language models (LLMs). The unique characteristics of time series data and the computational demands of model scaling necessitate innovative approaches. While researchers have explored various architectures such as Transformers, LSTMs, and GRUs to address these challenges, we propose a novel solution using RWKV-7, which incorporates meta-learning into its state update mechanism. By integrating RWKV-7's time mix and channel mix components into the transformer-based time series model Timer, we achieve a substantial performance improvement of approximately 1.13 to 43.3x and a 4.5x reduction in training time with 1/23 parameters, all while utilizing fewer parameters. Our code and model weights are publicly available for further research and development at https://github.com/Alic-Li/BlackGoose_Rimer.

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients. In many applications, e.g. learning with large output spaces, it has been empirically observed that these algorithms fail to converge to an optimal solution (or a critical point in nonconvex settings). We show that one cause for such failures is the exponential moving average used in the algorithms. We provide an explicit example of a simple convex optimization setting where Adam does not converge to the optimal solution, and describe the precise problems with the previous analysis of Adam algorithm. Our analysis suggests that the convergence issues can be fixed by endowing such algorithms with `long-term memory' of past gradients, and propose new variants of the Adam algorithm which not only fix the convergence issues but often also lead to improved empirical performance.

Mathematical capabilities were previously believed to emerge in common language models only at a very large scale or require extensive math-related pre-training. This paper shows that the LLaMA-2 7B model with common pre-training already exhibits strong mathematical abilities, as evidenced by its impressive accuracy of 97.7% and 72.0% on the GSM8K and MATH benchmarks, respectively, when selecting the best response from 256 random generations. The primary issue with the current base model is the difficulty in consistently eliciting its inherent mathematical capabilities. Notably, the accuracy for the first answer drops to 49.5% and 7.9% on the GSM8K and MATH benchmarks, respectively. We find that simply scaling up the SFT data can significantly enhance the reliability of generating correct answers. However, the potential for extensive scaling is constrained by the scarcity of publicly available math questions. To overcome this limitation, we employ synthetic data, which proves to be nearly as effective as real data and shows no clear saturation when scaled up to approximately one million samples. This straightforward approach achieves an accuracy of 82.6% on GSM8K and 40.6% on MATH using LLaMA-2 7B models, surpassing previous models by 14.2% and 20.8%, respectively. We also provide insights into scaling behaviors across different reasoning complexities and error types.

We propose MCGrad, a novel and scalable multicalibration algorithm. Multicalibration - calibration in subgroups of the data - is an important property for the performance of machine learning-based systems. Existing multicalibration methods have thus far received limited traction in industry. We argue that this is because existing methods (1) require such subgroups to be manually specified, which ML practitioners often struggle with, (2) are not scalable, or (3) may harm other notions of model performance such as log loss and Area Under the Precision-Recall Curve (PRAUC). MCGrad does not require explicit specification of protected groups, is scalable, and often improves other ML evaluation metrics instead of harming them. MCGrad has been in production at Meta, and is now part of hundreds of production models. We present results from these deployments as well as results on public datasets. We provide an open source implementation of MCGrad at https://github.com/facebookincubator/MCGrad.

Flow matching and diffusion models have shown impressive results in text-to-image generation, producing photorealistic images through an iterative denoising process. A common strategy to speed up synthesis is to perform early denoising at lower resolutions. However, traditional methods that downscale and upscale in pixel space often introduce artifacts and distortions. These issues arise when the upscaled images are re-encoded into the latent space, leading to degraded final image quality. To address this, we propose {\bf Latent Space Scaling Generation (LSSGen)}, a framework that performs resolution scaling directly in the latent space using a lightweight latent upsampler. Without altering the Transformer or U-Net architecture, LSSGen improves both efficiency and visual quality while supporting flexible multi-resolution generation. Our comprehensive evaluation covering text-image alignment and perceptual quality shows that LSSGen significantly outperforms conventional scaling approaches. When generating 1024^2 images at similar speeds, it achieves up to 246\% TOPIQ score improvement.

Quantization effectively reduces the serving costs of Large Language Models (LLMs) by speeding up data movement through compressed parameters and enabling faster operations via integer arithmetic. However, activating integer arithmetic requires quantizing both weights and activations, which poses challenges due to the significant outliers in LLMs that increase quantization error. In this work, we investigate these outliers with an emphasis on their effect on layer-wise quantization error, then examine how smoothing and rotation transform the observed values. Our primary contributions include introducing a new metric to measure and visualize quantization difficulty based on channel magnitudes, as well as proposing a hybrid approach that applies channel-wise scaling before rotation, supported by a mathematical formulation of its benefits.

Estimating depth from a single image is a challenging visual task. Compared to relative depth estimation, metric depth estimation attracts more attention due to its practical physical significance and critical applications in real-life scenarios. However, existing metric depth estimation methods are typically trained on specific datasets with similar scenes, facing challenges in generalizing across scenes with significant scale variations. To address this challenge, we propose a novel monocular depth estimation method called ScaleDepth. Our method decomposes metric depth into scene scale and relative depth, and predicts them through a semantic-aware scale prediction (SASP) module and an adaptive relative depth estimation (ARDE) module, respectively. The proposed ScaleDepth enjoys several merits. First, the SASP module can implicitly combine structural and semantic features of the images to predict precise scene scales. Second, the ARDE module can adaptively estimate the relative depth distribution of each image within a normalized depth space. Third, our method achieves metric depth estimation for both indoor and outdoor scenes in a unified framework, without the need for setting the depth range or fine-tuning model. Extensive experiments demonstrate that our method attains state-of-the-art performance across indoor, outdoor, unconstrained, and unseen scenes. Project page: https://ruijiezhu94.github.io/ScaleDepth

In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and illustrated on a simple example.

Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits of increasing test-time compute by extending the CoT lengths of Large Language Models (LLMs), we are concerned about a potential issue hidden behind the current pursuit of test-time scaling: Would excessively scaling the CoT length actually bring adverse effects to a model's reasoning performance? Our explorations on mathematical reasoning tasks reveal an unexpected finding that scaling with longer CoTs can indeed impair the reasoning performance of LLMs in certain domains. Moreover, we discover that there exists an optimal scaled length distribution that differs across different domains. Based on these insights, we propose a Thinking-Optimal Scaling strategy. Our method first uses a small set of seed data with varying response length distributions to teach the model to adopt different reasoning efforts for deep thinking. Then, the model selects its shortest correct response under different reasoning efforts on additional problems for self-improvement. Our self-improved models built upon Qwen2.5-32B-Instruct outperform other distillation-based 32B o1-like models across various math benchmarks, and achieve performance on par with QwQ-32B-Preview.

A lattice quantizer approximates an arbitrary real-valued source vector with a vector taken from a specific discrete lattice. The quantization error is the difference between the source vector and the lattice vector. In a classic 1996 paper, Zamir and Feder show that the globally optimal lattice quantizer (which minimizes the mean square error) has white quantization error: for a uniformly distributed source, the covariance of the error is the identity matrix, multiplied by a positive real factor. We generalize the theorem, showing that the same property holds (i) for any lattice whose mean square error cannot be decreased by a small perturbation of the generator matrix, and (ii) for an optimal product of lattices that are themselves locally optimal in the sense of (i). We derive an upper bound on the normalized second moment (NSM) of the optimal lattice in any dimension, by proving that any lower- or upper-triangular modification to the generator matrix of a product lattice reduces the NSM. Using these tools and employing the best currently known lattice quantizers to build product lattices, we construct improved lattice quantizers in dimensions 13 to 15, 17 to 23, and 25 to 48. In some dimensions, these are the first reported lattices with normalized second moments below the best known upper bound.

Pansharpening aims to generate high-resolution multi-spectral images by fusing the spatial detail of panchromatic images with the spectral richness of low-resolution MS data. However, most existing methods are evaluated under limited, low-resolution settings, limiting their generalization to real-world, high-resolution scenarios. To bridge this gap, we systematically investigate the data, algorithmic, and computational challenges of cross-scale pansharpening. We first introduce PanScale, the first large-scale, cross-scale pansharpening dataset, accompanied by PanScale-Bench, a comprehensive benchmark for evaluating generalization across varying resolutions and scales. To realize scale generalization, we propose ScaleFormer, a novel architecture designed for multi-scale pansharpening. ScaleFormer reframes generalization across image resolutions as generalization across sequence lengths: it tokenizes images into patch sequences of the same resolution but variable length proportional to image scale. A Scale-Aware Patchify module enables training for such variations from fixed-size crops. ScaleFormer then decouples intra-patch spatial feature learning from inter-patch sequential dependency modeling, incorporating Rotary Positional Encoding to enhance extrapolation to unseen scales. Extensive experiments show that our approach outperforms SOTA methods in fusion quality and cross-scale generalization. The datasets and source code are available upon acceptance.

In an era where wearable technology is reshaping applications, Scene Text Detection and Recognition (STDR) becomes a straightforward choice through the lens of egocentric vision. Leveraging Meta's Project Aria smart glasses, this paper investigates how environmental variables, such as lighting, distance, and resolution, affect the performance of state-of-the-art STDR algorithms in real-world scenarios. We introduce a novel, custom-built dataset captured under controlled conditions and evaluate two OCR pipelines: EAST with CRNN, and EAST with PyTesseract. Our findings reveal that resolution and distance significantly influence recognition accuracy, while lighting plays a less predictable role. Notably, image upscaling emerged as a key pre-processing technique, reducing Character Error Rate (CER) from 0.65 to 0.48. We further demonstrate the potential of integrating eye-gaze tracking to optimise processing efficiency by focusing on user attention zones. This work not only benchmarks STDR performance under realistic conditions but also lays the groundwork for adaptive, user-aware AR systems. Our contributions aim to inspire future research in robust, context-sensitive text recognition for assistive and research-oriented applications, such as asset inspection and nutrition analysis. The code is available at https://github.com/josepDe/Project_Aria_STR.

In the complex domain of large language models (LLMs), striking a balance between computational efficiency and maintaining model quality is a formidable challenge. Navigating the inherent limitations of uniform quantization, particularly when dealing with outliers, and motivated by the launch of NVIDIA's H100 hardware, this study delves into the viability of floating-point (FP) quantization, particularly focusing on FP8 and FP4, as a potential solution. Our comprehensive investigation reveals that for LLMs, FP8 activation consistently outshines its integer (INT8) equivalent, with the performance edge becoming more noticeable in models possessing parameters beyond one billion. For weight quantization, our findings indicate that FP4 exhibits comparable, if not superior, performance to INT4, simplifying deployment on FP-supported hardware like H100. To mitigate the overhead from precision alignment caused by the disparity between weights and activations, we propose two scaling constraints for weight quantization that negligibly impact the performance compared to the standard W4A8 model. We additionally enhance our quantization methods by integrating the Low Rank Compensation (LoRC) strategy, yielding improvements especially in smaller models. The results of our investigation emphasize the immense potential of FP quantization for LLMs, paving the way for high-efficiency deployment in resource-limited settings.

Large Language Models (LLMs) achieve strong performance on natural language tasks but remain unreliable in mathematical reasoning, frequently generating fluent yet logically inconsistent solutions. We present NeuroProlog, a neurosymbolic framework that ensures verifiable reasoning by compiling math word problems into executable Prolog programs with formal verification guarantees. We propose a multi-task Cocktail training strategy that jointly optimizes three synergistic objectives in a unified symbolic representation space: (i) mathematical formula-to-rule translation (KB), (ii) natural language-to-program synthesis (SOLVE), and (iii) program-answer alignment. This joint supervision enables positive transfer, where symbolic grounding in formula translation directly improves compositional reasoning capabilities. At inference, we introduce an execution-guided decoding pipeline with fine-grained error taxonomy that enables iterative program repair and quantifies model self-debugging capacity. Comprehensive evaluation on GSM8K across four model scales (3B--32B parameters) demonstrates consistent improvements: cocktail training achieves significant accuracy gains of +5.23\% (Qwen-32B, p < 0.01), +3.43\% (GPT-OSS-20B, p < 0.01), and +5.54\% (Llama-3B, p < 0.05) over single-task baselines. Systematic error analysis reveals scale-dependent learning dynamics: at 32B scale, cocktail training transforms unfixable type errors (12\% repair rate) into correctable domain errors (96\% repair rate), achieving 92.7\% overall correction; at 8B scale, the same training eliminates syntactic errors but introduces semantic failures, revealing a critical capacity threshold for type-safe symbolic reasoning.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

Many intellectual endeavors require mathematical problem solving, but this skill remains beyond the capabilities of computers. To measure this ability in machine learning models, we introduce MATH, a new dataset of 12,500 challenging competition mathematics problems. Each problem in MATH has a full step-by-step solution which can be used to teach models to generate answer derivations and explanations. To facilitate future research and increase accuracy on MATH, we also contribute a large auxiliary pretraining dataset which helps teach models the fundamentals of mathematics. Even though we are able to increase accuracy on MATH, our results show that accuracy remains relatively low, even with enormous Transformer models. Moreover, we find that simply increasing budgets and model parameter counts will be impractical for achieving strong mathematical reasoning if scaling trends continue. While scaling Transformers is automatically solving most other text-based tasks, scaling is not currently solving MATH. To have more traction on mathematical problem solving we will likely need new algorithmic advancements from the broader research community.

Inference-time scaling can enhance the reasoning capabilities of large language models (LLMs) on complex problems that benefit from step-by-step problem solving. Although lengthening generated scratchpads has proven effective for mathematical tasks, the broader impact of this approach on other tasks remains less clear. In this work, we investigate the benefits and limitations of scaling methods across nine state-of-the-art models and eight challenging tasks, including math and STEM reasoning, calendar planning, NP-hard problems, navigation, and spatial reasoning. We compare conventional models (e.g., GPT-4o) with models fine-tuned for inference-time scaling (e.g., o1) through evaluation protocols that involve repeated model calls, either independently or sequentially with feedback. These evaluations approximate lower and upper performance bounds and potential for future performance improvements for each model, whether through enhanced training or multi-model inference systems. Our extensive empirical analysis reveals that the advantages of inference-time scaling vary across tasks and diminish as problem complexity increases. In addition, simply using more tokens does not necessarily translate to higher accuracy in these challenging regimes. Results from multiple independent runs with conventional models using perfect verifiers show that, for some tasks, these models can achieve performance close to the average performance of today's most advanced reasoning models. However, for other tasks, a significant performance gap remains, even in very high scaling regimes. Encouragingly, all models demonstrate significant gains when inference is further scaled with perfect verifiers or strong feedback, suggesting ample potential for future improvements.

Phenomenological modeling of variable stars allows determination of a set of the parameters, which are needed for classification in the "General Catalogue of Variable Stars" and similar catalogs. We apply a recent method NAV ("New Algol Variable") to eclipsing binary stars of different types. Although all periodic functions may be represented as Fourier series with an infinite number of coefficients, this is impossible for a finite number of the observations. Thus one may use a restricted Fourier series, i.e. a trigonometric polynomial (TP) of order s either for fitting the light curve, or to make a periodogram analysis. However, the number of parameters needed drastically increases with decreasing width of minimum. In the NAV algorithm, the special shape of minimum is used, so the number of parameters is limited to 10 (if the period and initial epoch are fixed) or 12 (not fixed). We illustrate the NAV method by application to a recently discovered Algol-type eclipsing variable 2MASS J11080308-6145589 (in the field of previously known variable star RS Car) and compare results to that obtained using the TP fits. For this system, the statistically optimal number of parameters is 44, but the fit is still worse than that of the NAV fit. Application to the system GSC 3692-00624 argues that the NAV fit is better than the TP one even for the case of EW-type stars with much wider eclipses. Model parameters are listed.

The availability of high-quality data is one of the most important factors in improving the reasoning capability of LLMs. Existing works have demonstrated the effectiveness of creating more instruction data from seed questions or knowledge bases. Recent research indicates that continually scaling up data synthesis from strong models (e.g., GPT-4) can further elicit reasoning performance. Though promising, the open-sourced community still lacks high-quality data at scale and scalable data synthesis methods with affordable costs. To address this, we introduce ScaleQuest, a scalable and novel data synthesis method that utilizes "small-size" (e.g., 7B) open-source models to generate questions from scratch without the need for seed data with complex augmentation constraints. With the efficient ScaleQuest, we automatically constructed a mathematical reasoning dataset consisting of 1 million problem-solution pairs, which are more effective than existing open-sourced datasets. It can universally increase the performance of mainstream open-source models (i.e., Mistral, Llama3, DeepSeekMath, and Qwen2-Math) by achieving 29.2% to 46.4% gains on MATH. Notably, simply fine-tuning the Qwen2-Math-7B-Base model with our dataset can even surpass Qwen2-Math-7B-Instruct, a strong and well-aligned model on closed-source data, and proprietary models such as GPT-4-Turbo and Claude-3.5 Sonnet.

Recent significant advances in text-to-image models unlock the possibility of training vision systems using synthetic images, potentially overcoming the difficulty of collecting curated data at scale. It is unclear, however, how these models behave at scale, as more synthetic data is added to the training set. In this paper we study the scaling laws of synthetic images generated by state of the art text-to-image models, for the training of supervised models: image classifiers with label supervision, and CLIP with language supervision. We identify several factors, including text prompts, classifier-free guidance scale, and types of text-to-image models, that significantly affect scaling behavior. After tuning these factors, we observe that synthetic images demonstrate a scaling trend similar to, but slightly less effective than, real images in CLIP training, while they significantly underperform in scaling when training supervised image classifiers. Our analysis indicates that the main reason for this underperformance is the inability of off-the-shelf text-to-image models to generate certain concepts, a limitation that significantly impairs the training of image classifiers. Our findings also suggest that scaling synthetic data can be particularly effective in scenarios such as: (1) when there is a limited supply of real images for a supervised problem (e.g., fewer than 0.5 million images in ImageNet), (2) when the evaluation dataset diverges significantly from the training data, indicating the out-of-distribution scenario, or (3) when synthetic data is used in conjunction with real images, as demonstrated in the training of CLIP models.

We present a combined scaling method - named BASIC - that achieves 85.7% top-1 accuracy on the ImageNet ILSVRC-2012 validation set without learning from any labeled ImageNet example. This accuracy surpasses best published similar models - CLIP and ALIGN - by 9.3%. Our BASIC model also shows significant improvements in robustness benchmarks. For instance, on 5 test sets with natural distribution shifts such as ImageNet-{A,R,V2,Sketch} and ObjectNet, our model achieves 84.3% top-1 average accuracy, only a small drop from its original ImageNet accuracy. To achieve these results, we scale up the contrastive learning framework of CLIP and ALIGN in three dimensions: data size, model size, and batch size. Our dataset has 6.6B noisy image-text pairs, which is 4x larger than ALIGN, and 16x larger than CLIP. Our largest model has 3B weights, which is 3.75x larger in parameters and 8x larger in FLOPs than ALIGN and CLIP. Finally, our batch size is 65536 which is 2x more than CLIP and 4x more than ALIGN. We encountered two main challenges with the scaling rules of BASIC. First, the main challenge with implementing the combined scaling rules of BASIC is the limited memory of accelerators, such as GPUs and TPUs. To overcome the memory limit, we propose two simple methods which make use of gradient checkpointing and model parallelism. Second, while increasing the dataset size and the model size has been the defacto method to improve the performance of deep learning models like BASIC, the effect of a large contrastive batch size on such contrastive-trained image-text models is not well-understood. To shed light on the benefits of large contrastive batch sizes, we develop a theoretical framework which shows that larger contrastive batch sizes lead to smaller generalization gaps for image-text models such as BASIC.

Since the future of computing is heterogeneous, scalability is a crucial problem for single image super-resolution. Recent works try to train one network, which can be deployed on platforms with different capacities. However, they rely on the pixel-wise sparse convolution, which is not hardware-friendly and achieves limited practical speedup. As image can be divided into patches, which have various restoration difficulties, we present a scalable method based on Adaptive Patch Exiting (APE) to achieve more practical speedup. Specifically, we propose to train a regressor to predict the incremental capacity of each layer for the patch. Once the incremental capacity is below the threshold, the patch can exit at the specific layer. Our method can easily adjust the trade-off between performance and efficiency by changing the threshold of incremental capacity. Furthermore, we propose a novel strategy to enable the network training of our method. We conduct extensive experiments across various backbones, datasets and scaling factors to demonstrate the advantages of our method. Code is available at https://github.com/littlepure2333/APE

Scaling architectures have been proven effective for improving Scene Text Recognition (STR), but the individual contribution of vision encoder and text decoder scaling remain under-explored. In this work, we present an in-depth empirical analysis and demonstrate that, contrary to previous observations, scaling the decoder yields significant performance gains, always exceeding those achieved by encoder scaling alone. We also identify label noise as a key challenge in STR, particularly in real-world data, which can limit the effectiveness of STR models. To address this, we propose Cloze Self-Distillation (CSD), a method that mitigates label noise by distilling a student model from context-aware soft predictions and pseudolabels generated by a teacher model. Additionally, we enhance the decoder architecture by introducing differential cross-attention for STR. Our methodology achieves state-of-the-art performance on 10 out of 11 benchmarks using only real data, while significantly reducing the parameter size and computational costs.

We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models & extrapolates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest varies as amount of compute used for training (or inference), number of model parameters, training dataset size, model input size, number of training steps, or upstream performance varies) for various architectures & for each of various tasks within a large & diverse set of upstream & downstream tasks, in zero-shot, prompted, & finetuned settings. This set includes large-scale vision, language, audio, video, diffusion, generative modeling, multimodal learning, contrastive learning, AI alignment, AI capabilities, robotics, out-of-distribution (OOD) generalization, continual learning, transfer learning, uncertainty estimation / calibration, OOD detection, adversarial robustness, distillation, sparsity, retrieval, quantization, pruning, fairness, molecules, computer programming/coding, math word problems, "emergent phase transitions", arithmetic, supervised learning, unsupervised/self-supervised learning, & reinforcement learning (single agent & multi-agent). When compared to other functional forms for neural scaling, this functional form yields extrapolations of scaling behavior that are considerably more accurate on this set. Moreover, this functional form accurately models & extrapolates scaling behavior that other functional forms are incapable of expressing such as the nonmonotonic transitions present in the scaling behavior of phenomena such as double descent & the delayed, sharp inflection points present in the scaling behavior of tasks such as arithmetic. Lastly, we use this functional form to glean insights about the limit of the predictability of scaling behavior. Code is available at https://github.com/ethancaballero/broken_neural_scaling_laws

Reliable usage of object detectors require them to be calibrated -- a crucial problem that requires careful attention. Recent approaches towards this involve (1) designing new loss functions to obtain calibrated detectors by training them from scratch, and (2) post-hoc Temperature Scaling (TS) that learns to scale the likelihood of a trained detector to output calibrated predictions. These approaches are then evaluated based on a combination of Detection Expected Calibration Error (D-ECE) and Average Precision. In this work, via extensive analysis and insights, we highlight that these recent evaluation frameworks, evaluation metrics, and the use of TS have notable drawbacks leading to incorrect conclusions. As a step towards fixing these issues, we propose a principled evaluation framework to jointly measure calibration and accuracy of object detectors. We also tailor efficient and easy-to-use post-hoc calibration approaches such as Platt Scaling and Isotonic Regression specifically for object detection task. Contrary to the common notion, our experiments show that once designed and evaluated properly, post-hoc calibrators, which are extremely cheap to build and use, are much more powerful and effective than the recent train-time calibration methods. To illustrate, D-DETR with our post-hoc Isotonic Regression calibrator outperforms the recent train-time state-of-the-art calibration method Cal-DETR by more than 7 D-ECE on the COCO dataset. Additionally, we propose improved versions of the recently proposed Localization-aware ECE and show the efficacy of our method on these metrics as well. Code is available at: https://github.com/fiveai/detection_calibration.

Efficient LLM pre-training requires well-tuned hyperparameters (HPs), including learning rate {\eta} and weight decay {\lambda}. We study scaling laws for HPs: formulas for how to scale HPs as we scale model size N, dataset size D, and batch size B. Recent work suggests the AdamW timescale, B/({\eta}{\lambda}D), should remain constant across training settings, and we verify the implication that optimal {\lambda} scales linearly with B, for a fixed N,D. However, as N,D scale, we show the optimal timescale obeys a precise power law in the tokens-per-parameter ratio, D/N. This law thus provides a method to accurately predict {\lambda}opt in advance of large-scale training. We also study scaling laws for optimal batch size Bopt (the B enabling lowest loss at a given N,D) and critical batch size Bcrit (the B beyond which further data parallelism becomes ineffective). In contrast with prior work, we find both Bopt and Bcrit scale as power laws in D, independent of model size, N. Finally, we analyze how these findings inform the real-world selection of Pareto-optimal N and D under dual training time and compute objectives.

We revisit the well-studied problem of approximating a matrix product, A^TB, based on small space sketches S(A) and S(B) of A in R^{n times d} and Bin R^{n times m}. We are interested in the setting where the sketches must be computed independently of each other, except for the use of a shared random seed. We prove that, when A and B are sparse, methods based on coordinated random sampling can outperform classical linear sketching approaches, like Johnson-Lindenstrauss Projection or CountSketch. For example, to obtain Frobenius norm error epsilon|A|_F|B|_F, coordinated sampling requires sketches of size O(s/epsilon^2) when A and B have at most s leq d,m non-zeros per row. In contrast, linear sketching leads to sketches of size O(d/epsilon^2) and O(m/epsilon^2) for A and B. We empirically evaluate our approach on two applications: 1) distributed linear regression in databases, a problem motivated by tasks like dataset discovery and augmentation, and 2) approximating attention matrices in transformer-based language models. In both cases, our sampling algorithms yield an order of magnitude improvement over linear sketching.

We present an improvement in the ability to meaningfully track features in high speed videos of Caribbean steelpan drums illuminated by Electronic Speckle Pattern Interferometry (ESPI). This is achieved through the use of up-to-date computer vision libraries for object detection and image segmentation as well as a significant effort toward cleaning the dataset previously used to train systems for this application. Besides improvements on previous metric scores by 10% or more, noteworthy in this project are the introduction of a segmentation-regression map for the entire drum surface yielding interference fringe counts comparable to those obtained via object detection, as well as the accelerated workflow for coordinating the data-cleaning-and-model-training feedback loop for rapid iteration allowing this project to be conducted on a timescale of only 18 days.

Video generators are increasingly evaluated as potential world models, which requires them to encode and understand physical laws. We investigate their representation of a fundamental law: gravity. Out-of-the-box video generators consistently generate objects falling at an effectively slower acceleration. However, these physical tests are often confounded by ambiguous metric scale. We first investigate if observed physical errors are artifacts of these ambiguities (e.g., incorrect frame rate assumptions). We find that even temporal rescaling cannot correct the high-variance gravity artifacts. To rigorously isolate the underlying physical representation from these confounds, we introduce a unit-free, two-object protocol that tests the timing ratio t_1^2/t_2^2 = h_1/h_2, a relationship independent of g, focal length, and scale. This relative test reveals violations of Galileo's equivalence principle. We then demonstrate that this physical gap can be partially mitigated with targeted specialization. A lightweight low-rank adaptor fine-tuned on only 100 single-ball clips raises g_{eff} from 1.81,m/s^2 to 6.43,m/s^2 (reaching 65% of terrestrial gravity). This specialist adaptor also generalizes zero-shot to two-ball drops and inclined planes, offering initial evidence that specific physical laws can be corrected with minimal data.

The remarkable success of large language pretraining and the discovery of scaling laws signify a paradigm shift in machine learning. Notably, the primary objective has evolved from minimizing generalization error to reducing approximation error, and the most effective strategy has transitioned from regularization (in a broad sense) to scaling up models. This raises a critical question: Do the established principles that proved successful in the generalization-centric era remain valid in this new era of scaling? This paper examines several influential regularization-based principles that may no longer hold true in the scaling-centric, large language model (LLM) era. These principles include explicit L2 regularization and implicit regularization through small batch sizes and large learning rates. Additionally, we identify a new phenomenon termed ``scaling law crossover,'' where two scaling curves intersect at a certain scale, implying that methods effective at smaller scales may not generalize to larger ones. Together, these observations highlight two fundamental questions within this new paradigm: bullet Guiding Principles for Scaling: If regularization is no longer the primary guiding principle for model design, what new principles are emerging to guide scaling? bullet Model Comparison at Scale: How to reliably and effectively compare models at the scale where only a single experiment is feasible?

In speech enhancement and source separation, signal-to-noise ratio is a ubiquitous objective measure of denoising/separation quality. A decade ago, the BSS_eval toolkit was developed to give researchers worldwide a way to evaluate the quality of their algorithms in a simple, fair, and hopefully insightful way: it attempted to account for channel variations, and to not only evaluate the total distortion in the estimated signal but also split it in terms of various factors such as remaining interference, newly added artifacts, and channel errors. In recent years, hundreds of papers have been relying on this toolkit to evaluate their proposed methods and compare them to previous works, often arguing that differences on the order of 0.1 dB proved the effectiveness of a method over others. We argue here that the signal-to-distortion ratio (SDR) implemented in the BSS_eval toolkit has generally been improperly used and abused, especially in the case of single-channel separation, resulting in misleading results. We propose to use a slightly modified definition, resulting in a simpler, more robust measure, called scale-invariant SDR (SI-SDR). We present various examples of critical failure of the original SDR that SI-SDR overcomes.

In the realm of large language models (LLMs), enhancing instruction-following capability often involves curating expansive training data. This is achieved through two primary schemes: i) Scaling-Inputs: Amplifying (input, output) pairs per task instruction, aiming for better instruction adherence. ii) Scaling Input-Free Tasks: Enlarging tasks, each composed of an (instruction, output) pair (without requiring a separate input anymore). However, LLMs under Scaling-Inputs tend to be overly sensitive to inputs, leading to misinterpretation or non-compliance with instructions. Conversely, Scaling Input-Free Tasks demands a substantial number of tasks but is less effective in instruction following when dealing with instances in Scaling-Inputs. This work introduces MUFFIN, a new scheme of instruction-following dataset curation. Specifically, we automatically Scale Tasks per Input by diversifying these tasks with various input facets. Experimental results across four zero-shot benchmarks, spanning both Scaling-Inputs and Scaling Input-Free Tasks schemes, reveal that LLMs, at various scales, trained on MUFFIN generally demonstrate superior instruction-following capabilities compared to those trained on the two aforementioned schemes.

The Inversion-Denoising Paradigm, which is based on diffusion models, excels in diverse image editing and restoration tasks. We revisit its mechanism and reveal a critical, overlooked factor in reconstruction degradation: the approximate noise error. This error stems from approximating the noise at step t with the prediction at step t-1, resulting in severe error accumulation throughout the inversion process. We introduce Projection-Orthogonal Least Squares for Robust and Adaptive Inversion (POLARIS), which reformulates inversion from an error-compensation problem into an error-origin problem. Rather than optimizing embeddings or latent codes to offset accumulated drift, POLARIS treats the guidance scale ω as a step-wise variable and derives a mathematically grounded formula to minimize inversion error at each step. Remarkably, POLARIS improves inversion latent quality with just one line of code. With negligible performance overhead, it substantially mitigates noise approximation errors and consistently improves the accuracy of downstream tasks.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

The growing number of parameters and computational demands of large language models (LLMs) present significant challenges for their efficient deployment. Recently, there is an increasing interest in quantizing weights to extremely low precision while offsetting the resulting error with low-rank, high-precision error reconstruction terms. The combination of quantization and low-rank approximation is now popular in both adapter-based, parameter-efficient fine-tuning methods such as LoftQ and low-precision inference techniques including ZeroQuant-V2. Usually, the low-rank terms are calculated via the singular value decomposition (SVD) of the weight quantization error, minimizing the Frobenius and spectral norms of the weight approximation error. Recent methods like LQ-LoRA and LQER introduced hand-crafted heuristics to minimize errors in layer outputs (activations) rather than weights, resulting improved quantization results. However, these heuristic methods lack an analytical solution to guide the design of quantization error reconstruction terms. In this paper, we revisit this problem and formulate an analytical framework, named Quantization Error Reconstruction Analysis (QERA), and offer a closed-form solution to the problem. We show QERA benefits both existing low-precision fine-tuning and inference methods -- QERA achieves a fine-tuned accuracy gain of Δ_{acc} = 6.05% of 2-bit RoBERTa-base on GLUE compared to LoftQ; and obtains Δ_{acc} = 2.97% higher post-training quantization accuracy of 4-bit Llama-3.1-70B on average than ZeroQuant-V2 and Δ_{ppl} = - 0.28 lower perplexity on WikiText2 than LQER.

Mobile devices are transforming the way people interact with computers, and speech interfaces to applications are ever more important. Automatic Speech Recognition systems recently published are very accurate, but often require powerful machinery (specialised Graphical Processing Units) for inference, which makes them impractical to run on commodity devices, especially in streaming mode. Impressed by the accuracy of, but dissatisfied with the inference times of the baseline Kazakh ASR model of (Khassanov et al.,2021) when not using a GPU, we trained a new baseline acoustic model (on the same dataset as the aforementioned paper) and three language models for use with the Coqui STT framework. Results look promising, but further epochs of training and parameter sweeping or, alternatively, limiting the vocabulary that the ASR system must support, is needed to reach a production-level accuracy.

Large language models have seen widespread adoption in math problem-solving. However, in geometry problems that usually require visual aids for better understanding, even the most advanced multi-modal models currently still face challenges in effectively using image information. High-quality data is crucial for enhancing the geometric capabilities of multi-modal models, yet existing open-source datasets and related efforts are either too challenging for direct model learning or suffer from misalignment between text and images. To overcome this issue, we introduce a novel pipeline that leverages GPT-4 and GPT-4V to generate relatively basic geometry problems with aligned text and images, facilitating model learning. We have produced a dataset of 4.9K geometry problems and combined it with 19K open-source data to form our GeoGPT4V dataset. Experimental results demonstrate that the GeoGPT4V dataset significantly improves the geometry performance of various models on the MathVista and MathVision benchmarks. The code is available at https://github.com/Lanyu0303/GeoGPT4V_Project

LongRoPE2 is a novel approach that extends the effective context window of pre-trained large language models (LLMs) to the target length, while preserving the performance on the original shorter context window. This is achieved by three contributions: (1) a hypothesis that insufficient training in higher RoPE dimensions contributes to the persistent out-of-distribution (OOD) issues observed in existing methods; (2) an effective RoPE rescaling algorithm that adopts evolutionary search guided by "needle-driven" perplexity to address the insufficient training problem; (3) a mixed context window training approach that fine-tunes model weights to adopt rescaled RoPE for long-context sequences while preserving the short-context performance with the original RoPE. Extensive experiments on LLaMA3-8B and Phi3-mini-3.8B across various benchmarks validate the hypothesis and demonstrate the effectiveness of LongRoPE2. Remarkably, LongRoPE2 extends LLaMA3-8B to achieve a 128K effective context length while retaining over 98.5% of short-context performance, using only 10B tokens -- 80x fewer than Meta's approach, which fails to reach the target effective context length. Code will be available at https://github.com/microsoft/LongRoPE.

We report the delivery to the Mikulski Archive for Space Telescopes of target pixel and light curve files for up to 160,000 targets selected from full-frame images (FFI) for each TESS Northern hemisphere observing sector. The data include calibrated target pixels, simple aperture photometry flux time series, and presearch data conditioning corrected flux time series. These data provide TESS users with high quality, uniform pipeline products for a selection of FFI targets, that would otherwise not be readily available. Additionally, we deliver cotrending basis vectors derived from the FFI targets to allow users to perform their own systematic error corrections. The selected targets include all 2-minute targets and additional targets selected from the TESS Input Catalog with a maximum of 10,000 targets per sector on each of the sixteen TESS CCDs. The data products are in the same format as the project-delivered files for the TESS 2-minute targets. All of the TESS-SPOC data products are available at the MAST as a High Level Science Product via https://doi.org/10.17909/t9-wpz1-8s54.

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regime. Motivated by the recent stream of results on the Gaussian universality of the test and training errors in generalized linear estimation, we ask ourselves the question: "when is a single Gaussian enough to characterize the error?". Our formula allow us to give sharp answers to this question, both in the positive and negative directions. More precisely, we show that the sufficient conditions for Gaussian universality (or lack of thereof) crucially depend on the alignment between the target weights and the means and covariances of the mixture clusters, which we precisely quantify. In the particular case of least-squares interpolation, we prove a strong universality property of the training error, and show it follows a simple, closed-form expression. Finally, we apply our results to real datasets, clarifying some recent discussion in the literature about Gaussian universality of the errors in this context.

A long-term goal of machine learning is to build intelligent conversational agents. One recent popular approach is to train end-to-end models on a large amount of real dialog transcripts between humans (Sordoni et al., 2015; Vinyals & Le, 2015; Shang et al., 2015). However, this approach leaves many questions unanswered as an understanding of the precise successes and shortcomings of each model is hard to assess. A contrasting recent proposal are the bAbI tasks (Weston et al., 2015b) which are synthetic data that measure the ability of learning machines at various reasoning tasks over toy language. Unfortunately, those tests are very small and hence may encourage methods that do not scale. In this work, we propose a suite of new tasks of a much larger scale that attempt to bridge the gap between the two regimes. Choosing the domain of movies, we provide tasks that test the ability of models to answer factual questions (utilizing OMDB), provide personalization (utilizing MovieLens), carry short conversations about the two, and finally to perform on natural dialogs from Reddit. We provide a dataset covering 75k movie entities and with 3.5M training examples. We present results of various models on these tasks, and evaluate their performance.

We present the discovery of 118 new ultracool dwarf candidates, discovered using a new machine learning tool, named SMDET, applied to time series images from the Wide-field Infrared Survey Explorer. We gathered photometric and astrometric data to estimate each candidate's spectral type, distance, and tangential velocity. This sample has a photometrically estimated spectral class distribution of 28 M dwarfs, 64 L dwarfs, and 18 T dwarfs. We also identify a T subdwarf candidate, two extreme T subdwarf candidates, and two candidate young ultracool dwarfs. Five objects did not have enough photometric data for any estimations to be made. To validate our estimated spectral types, spectra were collected for 2 objects, yielding confirmed spectral types of T5 (estimated T5) and T3 (estimated T4). Demonstrating the effectiveness of machine learning tools as a new large-scale discovery technique.

Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix X in R^{N times d} and measurements or labels {y} in R^N where {y} = {X} {w}^* + {xi}, and {xi} is the noise in the measurements. Importantly, we have the additional constraint that the unknown signal vector {w}^* is sparse: it has k non-zero entries where k is much smaller than the ambient dimension. Our goal is to output a prediction vector {w} that has small prediction error: 1{N}cdot |{X} {w}^* - {X} {w}|^2_2. Information-theoretically, we know what is best possible in terms of measurements: under most natural noise distributions, we can get prediction error at most epsilon with roughly N = O(k log d/epsilon) samples. Computationally, this currently needs d^{Omega(k)} run-time. Alternately, with N = O(d), we can get polynomial-time. Thus, there is an exponential gap (in the dependence on d) between the two and we do not know if it is possible to get d^{o(k)} run-time and o(d) samples. We give the first generic positive result for worst-case design matrices {X}: For any {X}, we show that if the support of {w}^* is chosen at random, we can get prediction error epsilon with N = poly(k, log d, 1/epsilon) samples and run-time poly(d,N). This run-time holds for any design matrix {X} with condition number up to 2^{poly(d)}. Previously, such results were known for worst-case {w}^*, but only for random design matrices from well-behaved families, matrices that have a very low condition number (poly(log d); e.g., as studied in compressed sensing), or those with special structural properties.

Hand-drawn cartoon animation employs sketches and flat-color segments to create the illusion of motion. While recent advancements like CLIP, SVD, and Sora show impressive results in understanding and generating natural video by scaling large models with extensive datasets, they are not as effective for cartoons. Through our empirical experiments, we argue that this ineffectiveness stems from a notable bias in hand-drawn cartoons that diverges from the distribution of natural videos. Can we harness the success of the scaling paradigm to benefit cartoon research? Unfortunately, until now, there has not been a sizable cartoon dataset available for exploration. In this research, we propose the Sakuga-42M Dataset, the first large-scale cartoon animation dataset. Sakuga-42M comprises 42 million keyframes covering various artistic styles, regions, and years, with comprehensive semantic annotations including video-text description pairs, anime tags, content taxonomies, etc. We pioneer the benefits of such a large-scale cartoon dataset on comprehension and generation tasks by finetuning contemporary foundation models like Video CLIP, Video Mamba, and SVD, achieving outstanding performance on cartoon-related tasks. Our motivation is to introduce large-scaling to cartoon research and foster generalization and robustness in future cartoon applications. Dataset, Code, and Pretrained Models will be publicly available.

Motivated by the problem of fast processing of attention matrices, we study fast algorithms for computing matrix-vector products for asymmetric Gaussian Kernel matrices Kin R^{ntimes n}. K's columns are indexed by a set of n keys k_1,k_2ldots, k_nin R^d, rows by a set of n queries q_1,q_2,ldots,q_nin R^d , and its i,j entry is K_{ij} = e^{-|q_i-k_j|_2^2/2sigma^2} for some bandwidth parameter sigma>0. Given a vector xin R^n and error parameter epsilon>0, our task is to output a yin R^n such that |Kx-y|_2leq epsilon |x|_2 in time subquadratic in n and linear in d. Our algorithms rely on the following modelling assumption about the matrices K: the sum of the entries of K scales linearly in n, as opposed to worst case quadratic growth. We validate this assumption experimentally, for Gaussian kernel matrices encountered in various settings such as fast attention computation in LLMs. We obtain the first subquadratic-time algorithm that works under this assumption, for unrestricted vectors.

Modern single-image super-resolution (SISR) models deliver photo-realistic results at the scale factors on which they are trained, but collapse when asked to magnify far beyond that regime. We address this scalability bottleneck with Chain-of-Zoom (CoZ), a model-agnostic framework that factorizes SISR into an autoregressive chain of intermediate scale-states with multi-scale-aware prompts. CoZ repeatedly re-uses a backbone SR model, decomposing the conditional probability into tractable sub-problems to achieve extreme resolutions without additional training. Because visual cues diminish at high magnifications, we augment each zoom step with multi-scale-aware text prompts generated by a vision-language model (VLM). The prompt extractor itself is fine-tuned using Generalized Reward Policy Optimization (GRPO) with a critic VLM, aligning text guidance towards human preference. Experiments show that a standard 4x diffusion SR model wrapped in CoZ attains beyond 256x enlargement with high perceptual quality and fidelity. Project Page: https://bryanswkim.github.io/chain-of-zoom/ .

Scaling up language models has been empirically shown to improve performance on a wide range of downstream tasks. However, if we were to observe worse performance as a function of scale ("inverse scaling") on certain tasks, this would indicate that scaling can also encourage behaviors that are misaligned with human preferences. The Inverse Scaling Prize (McKenzie et al. 2022) identified eleven such inverse scaling tasks, evaluated on models of up to 280B parameters and up to 500 zettaFLOPs of training compute. This paper takes a closer look at these inverse scaling tasks. We evaluate models of up to 540B parameters, trained on five times more compute than those evaluated in the Inverse Scaling Prize. With this increased range of model sizes and training compute, only four out of the eleven tasks remain inverse scaling. Six out of the eleven tasks exhibit "U-shaped scaling", where performance decreases up to a certain size, and then increases again up to the largest model evaluated (the one remaining task displays positive scaling). In addition, we find that 1-shot examples and chain-of-thought can help mitigate undesirable scaling patterns even further. U-shaped scaling suggests that the inverse scaling trend observed in McKenzie et al. (2022) may not continue to hold for larger models, which we attribute to the presence of distractor tasks that only sufficiently large models can avoid.

Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported, they typically rely on the Central Limit Theorem (CLT). In this position paper, we argue that while CLT-based methods for uncertainty quantification are appropriate when benchmarks consist of thousands of examples, they fail to provide adequate uncertainty estimates for LLM evaluations that rely on smaller, highly specialized benchmarks. In these small-data settings, we demonstrate that CLT-based methods perform very poorly, usually dramatically underestimating uncertainty (i.e. producing error bars that are too small). We give recommendations for alternative frequentist and Bayesian methods that are both easy to implement and more appropriate in these increasingly common scenarios. We provide a simple Python library for these Bayesian methods at https://github.com/sambowyer/bayes_evals .

We present the first systematic investigation of supervised scaling laws outside of an ImageNet-like context - on images of galaxies. We use 840k galaxy images and over 100M annotations by Galaxy Zoo volunteers, comparable in scale to Imagenet-1K. We find that adding annotated galaxy images provides a power law improvement in performance across all architectures and all tasks, while adding trainable parameters is effective only for some (typically more subjectively challenging) tasks. We then compare the downstream performance of finetuned models pretrained on either ImageNet-12k alone vs. additionally pretrained on our galaxy images. We achieve an average relative error rate reduction of 31% across 5 downstream tasks of scientific interest. Our finetuned models are more label-efficient and, unlike their ImageNet-12k-pretrained equivalents, often achieve linear transfer performance equal to that of end-to-end finetuning. We find relatively modest additional downstream benefits from scaling model size, implying that scaling alone is not sufficient to address our domain gap, and suggest that practitioners with qualitatively different images might benefit more from in-domain adaption followed by targeted downstream labelling.

We present BigCodec, a low-bitrate neural speech codec. While recent neural speech codecs have shown impressive progress, their performance significantly deteriorates at low bitrates (around 1 kbps). Although a low bitrate inherently restricts performance, other factors, such as model capacity, also hinder further improvements. To address this problem, we scale up the model size to 159M parameters that is more than 10 times larger than popular codecs with about 10M parameters. Besides, we integrate sequential models into traditional convolutional architectures to better capture temporal dependency and adopt low-dimensional vector quantization to ensure a high code utilization. Comprehensive objective and subjective evaluations show that BigCodec, with a bitrate of 1.04 kbps, significantly outperforms several existing low-bitrate codecs. Furthermore, BigCodec achieves objective performance comparable to popular codecs operating at 4-6 times higher bitrates, and even delivers better subjective perceptual quality than the ground truth.

Deep neural networks have enabled progress in a wide variety of applications. Growing the size of the neural network typically results in improved accuracy. As model sizes grow, the memory and compute requirements for training these models also increases. We introduce a technique to train deep neural networks using half precision floating point numbers. In our technique, weights, activations and gradients are stored in IEEE half-precision format. Half-precision floating numbers have limited numerical range compared to single-precision numbers. We propose two techniques to handle this loss of information. Firstly, we recommend maintaining a single-precision copy of the weights that accumulates the gradients after each optimizer step. This single-precision copy is rounded to half-precision format during training. Secondly, we propose scaling the loss appropriately to handle the loss of information with half-precision gradients. We demonstrate that this approach works for a wide variety of models including convolution neural networks, recurrent neural networks and generative adversarial networks. This technique works for large scale models with more than 100 million parameters trained on large datasets. Using this approach, we can reduce the memory consumption of deep learning models by nearly 2x. In future processors, we can also expect a significant computation speedup using half-precision hardware units.

The astonishing breakthrough of multimodal large language models (MLLMs) has necessitated new benchmarks to quantitatively assess their capabilities, reveal their limitations, and indicate future research directions. However, this is challenging in the context of remote sensing (RS), since the imagery features ultra-high resolution that incorporates extremely complex semantic relationships. Existing benchmarks usually adopt notably smaller image sizes than real-world RS scenarios, suffer from limited annotation quality, and consider insufficient dimensions of evaluation. To address these issues, we present XLRS-Bench: a comprehensive benchmark for evaluating the perception and reasoning capabilities of MLLMs in ultra-high-resolution RS scenarios. XLRS-Bench boasts the largest average image size (8500times8500) observed thus far, with all evaluation samples meticulously annotated manually, assisted by a novel semi-automatic captioner on ultra-high-resolution RS images. On top of the XLRS-Bench, 16 sub-tasks are defined to evaluate MLLMs' 10 kinds of perceptual capabilities and 6 kinds of reasoning capabilities, with a primary emphasis on advanced cognitive processes that facilitate real-world decision-making and the capture of spatiotemporal changes. The results of both general and RS-focused MLLMs on XLRS-Bench indicate that further efforts are needed for real-world RS applications. We have open-sourced XLRS-Bench to support further research in developing more powerful MLLMs for remote sensing.

Neural network scaling has been critical for improving the model quality in many real-world machine learning applications with vast amounts of training data and compute. Although this trend of scaling is affirmed to be a sure-fire approach for better model quality, there are challenges on the path such as the computation cost, ease of programming, and efficient implementation on parallel devices. GShard is a module composed of a set of lightweight annotation APIs and an extension to the XLA compiler. It provides an elegant way to express a wide range of parallel computation patterns with minimal changes to the existing model code. GShard enabled us to scale up multilingual neural machine translation Transformer model with Sparsely-Gated Mixture-of-Experts beyond 600 billion parameters using automatic sharding. We demonstrate that such a giant model can efficiently be trained on 2048 TPU v3 accelerators in 4 days to achieve far superior quality for translation from 100 languages to English compared to the prior art.

During the deployment of Large Language Models (LLMs), the autoregressive decoding phase on heterogeneous NPU platforms (e.g., Ascend 910B) faces severe memory-bound challenges. This study reveals the ``Model Scaling Paradox'' caused by the static deployment of single-sized models. It also points out the kernel synchronization overhead of fine-grained speculative decoding leviathan2023fast, chen2023speculative under NPU computational graph compilation, and the severe limitations of purely relying on micro-level acceleration algorithms like Prompt LookUp Decoding (PLD)

Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less useful. We argue that low-precision floating points can perform well provided the error is properly compensated at the critical locations in the training process. We propose Collage which utilizes multi-component float representation in low-precision to accurately perform operations with numerical errors accounted. To understand the impact of imprecision to training, we propose a simple and novel metric which tracks the lost information during training as well as differentiates various precision strategies. Our method works with commonly used low-precision such as half-precision (16-bit floating points) and can be naturally extended to work with even lower precision such as 8-bit. Experimental results show that pre-training using Collage removes the requirement of using 32-bit floating-point copies of the model and attains similar/better training performance compared to (16, 32)-bit mixed-precision strategy, with up to 3.7times speedup and sim 15% to 23% less memory usage in practice.

Currently, vision encoder models like Vision Transformers (ViTs) typically excel at image recognition tasks but cannot simultaneously support text recognition like human visual recognition. To address this limitation, we propose UNIT, a novel training framework aimed at UNifying Image and Text recognition within a single model. Starting with a vision encoder pre-trained with image recognition tasks, UNIT introduces a lightweight language decoder for predicting text outputs and a lightweight vision decoder to prevent catastrophic forgetting of the original image encoding capabilities. The training process comprises two stages: intra-scale pretraining and inter-scale finetuning. During intra-scale pretraining, UNIT learns unified representations from multi-scale inputs, where images and documents are at their commonly used resolution, to enable fundamental recognition capability. In the inter-scale finetuning stage, the model introduces scale-exchanged data, featuring images and documents at resolutions different from the most commonly used ones, to enhance its scale robustness. Notably, UNIT retains the original vision encoder architecture, making it cost-free in terms of inference and deployment. Experiments across multiple benchmarks confirm that our method significantly outperforms existing methods on document-related tasks (e.g., OCR and DocQA) while maintaining the performances on natural images, demonstrating its ability to substantially enhance text recognition without compromising its core image recognition capabilities.

Scaling law principles indicate a power-law correlation between loss and variables such as model size, dataset size, and computational resources utilized during training. These principles play a vital role in optimizing various aspects of model pre-training, ultimately contributing to the success of large language models such as GPT-4, Llama and Gemini. However, the original scaling law paper by OpenAI did not disclose the complete details necessary to derive the precise scaling law formulas, and their conclusions are only based on models containing up to 1.5 billion parameters. Though some subsequent works attempt to unveil these details and scale to larger models, they often neglect the training dependency of important factors such as the learning rate, context length and batch size, leading to their failure to establish a reliable formula for predicting the test loss trajectory. In this technical report, we confirm that the scaling law formulations proposed in the original OpenAI paper remain valid when scaling the model size up to 33 billion, but the constant coefficients in these formulas vary significantly with the experiment setup. We meticulously identify influential factors and provide transparent, step-by-step instructions to estimate all constant terms in scaling-law formulas by training on models with only 1M~60M parameters. Using these estimated formulas, we showcase the capability to accurately predict various attributes for models with up to 33B parameters before their training, including (1) the minimum possible test loss; (2) the minimum required training steps and processed tokens to achieve a specific loss; (3) the critical batch size with an optimal time/computation trade-off at any loss value; and (4) the complete test loss trajectory with arbitrary batch size.