Daily Papers

Accurate estimation of uncertainty in deep learning is critical for deploying models in high-stakes domains such as medical diagnosis and autonomous decision-making, where overconfident predictions can lead to harmful outcomes. In practice, understanding the reason behind a model's uncertainty and the type of uncertainty it represents can support risk-aware decisions, enhance user trust, and guide additional data collection. However, many existing methods only address a single type of uncertainty or require modifications and retraining of the base model, making them difficult to adopt in real-world systems. We introduce CUPID (Comprehensive Uncertainty Plug-in estImation moDel), a general-purpose module that jointly estimates aleatoric and epistemic uncertainty without modifying or retraining the base model. CUPID can be flexibly inserted into any layer of a pretrained network. It models aleatoric uncertainty through a learned Bayesian identity mapping and captures epistemic uncertainty by analyzing the model's internal responses to structured perturbations. We evaluate CUPID across a range of tasks, including classification, regression, and out-of-distribution detection. The results show that it consistently delivers competitive performance while offering layer-wise insights into the origins of uncertainty. By making uncertainty estimation modular, interpretable, and model-agnostic, CUPID supports more transparent and trustworthy AI. Related code and data are available at https://github.com/a-Fomalhaut-a/CUPID.

Recently proposed self-supervised learning approaches have been successful for pre-training speech representation models. The utility of these learned representations has been observed empirically, but not much has been studied about the type or extent of information encoded in the pre-trained representations themselves. Developing such insights can help understand the capabilities and limits of these models and enable the research community to more efficiently develop their usage for downstream applications. In this work, we begin to fill this gap by examining one recent and successful pre-trained model (wav2vec 2.0), via its intermediate representation vectors, using a suite of analysis tools. We use the metrics of canonical correlation, mutual information, and performance on simple downstream tasks with non-parametric probes, in order to (i) query for acoustic and linguistic information content, (ii) characterize the evolution of information across model layers, and (iii) understand how fine-tuning the model for automatic speech recognition (ASR) affects these observations. Our findings motivate modifying the fine-tuning protocol for ASR, which produces improved word error rates in a low-resource setting.

This paper conducts a comprehensive layer-wise analysis of self-supervised learning (SSL) models for audio deepfake detection across diverse contexts, including multilingual datasets (English, Chinese, Spanish), partial, song, and scene-based deepfake scenarios. By systematically evaluating the contributions of different transformer layers, we uncover critical insights into model behavior and performance. Our findings reveal that lower layers consistently provide the most discriminative features, while higher layers capture less relevant information. Notably, all models achieve competitive equal error rate (EER) scores even when employing a reduced number of layers. This indicates that we can reduce computational costs and increase the inference speed of detecting deepfakes by utilizing only a few lower layers. This work enhances our understanding of SSL models in deepfake detection, offering valuable insights applicable across varied linguistic and contextual settings. Our trained models and code are publicly available: https://github.com/Yaselley/SSL_Layerwise_Deepfake.

Large Language Models (LLMs) often produce fluent yet factually incorrect statements-a phenomenon known as hallucination-posing serious risks in high-stakes domains. We present Layer-wise Semantic Dynamics (LSD), a geometric framework for hallucination detection that analyzes the evolution of hidden-state semantics across transformer layers. Unlike prior methods that rely on multiple sampling passes or external verification sources, LSD operates intrinsically within the model's representational space. Using margin-based contrastive learning, LSD aligns hidden activations with ground-truth embeddings derived from a factual encoder, revealing a distinct separation in semantic trajectories: factual responses preserve stable alignment, while hallucinations exhibit pronounced semantic drift across depth. Evaluated on the TruthfulQA and synthetic factual-hallucination datasets, LSD achieves an F1-score of 0.92, AUROC of 0.96, and clustering accuracy of 0.89, outperforming SelfCheckGPT and Semantic Entropy baselines while requiring only a single forward pass. This efficiency yields a 5-20x speedup over sampling-based methods without sacrificing precision or interpretability. LSD offers a scalable, model-agnostic mechanism for real-time hallucination monitoring and provides new insights into the geometry of factual consistency within large language models.

Transformer-based language models excel at both recall (retrieving memorized facts) and reasoning (performing multi-step inference), but whether these abilities rely on distinct internal mechanisms remains unclear. Distinguishing recall from reasoning is crucial for predicting model generalization, designing targeted evaluations, and building safer interventions that affect one ability without disrupting the other.We approach this question through mechanistic interpretability, using controlled datasets of synthetic linguistic puzzles to probe transformer models at the layer, head, and neuron level. Our pipeline combines activation patching and structured ablations to causally measure component contributions to each task type. Across two model families (Qwen and LLaMA), we find that interventions on distinct layers and attention heads lead to selective impairments: disabling identified "recall circuits" reduces fact-retrieval accuracy by up to 15\% while leaving reasoning intact, whereas disabling "reasoning circuits" reduces multi-step inference by a comparable margin. At the neuron level, we observe task-specific firing patterns, though these effects are less robust, consistent with neuronal polysemanticity.Our results provide the first causal evidence that recall and reasoning rely on separable but interacting circuits in transformer models. These findings advance mechanistic interpretability by linking circuit-level structure to functional specialization and demonstrate how controlled datasets and causal interventions can yield mechanistic insights into model cognition, informing safer deployment of large language models.

As the post-training of large language models (LLMs) advances from instruction-following to complex reasoning tasks, understanding how different data affect finetuning dynamics remains largely unexplored. In this paper, we present a spectral analysis of layer-wise gradients induced by low/high-quality instruction and reasoning data for LLM post-training. Our analysis reveals that widely-studied metrics for data evaluation, e.g., IFD, InsTag, Difficulty, and Reward, can be explained and unified by spectral properties computed from gradients' singular value decomposition (SVD). Specifically, higher-quality data are usually associated with lower nuclear norms and higher effective ranks. Notably, effective rank exhibits better robustness and resolution than nuclear norm in capturing subtle quality differences. For example, reasoning data achieves substantially higher effective ranks than instruction data, implying richer gradient structures on more complex tasks. Our experiments also highlight that models within the same family share similar gradient patterns regardless of their sizes, whereas different model families diverge significantly. Providing a unified view on the effects of data quality across instruction and reasoning data, this work illuminates the interplay between data quality and training stability, shedding novel insights into developing better data exploration strategies for post-training.

As Transformers have become state-of-the-art models for natural language processing (NLP) tasks, the need to understand and explain their predictions is increasingly apparent. Especially in unsupervised applications, such as information retrieval tasks, similarity models built on top of foundation model representations have been widely applied. However, their inner prediction mechanisms have mostly remained opaque. Recent advances in explainable AI have made it possible to mitigate these limitations by leveraging improved explanations for Transformers through layer-wise relevance propagation (LRP). Using BiLRP, an extension developed for computing second-order explanations in bilinear similarity models, we investigate which feature interactions drive similarity in NLP models. We validate the resulting explanations and demonstrate their utility in three corpus-level use cases, analyzing grammatical interactions, multilingual semantics, and biomedical text retrieval. Our findings contribute to a deeper understanding of different semantic similarity tasks and models, highlighting how novel explainable AI methods enable in-depth analyses and corpus-level insights.

Multilingual large language models (LLMs) are increasingly deployed in linguistically diverse regions like India, yet most interpretability tools remain tailored to English. Prior work reveals that LLMs often operate in English centric representation spaces, making cross lingual interpretability a pressing concern. We introduce Indic-TunedLens, a novel interpretability framework specifically for Indian languages that learns shared affine transformations. Unlike the standard Logit Lens, which directly decodes intermediate activations, Indic-TunedLens adjusts hidden states for each target language, aligning them with the target output distributions to enable more faithful decoding of model representations. We evaluate our framework on 10 Indian languages using the MMLU benchmark and find that it significantly improves over SOTA interpretability methods, especially for morphologically rich, low resource languages. Our results provide crucial insights into the layer-wise semantic encoding of multilingual transformers. Our model is available at https://huggingface.co/spaces/MihirRajeshPanchal/IndicTunedLens. Our code is available at https://github.com/MihirRajeshPanchal/IndicTunedLens.

Training large language models is a computationally intensive process that often requires substantial resources to achieve state-of-the-art results. Incremental layer-wise training has been proposed as a potential strategy to optimize the training process by progressively introducing layers, with the expectation that this approach would lead to faster convergence and more efficient use of computational resources. In this paper, we investigate the effectiveness of incremental training for LLMs, dividing the training process into multiple stages where layers are added progressively. Our experimental results indicate that while the incremental approach initially demonstrates some computational efficiency, it ultimately requires greater overall computational costs to reach comparable performance to traditional full-scale training. Although the incremental training process can eventually close the performance gap with the baseline, it does so only after significantly extended continual training. These findings suggest that incremental layer-wise training may not be a viable alternative for training large language models, highlighting its limitations and providing valuable insights into the inefficiencies of this approach.

This paper explores Large Batch Training techniques using layer-wise adaptive scaling ratio (LARS) across diverse settings, uncovering insights. LARS algorithms with warm-up tend to be trapped in sharp minimizers early on due to redundant ratio scaling. Additionally, a fixed steep decline in the latter phase restricts deep neural networks from effectively navigating early-phase sharp minimizers. Building on these findings, we propose Time Varying LARS (TVLARS), a novel algorithm that replaces warm-up with a configurable sigmoid-like function for robust training in the initial phase. TVLARS promotes gradient exploration early on, surpassing sharp optimizers and gradually transitioning to LARS for robustness in later phases. Extensive experiments demonstrate that TVLARS consistently outperforms LARS and LAMB in most cases, with up to 2\% improvement in classification scenarios. Notably, in all self-supervised learning cases, TVLARS dominates LARS and LAMB with performance improvements of up to 10\%.

Large language models are increasingly adapted to downstream tasks through fine-tuning. Full supervised fine-tuning (SFT) and parameter-efficient fine-tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), are two dominant approaches. While PEFT methods are widely used for their computational efficiency, the implications of their configurations (e.g., rank) remain under-explored in downstream Q&A tasks and generalisation. In this work, we perform a comprehensive evaluation across multiple reasoning and recall datasets, conducting a rank sweep to quantify the trade-off between SFT and PEFT. We also compare the accuracy of PEFT and SFT models across in-domain and out-of-domain adaptation, highlighting distinct generalisation behaviour and task-specific forgetting. We demonstrate that LoRA achieves competitive and in some cases superior performance compared to SFT, particularly on reasoning tasks at specific rank values. Additionally, we analyze the internal representations via spectral features and layer-wise attention structures, offering insights into representational drift and structural changes in attention patterns.

Multi-Agent System (MAS) powered by Visual Language Models (VLMs) enables challenging tasks but suffers from a novel failure term, multi-agent visual hallucination snowballing, where hallucinations are seeded in a single agent and amplified by following ones due to the over-reliance on textual flow to relay visual information. Through turn-, layer-, and token-wise attention analyses, we provide detailed insights into the essence of hallucination snowballing regarding the reduction of visual attention allocation. It leads us to identify a subset of vision tokens with a unimodal attention peak in middle layers that best preserve visual evidence but gradually diminish in deeper agent turns, resulting in the visual hallucination snowballing in MAS. Thus, we propose ViF, a lightweight, plug-and-play mitigation paradigm that relays inter-agent messages with Visual Flow powered by the selected visual relay tokens and applies attention reallocation to amplify this pattern. The experiment results demonstrate that our method markedly reduces hallucination snowballing, consistently improving the performance across eight benchmarks based on four common MAS structures and ten base models. The source code will be available at: https://github.com/YU-deep/ViF.git.

Pretrained Vision-Language-Action (VLA) policies have achieved strong single-step manipulation, but their inference remains largely memoryless, which is brittle in non-Markovian long-horizon settings with occlusion, state aliasing, and subtle post-action changes. Prior approaches inject history either by stacking frames, which scales visual tokens and latency while adding near-duplicate pixels, or by learning additional temporal interfaces that require (re-)training and may break the original single-frame inference graph. We present TempoFit, a training-free temporal retrofit that upgrades frozen VLAs through state-level memory. Our key insight is that prefix attention K/V already form a model-native, content-addressable runtime state; reusing them across timesteps introduces history without new tokens or trainable modules. TempoFit stores layer-wise FIFO prefix K/V at selected intermediate layers, performs parameter-free K-to-K retrieval with Frame-Gap Temporal Bias (FGTB), a fixed recency bias inspired by positional biases in NLP, to keep decisions present-dominant, and injects the retrieved context via pre-attention residual loading with norm-preserving rescaling to avoid distribution shift under frozen weights. On LIBERO-LONG, TempoFit improves strong pretrained backbones by up to +4.0% average success rate while maintaining near-real-time latency, and it transfers consistently to CALVIN and real-robot long-horizon tasks.

Diagnosing deep neural networks (DNNs) through the eigenspectrum of weight matrices has been an active area of research in recent years. At a high level, eigenspectrum analysis of DNNs involves measuring the heavytailness of the empirical spectral densities (ESD) of weight matrices. It provides insight into how well a model is trained and can guide decisions on assigning better layer-wise training hyperparameters. In this paper, we address a challenge associated with such eigenspectrum methods: the impact of the aspect ratio of weight matrices on estimated heavytailness metrics. We demonstrate that matrices of varying sizes (and aspect ratios) introduce a non-negligible bias in estimating heavytailness metrics, leading to inaccurate model diagnosis and layer-wise hyperparameter assignment. To overcome this challenge, we propose FARMS (Fixed-Aspect-Ratio Matrix Subsampling), a method that normalizes the weight matrices by subsampling submatrices with a fixed aspect ratio. Instead of measuring the heavytailness of the original ESD, we measure the average ESD of these subsampled submatrices. We show that measuring the heavytailness of these submatrices with the fixed aspect ratio can effectively mitigate the aspect ratio bias. We validate our approach across various optimization techniques and application domains that involve eigenspectrum analysis of weights, including image classification in computer vision (CV) models, scientific machine learning (SciML) model training, and large language model (LLM) pruning. Our results show that despite its simplicity, FARMS uniformly improves the accuracy of eigenspectrum analysis while enabling more effective layer-wise hyperparameter assignment in these application domains. In one of the LLM pruning experiments, FARMS reduces the perplexity of the LLaMA-7B model by 17.3% when compared with the state-of-the-art method.

Large language models (LLMs) have shown remarkable performances across a wide range of tasks. However, the mechanisms by which these models encode tasks of varying complexities remain poorly understood. In this paper, we explore the hypothesis that LLMs process concepts of varying complexities in different layers, introducing the idea of "Concept Depth" to suggest that more complex concepts are typically acquired in deeper layers. Specifically, we categorize concepts based on their level of abstraction, defining them in the order of increasing complexity within factual, emotional, and inferential tasks. We conduct extensive probing experiments using layer-wise representations across various LLM families (Gemma, LLaMA, QWen) on various datasets spanning the three domains of tasks. Our findings reveal that models could efficiently conduct probing for simpler tasks in shallow layers, and more complex tasks typically necessitate deeper layers for accurate understanding. Additionally, we examine how external factors, such as adding noise to the input and quantizing the model weights, might affect layer-wise representations. Our findings suggest that these factors can impede the development of a conceptual understanding of LLMs until deeper layers are explored. We hope that our proposed concept and experimental insights will enhance the understanding of the mechanisms underlying LLMs. Our codes are available at https://github.com/Luckfort/CD.

Previous work has showcased the intriguing capability of large language models (LLMs) in retrieving facts and processing context knowledge. However, only limited research exists on the layer-wise capability of LLMs to encode knowledge, which challenges our understanding of their internal mechanisms. In this paper, we devote the first attempt to investigate the layer-wise capability of LLMs through probing tasks. We leverage the powerful generative capability of ChatGPT to construct probing datasets, providing diverse and coherent evidence corresponding to various facts. We employ mathcal V-usable information as the validation metric to better reflect the capability in encoding context knowledge across different layers. Our experiments on conflicting and newly acquired knowledge show that LLMs: (1) prefer to encode more context knowledge in the upper layers; (2) primarily encode context knowledge within knowledge-related entity tokens at lower layers while progressively expanding more knowledge within other tokens at upper layers; and (3) gradually forget the earlier context knowledge retained within the intermediate layers when provided with irrelevant evidence. Code is publicly available at https://github.com/Jometeorie/probing_llama.

Traditional model merging methods for multi-task learning (MTL) address task conflicts with straightforward strategies such as weight averaging, sign consensus, or minimal test-time adjustments. This presumably counts on the assumption that a merged encoder still retains abundant task knowledge from individual encoders, implying that its shared representation is sufficiently general across tasks. However, our insight is that adding just a single trainable task-specific layer further can bring striking performance gains, as demonstrated by our pilot study. Motivated by this finding, we propose Model Tinting, a new test-time approach that introduces a single task-specific layer for each task as trainable adjustments. Our method jointly trains merging coefficients and task-specific layers, which effectively reduces task conflicts with minimal additional costs. Additionally, we propose a sampling method that utilizes the difference in confidence levels of both merged and individual encoders. Extensive experiments demonstrate our method's effectiveness, which achieves state-of-the-art performance across both computer vision and natural language processing tasks and significantly surpasses prior works. Our code is available at https://github.com/AIM-SKKU/ModelTinting.

We present a training-free framework for style-personalized image generation that controls content and style information during inference using a scale-wise autoregressive model. Our method employs a three-path design--content, style, and generation--each guided by a corresponding text prompt, enabling flexible and efficient control over image semantics without any additional training. A central contribution of this work is a step-wise and attention-wise intervention analysis. Through systematic prompt and feature injection, we find that early-to-middle generation steps play a pivotal role in shaping both content and style, and that query features predominantly encode content-specific information. Guided by these insights, we introduce two targeted mechanisms: Key Stage Attention Sharing, which aligns content and style during the semantically critical steps, and Adaptive Query Sharing, which reinforces content semantics in later steps through similarity-aware query blending. Extensive experiments demonstrate that our method achieves competitive style fidelity and prompt fidelity compared to fine-tuned baselines, while offering faster inference and greater deployment flexibility.

Despite the strong performance of large audio language models (LALMs) in various tasks, exactly how and where they integrate acoustic features with textual context remains unclear. We adapt causal tracing to investigate the internal information flow of LALMs during audio comprehension. By conducting layer-wise and token-wise analyses across DeSTA, Qwen, and Voxtral, we evaluate the causal effects of individual hidden states. Layer-wise analysis identifies different fusion strategies, from progressive integration in DeSTA to abrupt late-stage fusion in Qwen. Token-wise analysis shows that the final sequence token acts as an informational bottleneck where the network decisively retrieves relevant information from the audio. We also observe an attention-like query mechanism at intermediate token positions that triggers the model to pull task-relevant audio context. These findings provide a clear characterization of when and where multi-modal integration occurs within LALMs.

Recent progress in multimodal generation has increasingly combined autoregressive (AR) and diffusion-based approaches, leveraging their complementary strengths: AR models capture long-range dependencies and produce fluent, context-aware outputs, while diffusion models operate in continuous latent spaces to refine high-fidelity visual details. However, existing hybrids often lack systematic guidance on how and why to allocate model capacity between these paradigms. In this work, we introduce MADFormer, a Mixed Autoregressive and Diffusion Transformer that serves as a testbed for analyzing AR-diffusion trade-offs. MADFormer partitions image generation into spatial blocks, using AR layers for one-pass global conditioning across blocks and diffusion layers for iterative local refinement within each block. Through controlled experiments on FFHQ-1024 and ImageNet, we identify two key insights: (1) block-wise partitioning significantly improves performance on high-resolution images, and (2) vertically mixing AR and diffusion layers yields better quality-efficiency balances--improving FID by up to 75% under constrained inference compute. Our findings offer practical design principles for future hybrid generative models.

Most of the recent works on probing representations have focused on BERT, with the presumption that the findings might be similar to the other models. In this work, we extend the probing studies to two other models in the family, namely ELECTRA and XLNet, showing that variations in the pre-training objectives or architectural choices can result in different behaviors in encoding linguistic information in the representations. Most notably, we observe that ELECTRA tends to encode linguistic knowledge in the deeper layers, whereas XLNet instead concentrates that in the earlier layers. Also, the former model undergoes a slight change during fine-tuning, whereas the latter experiences significant adjustments. Moreover, we show that drawing conclusions based on the weight mixing evaluation strategy -- which is widely used in the context of layer-wise probing -- can be misleading given the norm disparity of the representations across different layers. Instead, we adopt an alternative information-theoretic probing with minimum description length, which has recently been proven to provide more reliable and informative results.

From extracting features to generating text, the outputs of large language models (LLMs) typically rely on their final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that intermediate layers can encode even richer representations, often improving performance on a wide range of downstream tasks. To explain and quantify these hidden-layer properties, we propose a unified framework of representation quality metrics based on information theory, geometry, and invariance to input perturbations. Our framework highlights how each model layer balances information compression and signal preservation, revealing why mid-depth embeddings can exceed the last layer's performance. Through extensive experiments on 32 text-embedding tasks and comparisons across model architectures (transformers, state-space models) and domains (language, vision), we demonstrate that intermediate layers consistently provide stronger features. These findings challenge the standard focus on final-layer embeddings and open new directions for model analysis and optimization, including strategic use of mid-layer representations for more robust and accurate AI systems.

Self-supervised geospatial foundation models (GeoFMs) learn transferable representations from remote sensing data, but their downstream behavior is difficult to characterize. We study six representative GeoFMs spanning joint-embedding, reconstruction, and multimodal pretraining families, and evaluate transfer across classification, regression, and segmentation benchmarks under different label availability and downstream pipelines. We find that model rankings change across tasks and adaptation settings. Layerwise probing shows that, in most cases, task-relevant information is more accessible in intermediate transformer blocks compared to final-layer embeddings, and that GeoFMs exhibit distinct depthwise profiles. In segmentation case studies on PASTIS and Sen1Floods11, downstream adaptation settings such as decoder design and fine-tuning can be as impactful as the choice of GeoFM, and standard dense-prediction heads may be poorly aligned with how GeoFMs organize information over depth. Finally, CKA analysis on case studies shows that fine-tuning does not rewrite GeoFMs uniformly across depth, and the strongest changes are localized to the first linear layer of the MLP in ViT blocks. These results help explain why GeoFM rankings shift across benchmarks and motivate more representation-aware evaluation and adaptation strategies.

Language models (LMs) require robust episodic grounding-the capacity to learn from and apply past experiences-to excel at physical planning tasks. Current episodic grounding approaches struggle with scalability and integration, limiting their effectiveness, especially for medium-sized LMs (7B parameters). While larger LMs (70-405B parameters) possess superior hierarchical representations and extensive pre-trained knowledge, they encounter a fundamental scale paradox: despite their advanced abstraction capabilities, they lack efficient mechanisms to leverage experience streams. We propose a scalable weak-to-strong episodic learning framework that effectively transfers episodic behaviors from smaller to larger LMs. This framework integrates Monte Carlo tree search for structured experience collection with a novel distillation method, preserving the inherent LM capabilities while embedding episodic memory. Experiments demonstrate our method surpasses state-of-the-art proprietary LMs by 3.45% across diverse planning and question-answering tasks. Layer-wise probing further indicates significant improvements in task alignment, especially within deeper LM layers, highlighting stable generalization even for previously unseen scenarios with increased planning complexity-conditions where baseline methods degrade markedly.

The development of effective explainability tools for Transformers is a crucial pursuit in deep learning research. One of the most promising approaches in this domain is Layer-wise Relevance Propagation (LRP), which propagates relevance scores backward through the network to the input space by redistributing activation values based on predefined rules. However, existing LRP-based methods for Transformer explainability entirely overlook a critical component of the Transformer architecture: its positional encoding (PE), resulting in violation of the conservation property, and the loss of an important and unique type of relevance, which is also associated with structural and positional features. To address this limitation, we reformulate the input space for Transformer explainability as a set of position-token pairs. This allows us to propose specialized theoretically-grounded LRP rules designed to propagate attributions across various positional encoding methods, including Rotary, Learnable, and Absolute PE. Extensive experiments with both fine-tuned classifiers and zero-shot foundation models, such as LLaMA 3, demonstrate that our method significantly outperforms the state-of-the-art in both vision and NLP explainability tasks. Our code is publicly available.

Embeddings have become a pivotal means to represent complex, multi-faceted information about entities, concepts, and relationships in a condensed and useful format. Nevertheless, they often preclude direct interpretation. While downstream tasks make use of these compressed representations, meaningful interpretation usually requires visualization using dimensionality reduction or specialized machine learning interpretability methods. This paper addresses the challenge of making such embeddings more interpretable and broadly useful, by employing Large Language Models (LLMs) to directly interact with embeddings -- transforming abstract vectors into understandable narratives. By injecting embeddings into LLMs, we enable querying and exploration of complex embedding data. We demonstrate our approach on a variety of diverse tasks, including: enhancing concept activation vectors (CAVs), communicating novel embedded entities, and decoding user preferences in recommender systems. Our work couples the immense information potential of embeddings with the interpretative power of LLMs.

We present a systematic investigation of layer-wise BERT activations for general-purpose text representations to understand what linguistic information they capture and how transferable they are across different tasks. Sentence-level embeddings are evaluated against two state-of-the-art models on downstream and probing tasks from SentEval, while passage-level embeddings are evaluated on four question-answering (QA) datasets under a learning-to-rank problem setting. Embeddings from the pre-trained BERT model perform poorly in semantic similarity and sentence surface information probing tasks. Fine-tuning BERT on natural language inference data greatly improves the quality of the embeddings. Combining embeddings from different BERT layers can further boost performance. BERT embeddings outperform BM25 baseline significantly on factoid QA datasets at the passage level, but fail to perform better than BM25 on non-factoid datasets. For all QA datasets, there is a gap between embedding-based method and in-domain fine-tuned BERT (we report new state-of-the-art results on two datasets), which suggests deep interactions between question and answer pairs are critical for those hard tasks.

Visual document retrieval has become essential for accessing information in visually rich documents. Existing approaches fall into two camps. Late-interaction retrievers achieve strong quality through fine-grained token-level matching but store hundreds of vectors per page, incurring large index footprints and high serving costs. By contrast, dense single-vector retrievers retain storage and latency advantages but consistently lag in quality because they compress all information into a single final-layer embedding. In this work, we first conduct a layerwise diagnostic on single-vector retrievers, revealing that retrieval-relevant signal resides in internal representations. Motivated by these findings, we propose MINER (Mining Multimodal Internal RepreseNtation for Efficient Retrieval), a lightweight plug-in module that probes and fuses internal signals across transformer layers into a single compact embedding without modifying the backbone or sacrificing single-vector efficiency. The first Retrieval-Aligned Layer Probing stage attaches a lightweight probe at each layer, surfacing which dimensions carry retrieval-relevant information. The subsequent Adaptive Sparse Multi-Layer Fusion stage applies performance-adaptive neuron-level masking to the selected layers and fuses the surviving signals into the final dense vector. Across ViDoRe V1/V2/V3, MINER outperforms existing dense single-vector retrievers on the majority of benchmarks, with up to 4.5% nDCG@5 improvement over its corresponding backbone. Compared to strong late-interaction baselines, in some settings MINER substantially narrows the nDCG@5 gap to 0.2 while preserving the storage and serving advantages of dense retrieval.

We introduce a new approach to systematically map features discovered by sparse autoencoder across consecutive layers of large language models, extending earlier work that examined inter-layer feature links. By using a data-free cosine similarity technique, we trace how specific features persist, transform, or first appear at each stage. This method yields granular flow graphs of feature evolution, enabling fine-grained interpretability and mechanistic insights into model computations. Crucially, we demonstrate how these cross-layer feature maps facilitate direct steering of model behavior by amplifying or suppressing chosen features, achieving targeted thematic control in text generation. Together, our findings highlight the utility of a causal, cross-layer interpretability framework that not only clarifies how features develop through forward passes but also provides new means for transparent manipulation of large language models.

Mechanistic interpretability aims to understand neural networks by identifying which learned features mediate specific behaviors. Attribution graphs reveal these feature pathways, but interpreting them requires extensive manual analysis -- a single prompt can take approximately 2 hours for an experienced circuit tracer. We present probe prompting, an automated pipeline that transforms attribution graphs into compact, interpretable subgraphs built from concept-aligned supernodes. Starting from a seed prompt and target logit, we select high-influence features, generate concept-targeted yet context-varying probes, and group features by cross-prompt activation signatures into Semantic, Relationship, and Say-X categories using transparent decision rules. Across five prompts including classic "capitals" circuits, probe-prompted subgraphs preserve high explanatory coverage while compressing complexity (Completeness 0.83, mean across circuits; Replacement 0.54). Compared to geometric clustering baselines, concept-aligned groups exhibit higher behavioral coherence: 2.3x higher peak-token consistency (0.425 vs 0.183) and 5.8x higher activation-pattern similarity (0.762 vs 0.130), despite lower geometric compactness. Entity-swap tests reveal a layerwise hierarchy: early-layer features transfer robustly (64% transfer rate, mean layer 6.3), while late-layer Say-X features specialize for output promotion (mean layer 16.4), supporting a backbone-and-specialization view of transformer computation. We release code (https://github.com/peppinob-ol/attribution-graph-probing), an interactive demo (https://huggingface.co/spaces/Peppinob/attribution-graph-probing), and minimal artifacts enabling immediate reproduction and community adoption.

Large language models (LLMs) can solve complex multi-step problems, but little is known about how these computations are implemented internally. Motivated by this, we study how LLMs answer multi-hop queries such as "The spouse of the performer of Imagine is". These queries require two information extraction steps: a latent one for resolving the first hop ("the performer of Imagine") into the bridge entity (John Lennon), and one for resolving the second hop ("the spouse of John Lennon") into the target entity (Yoko Ono). Understanding how the latent step is computed internally is key to understanding the overall computation. By carefully analyzing the internal computations of transformer-based LLMs, we discover that the bridge entity is resolved in the early layers of the model. Then, only after this resolution, the two-hop query is solved in the later layers. Because the second hop commences in later layers, there could be cases where these layers no longer encode the necessary knowledge for correctly predicting the answer. Motivated by this, we propose a novel "back-patching" analysis method whereby a hidden representation from a later layer is patched back to an earlier layer. We find that in up to 57% of previously incorrect cases there exists a back-patch that results in the correct generation of the answer, showing that the later layers indeed sometimes lack the needed functionality. Overall our methods and findings open further opportunities for understanding and improving latent reasoning in transformer-based LLMs.

Large language models (LLMs) demonstrate strong task-specific capabilities through fine-tuning, but merging multiple fine-tuned models often leads to degraded performance due to overlapping instruction-following components. Task Arithmetic (TA), which combines task vectors derived from fine-tuning, enables multi-task learning and task forgetting but struggles to isolate task-specific knowledge from general instruction-following behavior. To address this, we propose Layer-Aware Task Arithmetic (LATA), a novel approach that assigns layer-specific weights to task vectors based on their alignment with instruction-following or task-specific components. By amplifying task-relevant layers and attenuating instruction-following layers, LATA improves task learning and forgetting performance while preserving overall model utility. Experiments on multiple benchmarks, including WikiText-2, GSM8K, and HumanEval, demonstrate that LATA outperforms existing methods in both multi-task learning and selective task forgetting, achieving higher task accuracy and alignment with minimal degradation in output quality. Our findings highlight the importance of layer-wise analysis in disentangling task-specific and general-purpose knowledge, offering a robust framework for efficient model merging and editing.

Neural network models have a reputation for being black boxes. We propose to monitor the features at every layer of a model and measure how suitable they are for classification. We use linear classifiers, which we refer to as "probes", trained entirely independently of the model itself. This helps us better understand the roles and dynamics of the intermediate layers. We demonstrate how this can be used to develop a better intuition about models and to diagnose potential problems. We apply this technique to the popular models Inception v3 and Resnet-50. Among other things, we observe experimentally that the linear separability of features increase monotonically along the depth of the model.

Large transformers are powerful architectures used for self-supervised data analysis across various data types, including protein sequences, images, and text. In these models, the semantic structure of the dataset emerges from a sequence of transformations between one representation and the next. We characterize the geometric and statistical properties of these representations and how they change as we move through the layers. By analyzing the intrinsic dimension (ID) and neighbor composition, we find that the representations evolve similarly in transformers trained on protein language tasks and image reconstruction tasks. In the first layers, the data manifold expands, becoming high-dimensional, and then contracts significantly in the intermediate layers. In the last part of the model, the ID remains approximately constant or forms a second shallow peak. We show that the semantic information of the dataset is better expressed at the end of the first peak, and this phenomenon can be observed across many models trained on diverse datasets. Based on our findings, we point out an explicit strategy to identify, without supervision, the layers that maximize semantic content: representations at intermediate layers corresponding to a relative minimum of the ID profile are more suitable for downstream learning tasks.

Large Language Models are prone to biased predictions and hallucinations, underlining the paramount importance of understanding their model-internal reasoning process. However, achieving faithful attributions for the entirety of a black-box transformer model and maintaining computational efficiency is an unsolved challenge. By extending the Layer-wise Relevance Propagation attribution method to handle attention layers, we address these challenges effectively. While partial solutions exist, our method is the first to faithfully and holistically attribute not only input but also latent representations of transformer models with the computational efficiency similar to a singular backward pass. Through extensive evaluations against existing methods on Llama 2, Flan-T5 and the Vision Transformer architecture, we demonstrate that our proposed approach surpasses alternative methods in terms of faithfulness and enables the understanding of latent representations, opening up the door for concept-based explanations. We provide an open-source implementation on GitHub https://github.com/rachtibat/LRP-for-Transformers.

Interpretability of deep neural networks is a recently emerging area of machine learning research targeting a better understanding of how models perform feature selection and derive their classification decisions. This paper explores the interpretability of neural networks in the audio domain by using the previously proposed technique of layer-wise relevance propagation (LRP). We present a novel audio dataset of English spoken digits which we use for classification tasks on spoken digits and speaker's gender. We use LRP to identify relevant features for two neural network architectures that process either waveform or spectrogram representations of the data. Based on the relevance scores obtained from LRP, hypotheses about the neural networks' feature selection are derived and subsequently tested through systematic manipulations of the input data. The results confirm that the networks are highly reliant on features marked as relevant by LRP.

While LLMs are powerful embedding backbones, their application in training-free settings faces two structural challenges: causal attention restricts early tokens from accessing subsequent context, and the next-token prediction objective biases representations toward generation rather than semantic compression. To address these limitations, we propose KV-Embedding, a framework that activates the latent representation power of frozen LLMs. Our method leverages the observation that the key-value (KV) states of the final token at each layer encode a compressed view of the sequence. By re-routing these states as a prepended prefix, we enable all tokens to access sequence-level context within a single forward pass. To ensure model-agnostic applicability, we introduce an automated layer selection strategy based on intrinsic dimensionality. Evaluations on MTEB across Qwen, Mistral, and Llama backbones show that KV-Embedding outperforms existing training-free baselines by up to 10%, while maintaining robust performance on sequences up to 4,096 tokens. These results demonstrate that internal state manipulation offers an efficient alternative to input modification, and we hope this work encourages further exploration of LLM internals for representation learning.

Recent studies have shown that large language models (LLMs) can assess relevance and support information retrieval (IR) tasks such as document ranking and relevance judgment generation. However, the internal mechanisms by which off-the-shelf LLMs understand and operationalize relevance remain largely unexplored. In this paper, we systematically investigate how different LLM modules contribute to relevance judgment through the lens of mechanistic interpretability. Using activation patching techniques, we analyze the roles of various model components and identify a multi-stage, progressive process in generating either pointwise or pairwise relevance judgment. Specifically, LLMs first extract query and document information in the early layers, then process relevance information according to instructions in the middle layers, and finally utilize specific attention heads in the later layers to generate relevance judgments in the required format. Our findings provide insights into the mechanisms underlying relevance assessment in LLMs, offering valuable implications for future research on leveraging LLMs for IR tasks.

Understanding the inner workings of machine learning models like Transformers is vital for their safe and ethical use. This paper provides a comprehensive analysis of a one-layer Transformer model trained to perform n-digit integer addition. Our findings suggest that the model dissects the task into parallel streams dedicated to individual digits, employing varied algorithms tailored to different positions within the digits. Furthermore, we identify a rare scenario characterized by high loss, which we explain. By thoroughly elucidating the model's algorithm, we provide new insights into its functioning. These findings are validated through rigorous testing and mathematical modeling, thereby contributing to the broader fields of model understanding and interpretability. Our approach opens the door for analyzing more complex tasks and multi-layer Transformer models.

Interpretability work on the convolutional layers of CNNs has primarily focused on computer vision, but some studies also explore correspondences between the latent space and the output in the audio domain. However, it has not been thoroughly examined how acoustic and linguistic information is represented in the fully connected (FC) layer that bridges the latent space and convolutional layers. The current study presents the first exploration of how the FC layer of CNNs for speech synthesis encodes linguistically relevant information. We propose two techniques for exploration of the fully connected layer. In Experiment 1, we use weight matrices as inputs into convolutional layers. In Experiment 2, we manipulate the FC layer to explore how symbolic-like representations are encoded in CNNs. We leverage the fact that the FC layer outputs a feature map and that variable-specific weight matrices are temporally structured to (1) demonstrate how the distribution of learned weights varies between latent variables in systematic ways and (2) demonstrate how manipulating the FC layer while holding constant subsequent model parameters affects the output. We ultimately present an FC manipulation that can output a single segment. Using this technique, we show that lexically specific latent codes in generative CNNs (ciwGAN) have shared lexically invariant sublexical representations in the FC-layer weights, showing that ciwGAN encodes lexical information in a linguistically principled manner.

Applying language models to natural language processing tasks typically relies on the representations in the final model layer, as intermediate hidden layer representations are presumed to be less informative. In this work, we argue that due to the gradual improvement across model layers, additional information can be gleaned from the contrast between higher and lower layers during inference. Specifically, in choosing between the probable next token predictions of a generative model, the predictions of lower layers can be used to highlight which candidates are best avoided. We propose a novel approach that utilizes the contrast between layers to improve text generation outputs, and show that it mitigates degenerative behaviors of the model in open-ended generation, significantly improving the quality of generated texts. Furthermore, our results indicate that contrasting between model layers at inference time can yield substantial benefits to certain aspects of general language model capabilities, more effectively extracting knowledge during inference from a given set of model parameters.

Explaining why dense retrievers assign high relevance scores remains challenging because retrieval decisions are made through opaque high-dimensional embeddings. Existing explanations often focus on surface signals, such as lexical matches, token alignments, or post-hoc textual rationales, and thus provide limited insight into the latent factors that shape dense retrieval behavior at the embedding level. We propose Xetrieval, an embedding-level mechanistic framework for explaining dense retrieval. Xetrieval first introduces a lightweight reasoning internalizer that approximates Chain-of-Thought reasoning directly in the embedding space with a single forward pass, enriching sentence embeddings with reasoning-oriented information while avoiding expensive autoregressive generation. It then decomposes these reasoning-enhanced embeddings into sparse, human-interpretable features, each associated with a coherent natural language description. By aggregating sparse feature overlaps across multiple document-side views, Xetrieval provides feature-level explanations of individual retrieval decisions. Experiments on diverse retrievers and benchmarks show that Xetrieval uncovers coherent interpretable features, yields stronger pair-level intervention effects, and supports task-level feature steering. The project page and source code are available at https://hihiczx.github.io/Xetrieval .

Understanding what defines a good representation in large language models (LLMs) is fundamental to both theoretical understanding and practical applications. In this paper, we investigate the quality of intermediate representations in various LLM architectures, including Transformers and State Space Models (SSMs). We find that intermediate layers often yield more informative representations for downstream tasks than the final layers. To measure the representation quality, we adapt and apply a suite of metrics - such as prompt entropy, curvature, and augmentation-invariance - originally proposed in other contexts. Our empirical study reveals significant architectural differences, how representations evolve throughout training, and how factors like input randomness and prompt length affect each layer. Notably, we observe a bimodal pattern in the entropy of some intermediate layers and consider potential explanations tied to training data. Overall, our results illuminate the internal mechanics of LLMs and guide strategies for architectural optimization and training.

Modern LLMs are increasingly deep, and depth correlates with performance, albeit with diminishing returns. However, do these models use their depth efficiently? Do they compose more features to create higher-order computations that are impossible in shallow models, or do they merely spread the same kinds of computation out over more layers? To address these questions, we analyze the residual stream of the Llama 3.1 and Qwen 3 family of models. We find: First, comparing the output of the sublayers to the residual stream reveals that layers in the second half contribute much less than those in the first half, with a clear phase transition between the two halves. Second, skipping layers in the second half has a much smaller effect on future computations and output predictions. Third, for multihop tasks, we are unable to find evidence that models are using increased depth to compose subresults in examples involving many hops. Fourth, we seek to directly address whether deeper models are using their additional layers to perform new kinds of computation. To do this, we train linear maps from the residual stream of a shallow model to a deeper one. We find that layers with the same relative depth map best to each other, suggesting that the larger model simply spreads the same computations out over its many layers. All this evidence suggests that deeper models are not using their depth to learn new kinds of computation, but only using the greater depth to perform more fine-grained adjustments to the residual. This may help explain why increasing scale leads to diminishing returns for stacked Transformer architectures.

Although it is known that transformer language models (LMs) pass features from early layers to later layers, it is not well understood how this information is represented and routed by the model. By analyzing particular mechanism LMs use to accomplish this, we find that it is also used to recall items from a list, and show that this mechanism can explain an otherwise arbitrary-seeming sensitivity of the model to the order of items in the prompt. Specifically, we find that models write into low-rank subspaces of the residual stream to represent features which are then read out by specific later layers, forming low-rank communication channels between layers. By decomposing attention head weight matrices with the Singular Value Decomposition (SVD), we find that previously described interactions between heads separated by one or more layers can be predicted via analysis of their weight matrices. We show that it is possible to manipulate the internal model representations as well as edit model weights based on the mechanism we discover in order to significantly improve performance on our synthetic Laundry List task, which requires recall from a list, often improving task accuracy by over 20%. Our analysis reveals a surprisingly intricate interpretable structure learned from language model pretraining, and helps us understand why sophisticated LMs sometimes fail in simple domains, facilitating future analysis of more complex behaviors.

Deep classifiers are known to be sensitive to data distribution shifts, primarily due to their reliance on spurious correlations in training data. It has been suggested that these classifiers can still find useful features in the network's last layer that hold up under such shifts. In this work, we question the use of last-layer representations for out-of-distribution (OOD) generalisation and explore the utility of intermediate layers. To this end, we introduce Intermediate Layer Classifiers (ILCs). We discover that intermediate layer representations frequently offer substantially better generalisation than those from the penultimate layer. In many cases, zero-shot OOD generalisation using earlier-layer representations approaches the few-shot performance of retraining on penultimate layer representations. This is confirmed across multiple datasets, architectures, and types of distribution shifts. Our analysis suggests that intermediate layers are less sensitive to distribution shifts compared to the penultimate layer. These findings highlight the importance of understanding how information is distributed across network layers and its role in OOD generalisation, while also pointing to the limits of penultimate layer representation utility. Code is available at https://github.com/oshapio/intermediate-layer-generalization

Chain-of-thought (CoT) reasoning has enabled transformer-based language models to excel at complex mathematics and multi-step planning. However, in standard decoder-only architectures, these reasoning steps are externalized in natural language, improving interpretability at the cost of efficiency. To capture reasoning that is not easily represented in words, many works have explored recurrent architectures that aim to internalize reasoning in latent space, potentially supporting latent CoT. In this paper, we investigate whether such reasoning structures emerge in Huginn-3.5B, a depth-recurrent Transformer that reuses layers at inference time without increasing parameter count. We examine the model's internal behavior on arithmetic tasks using a suite of probing techniques including the Logit Lens and Coda Lens. Our findings reveal limited evidence of interpretable latent CoT by tracking rank trajectories of final and intermediate result tokens. Furthermore, we uncover significant probing inconsistencies across recurrent blocks, where the interpretability of hidden states depends heavily on both the layer index and the decoding method. Finally, we empirically show that increasing recurrence depth yields only marginal gains and falls well short of models that explicitly externalize reasoning steps. The code is available at https://github.com/wenquanlu/huginn-latent-cot.

Automated insight generation is a common tactic for helping knowledge workers, such as data scientists, to quickly understand the potential value of new and unfamiliar data. Unfortunately, automated insights produced by large-language models can generate code that does not correctly correspond (or align) to the insight. In this paper, we leverage the semantic knowledge of large language models to generate targeted and insightful questions about data and the corresponding code to answer those questions. Then through an empirical study on data from Open-WikiTable, we show that embeddings can be effectively used for filtering out semantically unaligned pairs of question and code. Additionally, we found that generating questions and code together yields more diverse questions.

Memory layers use a trainable key-value lookup mechanism to add extra parameters to a model without increasing FLOPs. Conceptually, sparsely activated memory layers complement compute-heavy dense feed-forward layers, providing dedicated capacity to store and retrieve information cheaply. This work takes memory layers beyond proof-of-concept, proving their utility at contemporary scale. On downstream tasks, language models augmented with our improved memory layer outperform dense models with more than twice the computation budget, as well as mixture-of-expert models when matched for both compute and parameters. We find gains are especially pronounced for factual tasks. We provide a fully parallelizable memory layer implementation, demonstrating scaling laws with up to 128B memory parameters, pretrained to 1 trillion tokens, comparing to base models with up to 8B parameters.

Large language models(LLMs) excel at text generation and knowledge question-answering tasks, but they are prone to generating hallucinated content, severely limiting their application in high-risk domains. Current hallucination detection methods based on uncertainty estimation and external knowledge retrieval suffer from the limitation that they still produce erroneous content at high confidence levels and rely heavily on retrieval efficiency and knowledge coverage. In contrast, probe methods that leverage the model's hidden-layer states offer real-time and lightweight advantages. However, traditional linear probes struggle to capture nonlinear structures in deep semantic spaces.To overcome these limitations, we propose a neural network-based framework for token-level hallucination detection. By freezing language model parameters, we employ lightweight MLP probes to perform nonlinear modeling of high-level hidden states. A multi-objective joint loss function is designed to enhance detection stability and semantic disambiguity. Additionally, we establish a layer position-probe performance response model, using Bayesian optimization to automatically search for optimal probe insertion layers and achieve superior training results.Experimental results on LongFact, HealthBench, and TriviaQA demonstrate that MLP probes significantly outperform state-of-the-art methods in accuracy, recall, and detection capability under low false-positive conditions.

With the increasing numbers of publicly available models, there are probably pretrained, online models for most tasks users require. However, current model search methods are rudimentary, essentially a text-based search in the documentation, thus users cannot find the relevant models. This paper presents ProbeLog, a method for retrieving classification models that can recognize a target concept, such as "Dog", without access to model metadata or training data. Differently from previous probing methods, ProbeLog computes a descriptor for each output dimension (logit) of each model, by observing its responses on a fixed set of inputs (probes). Our method supports both logit-based retrieval ("find more logits like this") and zero-shot, text-based retrieval ("find all logits corresponding to dogs"). As probing-based representations require multiple costly feedforward passes through the model, we develop a method, based on collaborative filtering, that reduces the cost of encoding repositories by 3x. We demonstrate that ProbeLog achieves high retrieval accuracy, both in real-world and fine-grained search tasks and is scalable to full-size repositories.

Large Language Models (LLMs) have demonstrated promising capabilities to generate responses that exhibit consistent personality traits. Despite the major attempts to analyze personality expression through output-based evaluations, little is known about how such traits are internally encoded within LLM parameters. In this paper, we introduce a layer-wise probing framework to systematically investigate the layer-wise capability of LLMs in encoding personality for responding. We conduct probing experiments on 11 open-source LLMs over the PersonalityEdit benchmark and find that LLMs predominantly encode personality for responding in their middle and upper layers, with instruction-tuned models demonstrating a slightly clearer separation of personality traits. Furthermore, by interpreting the trained probing hyperplane as a layer-wise boundary for each personality category, we propose a layer-wise perturbation method to edit the personality expressed by LLMs during inference. Our results show that even when the prompt explicitly specifies a particular personality, our method can still successfully alter the response personality of LLMs. Interestingly, the difficulty of converting between certain personality traits varies substantially, which aligns with the representational distances in our probing experiments. Finally, we conduct a comprehensive MMLU benchmark evaluation and time overhead analysis, demonstrating that our proposed personality editing method incurs only minimal degradation in general capabilities while maintaining low training costs and acceptable inference latency. Our code is publicly available at https://github.com/universe-sky/probing-then-editing-personality.

Recent work has shown that directly fine-tuning large language models (LLMs) for dense retrieval yields strong performance, but their substantial parameter counts make them computationally inefficient. While prior studies have revealed significant layer redundancy in LLMs for generative tasks, it remains unclear whether similar redundancy exists when these models are adapted for retrieval tasks, which require encoding entire sequences into fixed representations rather than generating tokens iteratively. To this end, we conduct a comprehensive analysis of layer redundancy in LLM-based dense retrievers. We find that, in contrast to generative settings, MLP layers are substantially more prunable, while attention layers remain critical for semantic aggregation. Building on this insight, we propose EffiR, a framework for developing efficient retrievers that performs large-scale MLP compression through a coarse-to-fine strategy (coarse-grained depth reduction followed by fine-grained width reduction), combined with retrieval-specific fine-tuning. Across diverse BEIR datasets and LLM backbones, EffiR achieves substantial reductions in model size and inference cost while preserving the performance of full-size models.

Deep learning sometimes appears to work in unexpected ways. In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network consisting of a sequence of first-order approximations telescoping out into a single empirically operational tool for practical analysis. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena in the literature -- including double descent, grokking, linear mode connectivity, and the challenges of applying deep learning on tabular data -- highlighting that this model allows us to construct and extract metrics that help predict and understand the a priori unexpected performance of neural networks. We also demonstrate that this model presents a pedagogical formalism allowing us to isolate components of the training process even in complex contemporary settings, providing a lens to reason about the effects of design choices such as architecture & optimization strategy, and reveals surprising parallels between neural network learning and gradient boosting.

Recent advances in large language models have led to specialized models excelling in specific domains, creating a need for efficient model merging techniques. While traditional merging approaches combine parameters into a single static model, they often compromise task-specific performance. However, task-specific routing methods maintain accuracy but introduce substantial storage overhead. We present 1bit-Merging, a novel framework that integrates task-specific routing with 1-bit quantized task vectors to balance performance and storage efficiency. Our approach leverages the observation that different task-specific models store knowledge in distinct layers-chat models primarily in attention layers and math/code models in MLP layers-enabling targeted compression strategies. Through extensive experiments with LLaMA2 and Mistral model families across chat, mathematical reasoning, and code generation tasks, we demonstrate that 1bit-Merging achieves comparable or superior performance to existing methods while significantly reducing storage requirements. Our framework offers a practical solution for combining specialized models while maintaining their individual strengths and addressing the storage challenges of current approaches.

This paper presents an in-depth analysis of Large Language Models (LLMs), focusing on LLaMA, a prominent open-source foundational model in natural language processing. Instead of assessing LLaMA through its generative output, we design multiple-choice tasks to probe its intrinsic understanding in high-order tasks such as reasoning and computation. We examine the model horizontally, comparing different sizes, and vertically, assessing different layers. We unveil several key and uncommon findings based on the designed probing tasks: (1) Horizontally, enlarging model sizes almost could not automatically impart additional knowledge or computational prowess. Instead, it can enhance reasoning abilities, especially in math problem solving, and helps reduce hallucinations, but only beyond certain size thresholds; (2) In vertical analysis, the lower layers of LLaMA lack substantial arithmetic and factual knowledge, showcasing logical thinking, multilingual and recognitive abilities, with top layers housing most computational power and real-world knowledge.

The integration of audio perception capabilities into Large Language Models (LLMs) has enabled significant advances in Audio-LLMs. Although application-focused developments, particularly in curating training data for specific capabilities e.g., audio reasoning, have progressed rapidly, the underlying mechanisms that govern efficient transfer of rich semantic representations from audio encoders to LLMs remain under-explored. We conceptualize effective audio-LLM interaction as the LLM's ability to proficiently probe the audio encoder representations to satisfy textual queries. This paper presents a systematic investigation on how architectural design choices can affect that. Beginning with a standard Pengi/LLaVA-style audio-LLM architecture, we propose and evaluate several modifications guided by hypotheses derived from mechanistic interpretability studies and LLM operational principles. Our experiments demonstrate that: (1) delaying audio integration until the LLM's initial layers establish textual context that enhances its ability to probe the audio representations for relevant information; (2) the LLM can proficiently probe audio representations exclusively through LLM layer's attention submodule, without requiring propagation to its Feed-Forward Network (FFN) submodule; (3) an efficiently integrated ensemble of diverse audio encoders provides richer, complementary representations, thereby broadening the LLM's capacity to probe a wider spectrum of audio information. All hypotheses are evaluated using an identical three-stage training curriculum on a dataset of 5.6 million audio-text pairs, ensuring controlled comparisons. Our final architecture, which incorporates all proposed modifications, achieves relative improvements from 10\% to 60\% over the baseline, validating our approach to optimizing cross-modal information transfer in audio-LLMs. Project page: https://ta012.github.io/PAL/

In this article, we use probing to investigate phenomena that occur during fine-tuning and knowledge distillation of a BERT-based natural language understanding (NLU) model. Our ultimate purpose was to use probing to better understand practical production problems and consequently to build better NLU models. We designed experiments to see how fine-tuning changes the linguistic capabilities of BERT, what the optimal size of the fine-tuning dataset is, and what amount of information is contained in a distilled NLU based on a tiny Transformer. The results of the experiments show that the probing paradigm in its current form is not well suited to answer such questions. Structural, Edge and Conditional probes do not take into account how easy it is to decode probed information. Consequently, we conclude that quantification of information decodability is critical for many practical applications of the probing paradigm.

Despite their capabilities, Large Language Models (LLMs) remain opaque with limited understanding of their internal representations. Current interpretability methods, such as direct logit attribution (DLA) and sparse autoencoders (SAEs), provide restricted insight due to limitations such as the model's output vocabulary or unclear feature names. This work introduces Hyperdimensional Probe, a novel paradigm for decoding information from the LLM vector space. It combines ideas from symbolic representations and neural probing to project the model's residual stream into interpretable concepts via Vector Symbolic Architectures (VSAs). This probe combines the strengths of SAEs and conventional probes while overcoming their key limitations. We validate our decoding paradigm with controlled input-completion tasks, probing the model's final state before next-token prediction on inputs spanning syntactic pattern recognition, key-value associations, and abstract inference. We further assess it in a question-answering setting, examining the state of the model both before and after text generation. Our experiments show that our probe reliably extracts meaningful concepts across varied LLMs, embedding sizes, and input domains, also helping identify LLM failures. Our work advances information decoding in LLM vector space, enabling extracting more informative, interpretable, and structured features from neural representations.

When a language model is fed a wrong answer, what happens inside the network? Current understanding treats truthfulness as a static property of individual-layer representations-a direction to be probed, a feature to be extracted. Less is known about the dynamics: how internal representations diverge across the full depth of the network when the model processes correct versus incorrect continuations. We introduce forced-completion probing, a method that presents identical queries with known correct and incorrect single-token continuations and tracks five geometric measurements across every layer of four decoder-only models(1.5B-13B parameters). We report three findings. First, correct and incorrect paths diverge through rotation, not rescaling: displacement vectors maintain near-identical magnitudes while their angular separation increases, meaning factual selection is encoded in direction on an approximate hypersphere. Second, the model does not passively fail on incorrect input-it actively suppresses the correct answer, driving internal probability away from the right token. Third, both phenomena are entirely absent below a parameter threshold and emerge at 1.6B, suggesting a phase transition in factual processing capability. These results show that factual constraint processing has a specific geometric character-rotational, not scalar; active, not passive-that is invisible to methods based on single-layer probes or magnitude comparisons.

Decoder-only transformers have become the standard architecture for large language models (LLMs) due to their strong performance. Recent studies suggest that, in pre-trained LLMs, early, middle, and late layers may serve distinct roles: Early layers focus on understanding the input context, middle layers handle task-specific processing, and late layers convert abstract representations into output tokens. We hypothesize that once representations have been processed by the early and middle layers, the resulting hidden states may encapsulate sufficient information to support the generation of multiple tokens using only the late layers, eliminating the need to repeatedly traverse the early and middle layers. We refer to this inference paradigm as Direct Multi-Token Decoding (DMTD). Unlike speculative decoding, our method introduces no additional parameters, auxiliary routines, or post-generation verification. Despite being trained on a limited dataset, a fine-tuned DMTD Qwen3-4B model has already demonstrated promising results, achieving up to a 2x speedup with only minor performance loss. Moreover, as shown in our scaling analysis, its performance is expected to further improve with larger training datasets.

We demonstrate and investigate the remarkable robustness of Large Language Models by deleting and swapping adjacent layers. We find that deleting and swapping interventions retain 72-95\% of the original model's prediction accuracy without fine-tuning, whereas models with more layers exhibit more robustness. Based on the results of the layer-wise intervention and further experiments, we hypothesize the existence of four universal stages of inference across eight different models: detokenization, feature engineering, prediction ensembling, and residual sharpening. The first stage integrates local information, lifting raw token representations into higher-level contextual representations. Next is the iterative refinement of task and entity-specific features. Then, the second half of the model begins with a phase transition, where hidden representations align more with the vocabulary space due to specialized model components. Finally, the last layer sharpens the following token distribution by eliminating obsolete features that add noise to the prediction.

Vector embeddings derived from large language models (LLMs) show promise in capturing latent information from the literature. Interestingly, these can be integrated into material embeddings, potentially useful for data-driven predictions of materials properties. We investigate the extent to which LLM-derived vectors capture the desired information and their potential to provide insights into material properties without additional training. Our findings indicate that, although LLMs can be used to generate representations reflecting certain property information, extracting the embeddings requires identifying the optimal contextual clues and appropriate comparators. Despite this restriction, it appears that LLMs still have the potential to be useful in generating meaningful materials-science representations.

Large Language Models (LLMs) show strong generalization across diverse tasks, yet the internal decision-making processes behind their predictions remain opaque. In this work, we study the geometry of hidden representations in LLMs through the lens of intrinsic dimension (ID), focusing specifically on decision-making dynamics in a multiple-choice question answering (MCQA) setting. We perform a large-scale study, with 28 open-weight transformer models and estimate ID across layers using multiple estimators, while also quantifying per-layer performance on MCQA tasks. Our findings reveal a consistent ID pattern across models: early layers operate on low-dimensional manifolds, middle layers expand this space, and later layers compress it again, converging to decision-relevant representations. Together, these results suggest LLMs implicitly learn to project linguistic inputs onto structured, low-dimensional manifolds aligned with task-specific decisions, providing new geometric insights into how generalization and reasoning emerge in language models.

Recent studies have observed that intermediate layers of foundation models often yield more discriminative representations than the final layer. While initially attributed to autoregressive pretraining, this phenomenon has also been identified in models trained via supervised and discriminative self-supervised objectives. In this paper, we conduct a comprehensive study to analyze the behavior of intermediate layers in pretrained vision transformers. Through extensive linear probing experiments across a diverse set of image classification benchmarks, we find that distribution shift between pretraining and downstream data is the primary cause of performance degradation in deeper layers. Furthermore, we perform a fine-grained analysis at the module level. Our findings reveal that standard probing of transformer block outputs is suboptimal; instead, probing the activation within the feedforward network yields the best performance under significant distribution shift, whereas the normalized output of the multi-head self-attention module is optimal when the shift is weak.

Representing and navigating hierarchy is a fundamental primitive of reasoning. Large language models have demonstrated proficiency in a wide variety of tasks requiring hierarchical reasoning, but there exists limited analysis on how the models geometrically represent the necessary latent constructions for such thinking. To this end, we develop H-probes, a collection of linear probes that extract hierarchical structure, specifically depth and pairwise distance, from latent representations. In synthetic tree traversal tasks, the H-probes robustly find the subspaces containing hierarchical structure necessary to complete the tasks; furthermore, in comprehensive ablation experiments, we show that these hierarchy-containing subspaces are low-dimensional, causally important for high task performance, and generalize within- and out-of-domain. Furthermore, we find analogous, though weaker, hierarchical structure in real-world hierarchical contexts such as mathematical reasoning traces. These results demonstrate that models represent hierarchy not only at the level of syntax and concepts, but at deeper levels of abstraction -- including the reasoning process itself.

Feed-forward layers constitute two-thirds of a transformer model's parameters, yet their role in the network remains under-explored. We show that feed-forward layers in transformer-based language models operate as key-value memories, where each key correlates with textual patterns in the training examples, and each value induces a distribution over the output vocabulary. Our experiments show that the learned patterns are human-interpretable, and that lower layers tend to capture shallow patterns, while upper layers learn more semantic ones. The values complement the keys' input patterns by inducing output distributions that concentrate probability mass on tokens likely to appear immediately after each pattern, particularly in the upper layers. Finally, we demonstrate that the output of a feed-forward layer is a composition of its memories, which is subsequently refined throughout the model's layers via residual connections to produce the final output distribution.

We present LayerSkip, an end-to-end solution to speed-up inference of large language models (LLMs). First, during training we apply layer dropout, with low dropout rates for earlier layers and higher dropout rates for later layers, and an early exit loss where all transformer layers share the same exit. Second, during inference, we show that this training recipe increases the accuracy of early exit at earlier layers, without adding any auxiliary layers or modules to the model. Third, we present a novel self-speculative decoding solution where we exit at early layers and verify and correct with remaining layers of the model. Our proposed self-speculative decoding approach has less memory footprint than other speculative decoding approaches and benefits from shared compute and activations of the draft and verification stages. We run experiments on different Llama model sizes on different types of training: pretraining from scratch, continual pretraining, finetuning on specific data domain, and finetuning on specific task. We implement our inference solution and show speedups of up to 2.16x on summarization for CNN/DM documents, 1.82x on coding, and 2.0x on TOPv2 semantic parsing task. We open source our code and checkpoints at https://github.com/facebookresearch/LayerSkip.

Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, especially when guided by explicit chain-of-thought (CoT) reasoning that verbalizes intermediate steps. While CoT improves both interpretability and accuracy, its dependence on natural language reasoning limits the model's expressive bandwidth. Latent reasoning tackles this bottleneck by performing multi-step inference entirely in the model's continuous hidden state, eliminating token-level supervision. To advance latent reasoning research, this survey provides a comprehensive overview of the emerging field of latent reasoning. We begin by examining the foundational role of neural network layers as the computational substrate for reasoning, highlighting how hierarchical representations support complex transformations. Next, we explore diverse latent reasoning methodologies, including activation-based recurrence, hidden state propagation, and fine-tuning strategies that compress or internalize explicit reasoning traces. Finally, we discuss advanced paradigms such as infinite-depth latent reasoning via masked diffusion models, which enable globally consistent and reversible reasoning processes. By unifying these perspectives, we aim to clarify the conceptual landscape of latent reasoning and chart future directions for research at the frontier of LLM cognition. An associated GitHub repository collecting the latest papers and repos is available at: https://github.com/multimodal-art-projection/LatentCoT-Horizon/.

Large Language Models (LLMs) often exhibit a gap between their internal knowledge and their explicit linguistic outputs. In this report, we empirically investigate whether Looped Transformers (LTs)--architectures that increase computational depth by iterating shared layers--can bridge this gap by utilizing their iterative nature as a form of introspection. Our experiments reveal that while increasing loop iterations narrows the gap, it is partly driven by a degradation of their internal knowledge carried by representations. Moreover, another empirical analysis suggests that current LTs' ability to perceive representations does not improve across loops; it is only present in the final loop. These results suggest that while LTs offer a promising direction for scaling computational depth, they have yet to achieve the introspection required to truly link representation space and natural language.

This work examines whether activating latent subspaces in language models (LLMs) can steer scientific code generation toward a specific programming language. Five causal LLMs were first evaluated on scientific coding prompts to quantify their baseline bias among four programming languages. A static neuron-attribution method, perturbing the highest activated MLP weight for a C++ or CPP token, proved brittle and exhibited limited generalization across prompt styles and model scales. To address these limitations, a gradient-refined adaptive activation steering framework (G-ACT) was developed: per-prompt activation differences are clustered into a small set of steering directions, and lightweight per-layer probes are trained and refined online to select the appropriate steering vector. In LLaMA-3.2 3B, this approach reliably biases generation towards the CPP language by increasing the average probe classification accuracy by 15% and the early layers (0-6) improving the probe classification accuracy by 61.5% compared to the standard ACT framework. For LLaMA-3.3 70B, where attention-head signals become more diffuse, targeted injections at key layers still improve language selection. Although per-layer probing introduces a modest inference overhead, it remains practical by steering only a subset of layers and enables reproducible model behavior. These results demonstrate a scalable, interpretable and efficient mechanism for concept-level control for practical agentic systems.

We demonstrate that LLMs may learn indicators of document usefulness and modulate their updates accordingly. We introduce random strings ("tags") as indicators of usefulness in a synthetic fine-tuning dataset. Fine-tuning on this dataset leads to implicit meta-learning (IML): in further fine-tuning, the model updates to make more use of text that is tagged as useful. We perform a thorough empirical investigation of this phenomenon, finding (among other things) that (i) it occurs in both pretrained LLMs and those trained from scratch, as well as on a vision task, and (ii) larger models and smaller batch sizes tend to give more IML. We also use probing to examine how IML changes the way models store knowledge in their parameters. Finally, we reflect on what our results might imply about capabilities, risks, and controllability of future AI systems. Our code can be found at https://github.com/krasheninnikov/internalization.

The rapid development of Artificial Intelligence (AI) has revolutionized numerous fields, with large language models (LLMs) and computer vision (CV) systems driving advancements in natural language understanding and visual processing, respectively. The convergence of these technologies has catalyzed the rise of multimodal AI, enabling richer, cross-modal understanding that spans text, vision, audio, and video modalities. Multimodal large language models (MLLMs), in particular, have emerged as a powerful framework, demonstrating impressive capabilities in tasks like image-text generation, visual question answering, and cross-modal retrieval. Despite these advancements, the complexity and scale of MLLMs introduce significant challenges in interpretability and explainability, essential for establishing transparency, trustworthiness, and reliability in high-stakes applications. This paper provides a comprehensive survey on the interpretability and explainability of MLLMs, proposing a novel framework that categorizes existing research across three perspectives: (I) Data, (II) Model, (III) Training \& Inference. We systematically analyze interpretability from token-level to embedding-level representations, assess approaches related to both architecture analysis and design, and explore training and inference strategies that enhance transparency. By comparing various methodologies, we identify their strengths and limitations and propose future research directions to address unresolved challenges in multimodal explainability. This survey offers a foundational resource for advancing interpretability and transparency in MLLMs, guiding researchers and practitioners toward developing more accountable and robust multimodal AI systems.

To discover the weaknesses of LLMs, researchers often embed prompts into a vector space and cluster them to extract insightful patterns. However, vector embeddings primarily capture topical similarity. As a result, prompts that share a topic but differ in specificity, and consequently in difficulty, are often represented similarly, making fine-grained weakness analysis difficult. To address this limitation, we propose PROMPT2BOX, which embeds prompts into a box embedding space using a trained encoder. The encoder, trained on existing and synthesized datasets, outputs box embeddings that capture not only semantic similarity but also specificity relations between prompts (e.g., "writing an adventure story" is more specific than "writing a story"). We further develop a novel dimension reduction technique for box embeddings to facilitate dataset visualization and comparison. Our experiments demonstrate that box embeddings consistently capture prompt specificity better than vector baselines. On the downstream task of creating hierarchical clustering trees for 17 LLMs from the UltraFeedback dataset, PROMPT2BOX can identify 8.9\% more LLM weaknesses than vector baselines and achieves an approximately 33\% stronger correlation between hierarchical depth and instruction specificity.

Deep neural networks are a promising tool for Audio Event Classification. In contrast to other data like natural images, there are many sensible and non-obvious representations for audio data, which could serve as input to these models. Due to their black-box nature, the effect of different input representations has so far mostly been investigated by measuring classification performance. In this work, we leverage eXplainable AI (XAI), to understand the underlying classification strategies of models trained on different input representations. Specifically, we compare two model architectures with regard to relevant input features used for Audio Event Detection: one directly processes the signal as the raw waveform, and the other takes in its time-frequency spectrogram representation. We show how relevance heatmaps obtained via "Siren"{Layer-wise Relevance Propagation} uncover representation-dependent decision strategies. With these insights, we can make a well-informed decision about the best input representation in terms of robustness and representativity and confirm that the model's classification strategies align with human requirements.

Can large language models introspect, that is, accurately detect perturbations to their own internal states? We systematically investigate this question using activation steering in Meta-Llama-3.1-8B-Instruct. First, we show that the binary detection paradigm used in prior work conflates introspection with a methodological artifact: apparent detection accuracy is entirely explained by global logit shifts that bias models toward affirmative responses regardless of question content. However, on tasks requiring differential sensitivity, we find robust evidence for partial introspection: models localize which of 10 sentences received an injection at up to 88\% accuracy (vs.\ 10\% chance) and discriminate relative injection strengths at 83\% accuracy (vs.\ 50\% chance). These capabilities are confined to early-layer injections and collapse to chance thereafter -- a pattern we explain mechanistically through attention-based signal routing and residual stream recovery dynamics. Our findings demonstrate that LLMs can compute meaningful functions over perturbations to their internal states, establishing introspection as a real but layer-dependent phenomenon that merits further investigation. Our code is open-sourced here: https://github.com/elyhahami18/llama-introspection-new

This paper studies the emergence of interpretable categorical features within large language models (LLMs), analyzing their behavior across training checkpoints (time), transformer layers (space), and varying model sizes (scale). Using sparse autoencoders for mechanistic interpretability, we identify when and where specific semantic concepts emerge within neural activations. Results indicate clear temporal and scale-specific thresholds for feature emergence across multiple domains. Notably, spatial analysis reveals unexpected semantic reactivation, with early-layer features re-emerging at later layers, challenging standard assumptions about representational dynamics in transformer models.

In recent years, many interpretability methods have been proposed to help interpret the internal states of Transformer-models, at different levels of precision and complexity. Here, to analyze encoder-decoder Transformers, we propose a simple, new method: DecoderLens. Inspired by the LogitLens (for decoder-only Transformers), this method involves allowing the decoder to cross-attend representations of intermediate encoder layers instead of using the final encoder output, as is normally done in encoder-decoder models. The method thus maps previously uninterpretable vector representations to human-interpretable sequences of words or symbols. We report results from the DecoderLens applied to models trained on question answering, logical reasoning, speech recognition and machine translation. The DecoderLens reveals several specific subtasks that are solved at low or intermediate layers, shedding new light on the information flow inside the encoder component of this important class of models.

Despite rapid adoption and deployment of large language models (LLMs), the internal computations of these models remain opaque and poorly understood. In this work, we seek to understand how high-level human-interpretable features are represented within the internal neuron activations of LLMs. We train k-sparse linear classifiers (probes) on these internal activations to predict the presence of features in the input; by varying the value of k we study the sparsity of learned representations and how this varies with model scale. With k=1, we localize individual neurons which are highly relevant for a particular feature, and perform a number of case studies to illustrate general properties of LLMs. In particular, we show that early layers make use of sparse combinations of neurons to represent many features in superposition, that middle layers have seemingly dedicated neurons to represent higher-level contextual features, and that increasing scale causes representational sparsity to increase on average, but there are multiple types of scaling dynamics. In all, we probe for over 100 unique features comprising 10 different categories in 7 different models spanning 70 million to 6.9 billion parameters.

Our work presents extensive empirical evidence that layer rotation, i.e. the evolution across training of the cosine distance between each layer's weight vector and its initialization, constitutes an impressively consistent indicator of generalization performance. In particular, larger cosine distances between final and initial weights of each layer consistently translate into better generalization performance of the final model. Interestingly, this relation admits a network independent optimum: training procedures during which all layers' weights reach a cosine distance of 1 from their initialization consistently outperform other configurations -by up to 30% test accuracy. Moreover, we show that layer rotations are easily monitored and controlled (helpful for hyperparameter tuning) and potentially provide a unified framework to explain the impact of learning rate tuning, weight decay, learning rate warmups and adaptive gradient methods on generalization and training speed. In an attempt to explain the surprising properties of layer rotation, we show on a 1-layer MLP trained on MNIST that layer rotation correlates with the degree to which features of intermediate layers have been trained.

LLMs usually exhibit limitations in their ability to incorporate new knowledge, the generation of hallucinations, and the transparency of their decision-making process. In this paper, we explore how to prompt LLMs with knowledge graphs (KG), working as a remedy to engage LLMs with up-to-date knowledge and elicit the reasoning pathways from LLMs. Specifically, we build a prompting pipeline that endows LLMs with the capability of comprehending KG inputs and inferring with a combined implicit knowledge and the retrieved external knowledge. In addition, we investigate eliciting the mind map on which LLMs perform the reasoning and generate the answers. It is identified that the produced mind map exhibits the reasoning pathways of LLMs grounded on the ontology of knowledge, hence bringing the prospects of probing and gauging LLM inference in production. The experiments on three question & answering datasets also show that MindMap prompting leads to a striking empirical gain. For instance, prompting a GPT-3.5 with MindMap yields an overwhelming performance over GPT-4 consistently. We also demonstrate that with structured facts retrieved from KG, MindMap can outperform a series of prompting-with-document-retrieval methods, benefiting from more accurate, concise, and comprehensive knowledge from KGs. To reproduce our results and extend the framework further, we make our codebase available at https://github.com/wyl.willing/MindMap.

We study the geometric structure of layer updates in deep language models. Rather than analyzing what information is encoded in intermediate representations, we ask how representations change from one layer to the next. We show that layerwise updates admit a decomposition into a dominant tokenwise component and a residual that is not captured by restricted tokenwise function classes. Across multiple architectures, including Transformers and state-space models, we find that the full layer update is almost perfectly aligned with the tokenwise component, while the residual exhibits substantially weaker alignment, larger angular deviation, and significantly lower projection onto the dominant tokenwise subspace. This indicates that the residual is not merely a small correction, but a geometrically distinct component of the transformation. This geometric separation has functional consequences: approximation error under the restricted tokenwise model is strongly associated with output perturbation, with Spearman correlations often exceeding 0.7 and reaching up to 0.95 in larger models. Together, these results suggest that most layerwise updates behave like structured reparameterizations along a dominant direction, while functionally significant computation is concentrated in a geometrically distinct residual component. Our framework provides a simple, architecture-agnostic method for probing the geometric and functional structure of layer updates in modern language models.

Given the complexity and lack of transparency in deep neural networks (DNNs), extensive efforts have been made to make these systems more interpretable or explain their behaviors in accessible terms. Unlike most reviews, which focus on algorithmic and model-centric perspectives, this work takes a "data-centric" view, examining how data collection, processing, and analysis contribute to explainable AI (XAI). We categorize existing work into three categories subject to their purposes: interpretations of deep models, referring to feature attributions and reasoning processes that correlate data points with model outputs; influences of training data, examining the impact of training data nuances, such as data valuation and sample anomalies, on decision-making processes; and insights of domain knowledge, discovering latent patterns and fostering new knowledge from data and models to advance social values and scientific discovery. Specifically, we distill XAI methodologies into data mining operations on training and testing data across modalities, such as images, text, and tabular data, as well as on training logs, checkpoints, models and other DNN behavior descriptors. In this way, our study offers a comprehensive, data-centric examination of XAI from a lens of data mining methods and applications.

If an AI agent makes decisions on a person's behalf, those decisions must align with its user. We introduce representational accuracy to measure how faithfully a system captures a person's interpretation. An interpretive layer is operationalized as a Behavioral Specification. Our reference implementation aggressively compresses a person's data into interpretive patterns, served as context to a language model. We evaluate the Specification on a prototype benchmark of held-out behavioral predictions scored by a calibrated 5-judge LLM panel. We test it independently and in composition with a range of context conditions: full raw corpus, full extracted facts, and four commercial memory systems (Mem0, Letta, Supermemory, Zep). Across 14 public-domain autobiographical corpora, the Specification lifts representational accuracy in aggregate and nearly eliminates model hedging. It recovers most of what the raw corpus delivers, at ~25x less context cost. The Specification lifts subjects toward a common predictive level regardless of pretraining baseline; the lift in absolute points is therefore largest where the baseline is lowest, suggesting the population of relevance is anyone not adequately represented in pretraining. Lift is greatest on interpretation-required questions, where providing an interpretive layer enables model behavior that extracted facts or raw corpus do not. Conversely, on recall-required questions, this layer can interfere rather than help. We conclude that representational accuracy is distinct from recall and that human-AI alignment is dependent on how accurately the user is represented. Representational accuracy makes that alignment testable.

In contrast to RNNs, which compress previous tokens into a single hidden state, Transformers can attend to all previous tokens directly. However, standard Transformers only use representations from the immediately preceding layer. In this paper, we show that this design choice causes representation collapse and leads to suboptimal performance. To address this issue, we introduce Layer-Integrated Memory (LIMe), a simple yet powerful approach that preserves the model's overall memory footprint while expanding its representational capacity by allowing access to hidden states from earlier layers. Through extensive experiments across various architectures and different lookup mechanisms, we demonstrate consistent performance improvements on a wide range of tasks. Moreover, our analysis of the learned representation dynamics and our exploration of depthwise circuits reveal how LIMe integrates information across layers, pointing to promising directions for future research.

Native Omni-modal Large Language Models (OLLMs) have shifted from pipeline architectures to unified representation spaces. However, this native integration gives rise to a critical yet underexplored phenomenon: modality preference. To bridge this gap, we first systematically quantify modality preference of OLLMs using a newly-curated conflict-based benchmark and the modality selection rate metric. Our evaluation of ten representative OLLMs reveals a notable paradigm shift: unlike the ``text-dominance'' of traditional VLMs, most OLLMs exhibit a pronounced visual preference. To further understand the underlying mechanism, we conduct layer-wise probing and demonstrate that such modality preference is not static but emerges progressively in the mid-to-late layers. Building upon these insights, we leverage these internal signals to diagnose cross-modal hallucinations, achieving competitive performance across three downstream multi-modal benchmarks without task-specific data. Our work provides both a mechanistic understanding and a practical tool for building more trustworthy OLLMs. Our code and related resources are publicly available at: https://github.com/icip-cas/OmniPreference

Transformers are widely used to extract semantic meanings from input tokens, yet they usually operate as black-box models. In this paper, we present a simple yet informative decomposition of hidden states (or embeddings) of trained transformers into interpretable components. For any layer, embedding vectors of input sequence samples are represented by a tensor h in R^{C times T times d}. Given embedding vector h_{c,t} in R^d at sequence position t le T in a sequence (or context) c le C, extracting the mean effects yields the decomposition \[ h_{c,t} = \mu + pos_t + ctx_c + resid_{c,t} \] where mu is the global mean vector, pos_t and ctx_c are the mean vectors across contexts and across positions respectively, and resid_{c,t} is the residual vector. For popular transformer architectures and diverse text datasets, empirically we find pervasive mathematical structure: (1) (pos_t)_{t} forms a low-dimensional, continuous, and often spiral shape across layers, (2) (ctx_c)_c shows clear cluster structure that falls into context topics, and (3) (pos_t)_{t} and (ctx_c)_c are mutually nearly orthogonal. We argue that smoothness is pervasive and beneficial to transformers trained on languages, and our decomposition leads to improved model interpretability.

Audio-Visual Large Language Models (AVLLMs) are emerging as unified interfaces to multimodal perception. We present the first mechanistic interpretability study of AVLLMs, analyzing how audio and visual features evolve and fuse through different layers of an AVLLM to produce the final text outputs. We find that although AVLLMs encode rich audio semantics at intermediate layers, these capabilities largely fail to surface in the final text generation when audio conflicts with vision. Probing analyses show that useful latent audio information is present, but deeper fusion layers disproportionately privilege visual representations that tend to suppress audio cues. We further trace this imbalance to training: the AVLLM's audio behavior strongly matches its vision-language base model, indicating limited additional alignment to audio supervision. Our findings reveal a fundamental modality bias in AVLLMs and provide new mechanistic insights into how multimodal LLMs integrate audio and vision.

Recent advances in interpretability suggest we can project weights and hidden states of transformer-based language models (LMs) to their vocabulary, a transformation that makes them human interpretable and enables us to assign semantics to what was seen only as numerical vectors. In this paper, we interpret LM attention heads and memory values, the vectors the models dynamically create and recall while processing a given input. By analyzing the tokens they represent through this projection, we identify patterns in the information flow inside the attention mechanism. Based on these discoveries, we create a tool to visualize a forward pass of Generative Pre-trained Transformers (GPTs) as an interactive flow graph, with nodes representing neurons or hidden states and edges representing the interactions between them. Our visualization simplifies huge amounts of data into easy-to-read plots that reflect why models output their results. We demonstrate the utility of our modeling by identifying the effect LM components have on the intermediate processing in the model before outputting a prediction. For instance, we discover that layer norms are used as semantic filters and find neurons that act as regularization vectors.

Attention layers, as commonly used in transformers, form the backbone of modern deep learning, yet there is no mathematical description of their benefits and deficiencies as compared with other architectures. In this work we establish both positive and negative results on the representation power of attention layers, with a focus on intrinsic complexity parameters such as width, depth, and embedding dimension. On the positive side, we present a sparse averaging task, where recurrent networks and feedforward networks all have complexity scaling polynomially in the input size, whereas transformers scale merely logarithmically in the input size; furthermore, we use the same construction to show the necessity and role of a large embedding dimension in a transformer. On the negative side, we present a triple detection task, where attention layers in turn have complexity scaling linearly in the input size; as this scenario seems rare in practice, we also present natural variants that can be efficiently solved by attention layers. The proof techniques emphasize the value of communication complexity in the analysis of transformers and related models, and the role of sparse averaging as a prototypical attention task, which even finds use in the analysis of triple detection.

Understanding which information is encoded in deep models of spoken and written language has been the focus of much research in recent years, as it is crucial for debugging and improving these architectures. Most previous work has focused on probing for speaker characteristics, acoustic and phonological information in models of spoken language, and for syntactic information in models of written language. Here we focus on the encoding of syntax in several self-supervised and visually grounded models of spoken language. We employ two complementary probing methods, combined with baselines and reference representations to quantify the degree to which syntactic structure is encoded in the activations of the target models. We show that syntax is captured most prominently in the middle layers of the networks, and more explicitly within models with more parameters.

Layer-wise Relevance Propagation (LRP) provides principled attribution for neural networks through conservation properties and foundations in Deep Taylor Decomposition. However, existing implementations operate at the module level, requiring architecture-specific propagation rules and modifications. These limit the generality of target model and sustainability of implementations as architectures evolve. We introduce DynamicLRP, a model-agnostic LRP framework operating at the tensor operation level. By decomposing attribution to individual operations within computation graphs and introducing a novel mechanism for deferred activation resolution, named the Promise System, our approach achieves true architecture agnosticity while maintaining LRP's theoretical guarantees. This design operates independently of backpropagation machinery, enabling operation on arbitrary computation graphs without model modification and side-by-side execution with gradient backpropagation. Being based on computation graphs, this method is theoretically extensible to other deep learning libraries that support auto-differentiation. We demonstrate faithfulness matching or exceeding specialized implementations (1.77 vs 1.69 ABPC on VGG, equivalent performance on ViT, 93.70\% and 95.06\% top-1 attribution accuracy for explaining RoBERTa-large and Flan-T5-large answers on SQuADv2, respectively) while maintaining practical efficiency on models with hundreds of millions of parameters. We achieved 99.92\% node coverage across 31,465 computation graph nodes from 15 diverse architectures, including state-space models (Mamba), audio transformers (Whisper), and multimodal systems (DePlot) without any model-specific code with rules for 47 fundamental operations implemented. Our operation-level decomposition and Promise System establish a sustainable, extensible foundation for LRP across evolving architectures.

Recent years have witnessed a surge in the number of large language models (LLMs), yet efficiently managing and utilizing these vast resources remains a significant challenge. In this work, we explore how to learn compact representations of LLM abilities that can facilitate downstream tasks, such as model routing and performance prediction on new benchmarks. We frame this problem as estimating the probability that a given model will correctly answer a specific query. Inspired by the item response theory (IRT) in psychometrics, we model this probability as a function of three key factors: (i) the model's multi-skill ability vector, (2) the query's discrimination vector that separates models of differing skills, and (3) the query's difficulty scalar. To learn these parameters jointly, we introduce a Mixture-of-Experts (MoE) network that couples model- and query-level embeddings. Extensive experiments demonstrate that our approach leads to state-of-the-art performance in both model routing and benchmark accuracy prediction. Moreover, analysis validates that the learned parameters encode meaningful, interpretable information about model capabilities and query characteristics.

We view large language models (LLMs) as stochastic language layers in a network, where the learnable parameters are the natural language prompts at each layer. We stack two such layers, feeding the output of one layer to the next. We call the stacked architecture a Deep Language Network (DLN). We first show how to effectively perform prompt optimization for a 1-Layer language network (DLN-1). We then show how to train 2-layer DLNs (DLN-2), where two prompts must be learnt. We consider the output of the first layer as a latent variable to marginalize, and devise a variational inference algorithm for joint prompt training. A DLN-2 reaches higher performance than a single layer, sometimes comparable to few-shot GPT-4 even when each LLM in the network is smaller and less powerful. The DLN code is open source: https://github.com/microsoft/deep-language-networks .

Large Language Models (LLMs) often encode whether a statement is true as a vector in their residual stream activations. These vectors, also known as truth vectors, have been studied in prior work, however how they change when context is introduced remains unexplored. We study this question by measuring (1) the directional change (θ) between the truth vectors with and without context and (2) the relative magnitude of the truth vectors upon adding context. Across four LLMs and four datasets, we find that (1) truth vectors are roughly orthogonal in early layers, converge in middle layers, and may stabilize or continue increasing in later layers; (2) adding context generally increases the truth vector magnitude, i.e., the separation between true and false representations in the activation space is amplified; (3) larger models distinguish relevant from irrelevant context mainly through directional change (θ), while smaller models show this distinction through magnitude differences. We also find that context conflicting with parametric knowledge produces larger geometric changes than parametrically aligned context. To the best of our knowledge, this is the first work that provides a geometric characterization of how context transforms the truth vector in the activation space of LLMs.

The rapid growth of AI has led to more complex deep learning models, often operating as opaque "black boxes" with limited transparency in their decision-making. This lack of interpretability poses challenges, especially in high-stakes applications where understanding model output is crucial. This work highlights the importance of interpretability in fostering trust, accountability, and responsible deployment. To address these challenges, we introduce DLBacktrace, a novel, model-agnostic technique designed to provide clear insights into deep learning model decisions across a wide range of domains and architectures, including MLPs, CNNs, and Transformer-based LLM models. We present a comprehensive overview of DLBacktrace and benchmark its performance against established interpretability methods such as SHAP, LIME, and GradCAM. Our results demonstrate that DLBacktrace effectively enhances understanding of model behavior across diverse tasks. DLBacktrace is compatible with models developed in both PyTorch and TensorFlow, supporting architectures such as BERT, ResNet, U-Net, and custom DNNs for tabular data. The library is open-sourced and available at https://github.com/AryaXAI/DLBacktrace .

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any query and any notion of relevance that could be given. While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries, and those that are not can be overcome with better training data and larger models. In this work, we demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries. We connect known results in learning theory, showing that the number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding. We empirically show that this holds true even if we restrict to k=2, and directly optimize on the test set with free parameterized embeddings. We then create a realistic dataset called LIMIT that stress tests models based on these theoretical results, and observe that even state-of-the-art models fail on this dataset despite the simple nature of the task. Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.

Probing studies what information is encoded in a frozen LLM's layer representations by training a lightweight predictor on top of them. Beyond analysis, probes are often used operationally in probe-then-steer pipelines: a learned concept vector is extracted from a probe and injected via additive activation steering by adding it to a layer representation during the forward pass. The effectiveness of this pipeline hinges on estimating concept vectors that are accurate, directionally stable under ablation, and inexpensive to obtain. Motivated by these desiderata, we propose RAPTOR (Ridge-Adaptive Logistic Probe), a simple L2-regularized logistic probe whose validation-tuned ridge strength yields concept vectors from normalized weights. Across extensive experiments on instruction-tuned LLMs and human-written concept datasets, RAPTOR matches or exceeds strong baselines in accuracy while achieving competitive directional stability and substantially lower training cost; these quantitative results are supported by qualitative downstream steering demonstrations. Finally, using the Convex Gaussian Min-max Theorem (CGMT), we provide a mechanistic characterization of ridge logistic regression in an idealized Gaussian teacher-student model in the high-dimensional few-shot regime, explaining how penalty strength mediates probe accuracy and concept-vector stability and yielding structural predictions that qualitatively align with trends observed on real LLM embeddings.

The inference phase of Large Language Models (LLMs) is very expensive. An ideal inference stage of LLMs could utilize fewer computational resources while still maintaining its capabilities (e.g., generalization and in-context learning ability). In this paper, we try to answer the question, "During LLM inference, can we use shallow layers for easy instances; and deep layers for hard ones?" To answer this question, we first indicate that Not all Layers are Necessary during Inference by statistically analyzing the activated layers across tasks. Then, we propose a simple algorithm named AdaInfer to determine the inference termination moment based on the input instance adaptively. More importantly, AdaInfer does not alter LLM parameters and maintains generalizability across tasks. Experiments on well-known LLMs (i.e., Llama2 series and OPT) show that AdaInfer saves an average of 14.8% of computational resources, even up to 50% on sentiment tasks, while maintaining comparable performance. Additionally, this method is orthogonal to other model acceleration techniques, potentially boosting inference efficiency further.

Despite the growing use of transformer models in computer vision, a mechanistic understanding of these networks is still needed. This work introduces a method to reverse-engineer Vision Transformers trained to solve image classification tasks. Inspired by previous research in NLP, we demonstrate how the inner representations at any level of the hierarchy can be projected onto the learned class embedding space to uncover how these networks build categorical representations for their predictions. We use our framework to show how image tokens develop class-specific representations that depend on attention mechanisms and contextual information, and give insights on how self-attention and MLP layers differentially contribute to this categorical composition. We additionally demonstrate that this method (1) can be used to determine the parts of an image that would be important for detecting the class of interest, and (2) exhibits significant advantages over traditional linear probing approaches. Taken together, our results position our proposed framework as a powerful tool for mechanistic interpretability and explainability research.

A growing body of work makes use of probing to investigate the working of neural models, often considered black boxes. Recently, an ongoing debate emerged surrounding the limitations of the probing paradigm. In this work, we point out the inability to infer behavioral conclusions from probing results and offer an alternative method that focuses on how the information is being used, rather than on what information is encoded. Our method, Amnesic Probing, follows the intuition that the utility of a property for a given task can be assessed by measuring the influence of a causal intervention that removes it from the representation. Equipped with this new analysis tool, we can ask questions that were not possible before, e.g. is part-of-speech information important for word prediction? We perform a series of analyses on BERT to answer these types of questions. Our findings demonstrate that conventional probing performance is not correlated to task importance, and we call for increased scrutiny of claims that draw behavioral or causal conclusions from probing results.

Large Lanugage Models (LLMs) are gaining increasing popularity in a variety of use cases, from language understanding and writing to assistance in application development. One of the most important aspects for optimal funcionality of LLMs is embedding layers. Word embeddings are distributed representations of words in a continuous vector space. In the context of LLMs, words or tokens from the input text are transformed into high-dimensional vectors using unique algorithms specific to the model. Our research examines the embedding algorithms from leading companies in the industry, such as OpenAI, Google's PaLM, and BERT. Using medical data, we have analyzed similarity scores of each embedding layer, observing differences in performance among each algorithm. To enhance each model and provide an additional encoding layer, we also implemented Siamese Neural Networks. After observing changes in performance with the addition of the model, we measured the carbon footage per epoch of training. The carbon footprint associated with large language models (LLMs) is a significant concern, and should be taken into consideration when selecting algorithms for a variety of use cases. Overall, our research compared the accuracy different, leading embedding algorithms and their carbon footage, allowing for a holistic review of each embedding algorithm.

With hundreds of thousands of language models available on Huggingface today, efficiently evaluating and utilizing these models across various downstream, tasks has become increasingly critical. Many existing methods repeatedly learn task-specific representations of Large Language Models (LLMs), which leads to inefficiencies in both time and computational resources. To address this, we propose EmbedLLM, a framework designed to learn compact vector representations, of LLMs that facilitate downstream applications involving many models, such as model routing. We introduce an encoder-decoder approach for learning such embeddings, along with a systematic framework to evaluate their effectiveness. Empirical results show that EmbedLLM outperforms prior methods in model routing both in accuracy and latency. Additionally, we demonstrate that our method can forecast a model's performance on multiple benchmarks, without incurring additional inference cost. Extensive probing experiments validate that the learned embeddings capture key model characteristics, e.g. whether the model is specialized for coding tasks, even without being explicitly trained on them. We open source our dataset, code and embedder to facilitate further research and application.

Although concept-based models promise interpretability by explaining predictions with human-understandable concepts, they typically rely on exhaustive annotations and treat concepts as flat and independent. To circumvent this, recent work has introduced Hierarchical Concept Embedding Models (HiCEMs) to explicitly model concept relationships, and Concept Splitting to discover sub-concepts using only coarse annotations. However, both HiCEMs and Concept Splitting are restricted to shallow hierarchies. We overcome this limitation with Multi-Level Concept Splitting (MLCS), which discovers multi-level concept hierarchies from only top-level supervision, and Deep-HiCEMs, an architecture that represents these discovered hierarchies and enables interventions at multiple levels of abstraction. Experiments across multiple datasets show that MLCS discovers human-interpretable concepts absent during training and that Deep-HiCEMs maintain high accuracy while supporting test-time concept interventions that can improve task performance.

Transformers have achieved remarkable success across diverse domains, but their monolithic architecture presents challenges in interpretability, adaptability, and scalability. This paper introduces a novel modular Transformer architecture that explicitly decouples knowledge and reasoning through a generalized cross-attention mechanism to a globally shared knowledge base with layer-specific transformations, specifically designed for effective knowledge retrieval. Critically, we provide a rigorous mathematical derivation demonstrating that the Feed-Forward Network (FFN) in a standard Transformer is a specialized case (a closure) of this generalized cross-attention, revealing its role in implicit knowledge retrieval and validating our design. This theoretical framework provides a new lens for understanding FFNs and lays the foundation for future research exploring enhanced interpretability, adaptability, and scalability, enabling richer interplay with external knowledge bases and other systems.

Large Language Models (LLMs) often encounter conflicts between their learned, internal (parametric knowledge, PK) and external knowledge provided during inference (contextual knowledge, CK). Understanding how LLMs models prioritize one knowledge source over the other remains a challenge. In this paper, we propose a novel probing framework to explore the mechanisms governing the selection between PK and CK in LLMs. Using controlled prompts designed to contradict the model's PK, we demonstrate that specific model activations are indicative of the knowledge source employed. We evaluate this framework on various LLMs of different sizes and demonstrate that mid-layer activations, particularly those related to relations in the input, are crucial in predicting knowledge source selection, paving the way for more reliable models capable of handling knowledge conflicts effectively.

Fine-tuning all the layers of a pre-trained neural language encoder (either using all the parameters or using parameter-efficient methods) is often the de-facto way of adapting it to a new task. We show evidence that for different downstream language tasks, fine-tuning only a subset of layers is sufficient to obtain performance that is close to and often better than fine-tuning all the layers in the language encoder. We propose an efficient metric based on the diagonal of the Fisher information matrix (FIM score), to select the candidate layers for selective fine-tuning. We show, empirically on GLUE and SuperGLUE tasks and across distinct language encoders, that this metric can effectively select layers leading to a strong downstream performance. Our work highlights that task-specific information corresponding to a given downstream task is often localized within a few layers, and tuning only those is sufficient for strong performance. Additionally, we demonstrate the robustness of the FIM score to rank layers in a manner that remains constant during the optimization process.

Recent advances in efficient sequence modeling have led to attention-free layers, such as Mamba, RWKV, and various gated RNNs, all featuring sub-quadratic complexity in sequence length and excellent scaling properties, enabling the construction of a new type of foundation models. In this paper, we present a unified view of these models, formulating such layers as implicit causal self-attention layers. The formulation includes most of their sub-components and is not limited to a specific part of the architecture. The framework compares the underlying mechanisms on similar grounds for different layers and provides a direct means for applying explainability methods. Our experiments show that our attention matrices and attribution method outperform an alternative and a more limited formulation that was recently proposed for Mamba. For the other architectures for which our method is the first to provide such a view, our method is effective and competitive in the relevant metrics compared to the results obtained by state-of-the-art transformer explainability methods. Our code is publicly available.

Deep learning methods employ multiple processing layers to learn hierarchical representations of data and have produced state-of-the-art results in many domains. Recently, a variety of model designs and methods have blossomed in the context of natural language processing (NLP). In this paper, we review significant deep learning related models and methods that have been employed for numerous NLP tasks and provide a walk-through of their evolution. We also summarize, compare and contrast the various models and put forward a detailed understanding of the past, present and future of deep learning in NLP.

Attention layers -- which map a sequence of inputs to a sequence of outputs -- are core building blocks of the Transformer architecture which has achieved significant breakthroughs in modern artificial intelligence. This paper presents a rigorous theoretical study on the learning and generalization of a single multi-head attention layer, with a sequence of key vectors and a separate query vector as input. We consider the random feature setting where the attention layer has a large number of heads, with randomly sampled frozen query and key matrices, and trainable value matrices. We show that such a random-feature attention layer can express a broad class of target functions that are permutation invariant to the key vectors. We further provide quantitative excess risk bounds for learning these target functions from finite samples, using random feature attention with finitely many heads. Our results feature several implications unique to the attention structure compared with existing random features theory for neural networks, such as (1) Advantages in the sample complexity over standard two-layer random-feature networks; (2) Concrete and natural classes of functions that can be learned efficiently by a random-feature attention layer; and (3) The effect of the sampling distribution of the query-key weight matrix (the product of the query and key matrix), where Gaussian random weights with a non-zero mean result in better sample complexities over the zero-mean counterpart for learning certain natural target functions. Experiments on simulated data corroborate our theoretical findings and further illustrate the interplay between the sample size and the complexity of the target function.

The significant advancements of Large Language Models (LLMs) in generative tasks have led to a growing body of work exploring LLM-based embedding models. While these models, employing different pooling and attention strategies, have achieved state-of-the-art performance on public embedding benchmarks, questions still arise about what constitutes an effective design for LLM-based embedding models. However, these models are often trained on different datasets, using different LLM base models or training settings. Moreover, evaluations on public embedding benchmarks often fail to report statistical significance, making it difficult to determine which designs truly contribute to final performance. This complicates the process for practitioners seeking optimal training recipes for LLM-based embedding models. In this study, we conduct a large-scale experiment by training a series of LLM-based embedding models using the same training data and base model but differing in their pooling and attention strategies. The results show that there is no one-size-fits-all solution: while bidirectional attention and an additional trainable pooling layer outperform in text similarity and information retrieval tasks, they do not significantly surpass simpler designs like EOS-last token pooling and default causal attention in clustering and classification tasks. Furthermore, we propose a new pooling strategy, Multi-Layers Trainable Pooling, which transforms the outputs of all hidden layers, rather than just the last layer, using a cross-attention network. This method proves to be statistically superior in text similarity and retrieval tasks compared to existing pooling methods. Overall, this paper sheds light on effective training strategies for LLM-based embedding models.

Joint Embedding Predictive Architectures (JEPAs) have reshaped self-supervised representation learning in vision. The recent LLM-JEPA ported JEPA to autoregressive language models but inherited two steep costs from the causal-attention substrate: it demands explicit multi-view data (e.g., text-code pairs), and it requires two gradient-carrying forward passes per step. We introduce DLLM-JEPA, which pairs JEPA with masked-diffusion language models to eliminate both costs at once. The bidirectional attention of diffusion models yields two semantically distinct views of the same input via different masking rates -- no explicit pairs needed -- and supports a single gradient-carrying forward pass, cutting training FLOPs by 33% relative to LLM-JEPA. DLLM-JEPA improves over diffusion-only fine-tuning in every (task, architecture) combination we evaluate: up to +18.7 pp on LLaDA-8B GSM8K and +11.4 pp on Dream-7B GSM8K, with consistent positive gains on Spider, NL-RX-SYNTH, and Django. Beyond accuracy, DLLM-JEPA exhibits a dual-win property: on LLaDA-8B with the Wide-t configuration, it simultaneously raises GSM8K accuracy (67.1 vs. 65.2, +1.8 pp), drives held-out Wikitext loss below the pre-trained base, and preserves MMLU accuracy at base level across three fine-tuning seeds -- whereas an L2-to-base parameter anchor matches baseline accuracy with no task gain. Layer-wise probing reveals the mechanism: a geometric-functional drift dissociation in which the fine-tuned backbone moves further from the pre-trained weights than the baseline yet forgets less on held-out Wikitext, with the amplification concentrated in middle transformer layers. The pattern appears on Dream-7B as well, indicating the phenomenon is not specific to a single backbone.

Implicit models separate the definition of a layer from the description of its solution process. While implicit layers allow features such as depth to adapt to new scenarios and inputs automatically, this adaptivity makes its computational expense challenging to predict. In this manuscript, we increase the "implicitness" of the DEQ by redefining the method in terms of an infinite time neural ODE, which paradoxically decreases the training cost over a standard neural ODE by 2-4x. Additionally, we address the question: is there a way to simultaneously achieve the robustness of implicit layers while allowing the reduced computational expense of an explicit layer? To solve this, we develop Skip and Skip Reg. DEQ, an implicit-explicit (IMEX) layer that simultaneously trains an explicit prediction followed by an implicit correction. We show that training this explicit predictor is free and even decreases the training time by 1.11-3.19x. Together, this manuscript shows how bridging the dichotomy of implicit and explicit deep learning can combine the advantages of both techniques.

The Transformer is an extremely powerful and prominent deep learning architecture. In this work, we challenge the commonly held belief in deep learning that going deeper is better, and show an alternative design approach that is building wider attention Transformers. We demonstrate that wide single layer Transformer models can compete with or outperform deeper ones in a variety of Natural Language Processing (NLP) tasks when both are trained from scratch. The impact of changing the model aspect ratio on Transformers is then studied systematically. This ratio balances the number of layers and the number of attention heads per layer while keeping the total number of attention heads and all other hyperparameters constant. On average, across 4 NLP tasks and 10 attention types, single layer wide models perform 0.3% better than their deep counterparts. We show an in-depth evaluation and demonstrate how wide models require a far smaller memory footprint and can run faster on commodity hardware, in addition, these wider models are also more interpretable. For example, a single layer Transformer on the IMDb byte level text classification has 3.1x faster inference latency on a CPU than its equally accurate deeper counterpart, and is half the size. We therefore put forward wider and shallower models as a viable and desirable alternative for small models on NLP tasks, and as an important area of research for domains beyond this.

Language models and specialized table embedding models have recently demonstrated strong performance on many tasks over tabular data. Researchers and practitioners are keen to leverage these models in many new application contexts; but limited understanding of the strengths and weaknesses of these models, and the table representations they generate, makes the process of finding a suitable model for a given task reliant on trial and error. There is an urgent need to gain a comprehensive understanding of these models to minimize inefficiency and failures in downstream usage. To address this need, we propose Observatory, a formal framework to systematically analyze embedding representations of relational tables. Motivated both by invariants of the relational data model and by statistical considerations regarding data distributions, we define eight primitive properties, and corresponding measures to quantitatively characterize table embeddings for these properties. Based on these properties, we define an extensible framework to evaluate language and table embedding models. We collect and synthesize a suite of datasets and use Observatory to analyze nine such models. Our analysis provides insights into the strengths and weaknesses of learned representations over tables. We find, for example, that some models are sensitive to table structure such as column order, that functional dependencies are rarely reflected in embeddings, and that specialized table embedding models have relatively lower sample fidelity. Such insights help researchers and practitioners better anticipate model behaviors and select appropriate models for their downstream tasks, while guiding researchers in the development of new models.

We often attribute human characteristics to large language models (LLMs) and claim that they "know" certain things. LLMs have an internal probabilistic knowledge that represents information retained during training. How can we assess the veracity of this knowledge? We examine two common methods for probing the veracity of LLMs and discover several assumptions that are flawed. To address these flawed assumptions, we introduce sAwMIL (short for Sparse Aware Multiple-Instance Learning), a probing method that utilizes the internal activations of LLMs to separate statements into true, false, and neither. sAwMIL is based on multiple-instance learning and conformal prediction. We evaluate sAwMIL on 5 validity criteria across 16 open-source LLMs, including both default and chat-based variants, as well as on 3 new datasets. Among the insights we provide are: (1) the veracity signal is often concentrated in the third quarter of an LLM's depth; (2) truth and falsehood signals are not always symmetric; (3) linear probes perform better on chat models than on default models; (4) nonlinear probes may be required to capture veracity signals for some LLMs with reinforcement learning from human feedback or knowledge distillation; and (5) LLMs capture a third type of signal that is distinct from true and false and is neither true nor false. These findings provide a reliable method for verifying what LLMs "know" and how certain they are of their probabilistic internal knowledge.

This position paper argues that the text embedding research community should move beyond surface meaning and embrace implicit semantics as a central modeling goal. Text embedding models have become foundational in modern NLP, powering a wide range of applications and drawing increasing research attention. Yet, much of this progress remains narrowly focused on surface-level semantics. In contrast, linguistic theory emphasizes that meaning is often implicit, shaped by pragmatics, speaker intent, and sociocultural context. Current embedding models are typically trained on data that lacks such depth and evaluated on benchmarks that reward the capture of surface meaning. As a result, they struggle with tasks requiring interpretive reasoning, speaker stance, or social meaning. Our pilot study highlights this gap, showing that even state-of-the-art models perform only marginally better than simplistic baselines on implicit semantics tasks. To address this, we call for a paradigm shift: embedding research should prioritize more diverse and linguistically grounded training data, design benchmarks that evaluate deeper semantic understanding, and explicitly frame implicit meaning as a core modeling objective, better aligning embeddings with real-world language complexity.

While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and reasoning tasks -- but mathematical understanding is lagging substantially behind. Recent lines of work have begun studying representational aspects of this question: that is, the size/depth/complexity of attention-based networks to perform certain tasks. However, there is no guarantee the learning dynamics will converge to the constructions proposed. In our paper, we provide fine-grained mechanistic understanding of how transformers learn "semantic structure", understood as capturing co-occurrence structure of words. Precisely, we show, through a combination of experiments on synthetic data modeled by Latent Dirichlet Allocation (LDA), Wikipedia data, and mathematical analysis that the embedding layer and the self-attention layer encode the topical structure. In the former case, this manifests as higher average inner product of embeddings between same-topic words. In the latter, it manifests as higher average pairwise attention between same-topic words. The mathematical results involve several assumptions to make the analysis tractable, which we verify on data, and might be of independent interest as well.

Recently, Transformer-like deep architectures have shown strong performance on tabular data problems. Unlike traditional models, e.g., MLP, these architectures map scalar values of numerical features to high-dimensional embeddings before mixing them in the main backbone. In this work, we argue that embeddings for numerical features are an underexplored degree of freedom in tabular DL, which allows constructing more powerful DL models and competing with GBDT on some traditionally GBDT-friendly benchmarks. We start by describing two conceptually different approaches to building embedding modules: the first one is based on a piecewise linear encoding of scalar values, and the second one utilizes periodic activations. Then, we empirically demonstrate that these two approaches can lead to significant performance boosts compared to the embeddings based on conventional blocks such as linear layers and ReLU activations. Importantly, we also show that embedding numerical features is beneficial for many backbones, not only for Transformers. Specifically, after proper embeddings, simple MLP-like models can perform on par with the attention-based architectures. Overall, we highlight embeddings for numerical features as an important design aspect with good potential for further improvements in tabular DL.

The scaling of large language models (LLMs) emphasizes increasing depth, yet performance gains diminish with added layers. Prior work introduces the concept of "effective depth", arguing that deeper models fail to fully utilize their layers for meaningful computation. Building on this, we systematically study how effective depth varies with model scale, training type, and task difficulty. First, we analyze the model behavior of Qwen-2.5 family (1.5B-32B) and find that while the number of effective layers grows with model size, the effective depth ratio remains stable. Besides, comparisons between base and corresponding long-CoT models show no increase in effective depth, suggesting that improved reasoning stems from longer context rather than deeper per-token computation. Furthermore, evaluations across tasks of varying difficulty indicate that models do not dynamically use more layers for harder problems. Our results suggest that current LLMs underuse available depth across scales, training paradigms and tasks of varying difficulties, pointing out research opportunities on increasing the layer utilization rate of LLMs, model pruning, and early exiting. Our code is released at https://github.com/AheadOFpotato/what_affects_effective_depth.