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7 papers in the last four weeks, up 75% on the four weeks before. 0.1% of all new papers.

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Latest papers 104

May 26, 2026cs.CV

The Rescue Effect: Spatio-Semantic Early Exit Bypasses Quantization Collapse in CLIP

Deploying Vision-Language Models on resource-constrained hardware typically requires INT8 quantization, but in joint-embedding architectures such as CLIP this introduces a failure mode distinct from quantized CNN classifiers: activation noise accumulated across transformer blocks perturbs the direction of the multimodal embedding, eroding the cosine alignment on which zero-shot retrieval depends. We characterize this as Quantization-Induced Representation Collapse (QIRC) and quantify it on INT8 CLIP ViT-B/32, where the layer-wise noise-to-signal ratio grows from below 10% in shallow blocks to 52% at Layer 11. We propose LRA-EE (Layer-wise Representation-Aware Early Exit), which bypasses noise-saturated deep layers via Spatio-Semantic Aggregation (replacing the immature shallow [CLS] with a global patch-token average), a learned multi-feature gate (confidence, top-2 margin, spatial-activation variance), and Layer-adaptive Confidence Thresholding calibrated to each layer's Information-to-Noise Ratio. On ImageNet-1K zero-shot classification, LRA-EE reduces FLOPs by 13.4% and improves Top-1 accuracy by +2.44%p (58.72% -> 61.16%) over the INT8 baseline. A four-quadrant decomposition isolates the Rescue Effect: 9.5% of samples are correctly classified at shallow exits but lost to noise at full depth, against only 7.1% suffering the inverse.

Kahyeon Nam, Hyesong Choi

Soongsil University Seoul, Republic of Korea

Frozen Contrastive Language-Image Pre-Training Visual Encoder Quantized Layer-Wise Imagenet Signal-To-Noise Ratio Impact Analysis

May 21, 2026cs.LG

Uncovering the Latent Potential of Deep Intermediate Representations

Foundational Models pretrained on huge amount of data learn representations that evolve across depth, forming a hierarchy of embeddings with distinct semantic content and geometric structure. Contrary to the widespread practice of using only the final layer or shallow mixtures, we show that task-relevant information is distributed non-monotonically across layers and cannot be recovered by naïve aggregation. Through a geometric and empirical study across multiple modalities, we show that effective transfer depends on identifying which layers encode task-discriminative structure and how their embeddings are geometrically organized. We introduce Layer-wise Optimal Embedding Selection (LOES), a constructive spectral method that identifies task-discriminative subspaces by minimizing residual error under orthogonality and isotropy constraints. To align fine-tuning with this selection principle, we further propose Geometric Regularization Loss (GeoReg), which enforces a simplicial structure on class manifolds and stabilizes representation geometry during fine-tuning. Across a wide range of architectures, depths, modalities, and data regimes, LOES consistently outperforms standard baselines, with gains that grow as model depth increases. Beyond accuracy, our method reveals how semantic factors are distributed across layers, thereby enabling cross-lingual and cross-modal interpretability analyses. Together, our results provide strong evidence that layerwise embedding geometry is not incidental but central to how deep models represent and transfer knowledge.

Arnesh Batra, Arush Gumber, Aniket Khandelwal +2

SBILab, Indraprastha Institute of Information Technology Delhi, Delhi, India.

Layer-Wise Cross-Modal

May 21, 2026cs.LG

Relational Linear Properties in Language Models: An Empirical Investigation

Linear properties are ubiquitous in the representations of language models; however, testing them experimentally remains a challenging task. This work focuses on relational linearity: the hypothesis that, for a fixed relation (e.g., "plays"), the unembedding of an object (e.g., "trumpet") can be predicted from the embedding of its subject (e.g.,"Miles Davis") by a linear map. We present an experimental method to test the formulation of relational linearity by Marconato et al. (2025). Specifically, we introduce a probing method, based on Kullback-Leibler divergence, to evaluate this property and examine its variation across layers and paraphrased relational queries. It is also more efficient than previous work; for example, it avoids the crude Jacobian approximations used in Linear Relational Embeddings by Hernandez et al. (2024). Our findings across four datasets show that relational linearity varies across models, exhibits layer-wise patterns consistent with prior observations about linguistic information in model representations, and is differently affected by changes in how the relation is phrased.

Giovanni Valer, Luigi Gresele, Marco Bronzini +1

Fondazione Bruno Kessler, Trento, Italy · University of Bologna, Bologna, Italy · University of Pisa, Pisa, Italy +2

Language Modeling Layer-Wise Empirical Study Kullback-Leibler Divergence

May 18, 2026cs.LG

Distilling Linearized Behavior into Non-Linear Fine-Tuning for Effective Task Arithmetic

Task vector composition has emerged as a promising paradigm for editing pre-trained models, enabling model merging through addition and unlearning through subtraction. Fine-tuning in the tangent space of a pre-trained model (linear fine-tuning) has proven effective, as it produces task vectors that are naturally disentangled and resistant to interference. However, linearized models suffer from limited expressivity during training and incur higher computational costs at inference time, which restrict their practical applicability. In this work, we bridge the gap between linear and standard non-linear fine-tuning. We show that linearity with respect to weight perturbations, a property defined in parameter space, can be enforced through constraints in activation space during training. Concretely, we distill hidden representations from a curvature-regularized linearized teacher into a non-linear student trained via conventional fine-tuning. We find that the resulting model inherits key properties of linearized models for task arithmetic, enabling effective composition of task vectors and achieving strong performance across vision and language benchmarks without incurring any inference-time overhead.

Thomas Sommariva, Francesca Morandi, Simone Calderara +1

ImageLab, Department of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, Italy · University of Pisa, Italy

Model Fine-Tuning Continual Fine-Tuning Layer-Wise Pretraining Nonlinearity Agent Behavior Modeling

May 14, 2026cs.LG

Enjoy Your Layer Normalization with the Computational Efficiency of RMSNorm

Layer normalization (LN) is a fundamental component in modern deep learning, but its per-sample centering and scaling introduce non-negligible inference overhead. RMSNorm improves efficiency by removing the centering operation, yet this may discard benefits associated with centering. This paper propose a framework to determine whether an LN in an arbitrary DNN can be replaced by RMSNorm without changing the model function. The key idea is to fold LN's centering operation into upstream general linear layers by enforcing zero-mean outputs through the column-centered constraint (CCC) and column-based weight centering (CBWC). We extend the analysis to arbitrary DNNs, define such LNs as foldable LNs, and develop a graph-based detection algorithm. Our analysis shows that many LNs in widely used architectures are foldable, enabling exact inference-time conversion and end-to-end acceleration of 2% to 12% without changing model predictions. Experiments across multiple task families further show that, when exact equivalence is partially broken in practical training settings, our method remains competitive with vanilla LN while improving efficiency.

Yuxin Guo, Yihao Yue, Yunhao Ni +4

State Key Laboratory of Complex and Critical Software Environment (SKLCCSE), Beihang University, Beijing, China · Hangzhou International Innovation Institute, Beihang University, Hangzhou, China

Batch Normalization Neural Network Inference Layer-Wise Modern Deep Networks Efficiency Structural Constraints

May 14, 2026cs.LG

Dynamics of the Transformer Residual Stream: Coupling Spectral Geometry to Network Topology

Large language models are remarkably capable, yet how computation propagates through their layers remains poorly understood. A growing line of work treats depth as discrete time and the residual stream as a dynamical system, where each layer's nonlinear update has a local linear description. However, previous analyses have relied on scalar summaries or approximate linearizations, leaving the full spectral geometry of trained LLMs unknown. We perform full Jacobian eigendecomposition across three production--scale LLMs and show that training installs a monotonic spectral gradient through depth -- from non-normal, rotation-dominated early layers to near--symmetric late layers -- together with a cumulative low-rank bottleneck that funnels perturbations into a small fraction of the residual stream's effective dimensions. Our experiments reveal that this gradient and the dimensional collapse are learned rather than architectural, and is largely dissolved when structured non-normality is removed. We further show that the topological positioning of graph communities predicts whether the Jacobian amplifies or suppresses them, with the sign of the coupling determined by the local operator type, a relationship absent at initialization. These results map a learned spectral geometry in LLMs that links perturbation propagation and compression to the network's functional topology.

Jesseba Fernando, Grigori Guitchounts

Network Science Institute, Northeastern University · Flagship Pioneering

Transformer Residual Streams Residual Stream Layer-Wise Transformer Architectures Spectral Decomposition Network Topology

May 13, 2026cs.LG

Delta Attention Residuals

Attention Residuals replace standard additive residual connections with learned softmax attention over previous layer outputs, enabling selective cross-layer routing. However, standard Attention Residuals still attend over cumulative hidden states in previous layers, which are highly redundant. We show that this redundancy leads to routing collapse in deeper layers: attention weights become low-contrast and closer to uniform (max weight

{\approx}

0.2), limiting the model's ability to select informative states in previous layers. This raises a key but underexplored design question: what layer-wise representations should be routed in Attention Residuals? To answer this question, we propose Delta Attention Residuals, which attend over deltas -- the change introduced by each sublayer (

\mathbf{v}_i = \mathbf{h}_{i+1} - \mathbf{h}_i

) -- instead of cumulative states. Delta representations are structurally diverse and yield higher-contrast attention distributions (max weight

{\approx}

0.6), enabling more selective and effective routing across layers. This principle applies at both per-sublayer and block granularity. Across all tested scales (220M--7.6B), Delta Attention Residuals consistently outperform both standard residuals and Attention Residuals, with 1.7--8.2% validation perplexity gains. Delta Attention Residuals also enables converting pretrained checkpoints into Delta Attention Residuals via standard fine-tuning. Code is available at https://github.com/wdlctc/delta-attention-residuals-code.

Cheng Luo, Zefan Cai, Junjie Hu

Independent Researcher · University of Wisconsin–Madison

Layer-Wise Cross-Layer Interactions

May 12, 2026cs.LG

Layer-wise Representation Dynamics: An Empirical Investigation Across Embedders and Base LLMs

Hidden states change substantially across the layers of modern language models, but most layer-wise analyses focus on one aspect of that change. We propose Layer-wise Representation Dynamics (LRD), a framework with three layer-wise measurement families: Frenet (Grassmann speed and curvature) for global subspace motion, Neighborhood Retention Score (NRS) for local nearest-neighbor retention, and Graph Filtration Mutual Information (GFMI) for alignment with the final layer. Applying LRD to 31 models (encoder-based and decoder-based embedders, plus base LLMs) on 30 MTEB tasks reveals architectural and task-level differences that are not apparent from final-layer representations alone. We then use LRD for two applications: label-free model selection and inference-time layer pruning. For selection, all three model-level scores correlate positively with downstream MTEB performance, with end-to-end subspace displacement (d_{0,L}) the strongest, and the same direction holds on a smaller base-LLM MMLU panel. For pruning, GFMI is the only measurement-guided rule that beats Random at the 15% and 20% budgets and has the best median change at every budget. Frenet is effective only at the lightest budget, while NRS does not transfer from model selection to pruning. These results show that layer-wise structure provides signal for both interpretation and deployment decisions.

Jingzhou Jiang, Yi Yang, Kar Yan Tam

The Hong Kong University of Science and Technology

Layer-Wise Model Selection

May 12, 2026cs.CL

Freeze Deep, Train Shallow: Interpretable Layer Allocation for Continued Pre-Training

Selective layer-wise updates are essential for low-cost continued pre-training of Large Language Models (LLMs), yet determining which layers to freeze or train remains an empirical black-box problem due to the lack of interpretable guidance. To address this issue, we propose LayerTracer, an architecture-agnostic diagnostic framework that reveals the evolution patterns of layer-wise representations and stability by locating task execution positions and quantifying layer sensitivity. Analysis results reveal that deep layers act as critical regions for task execution and maintain high stability against disruptive updates. Guided by this finding, we conduct three controlled continued pre-training trials to compare diverse freeze-train strategies, demonstrating that training shallow layers while freezing deep layers consistently outperforms full-parameter fine-tuning and the opposite allocation on both C-Eval and CMMLU benchmarks. We further present a hybrid model case study, which validates that placing high-quality pre-trained modules in deep layers effectively preserves inherent knowledge of the model. This work delivers a low-cost and interpretable solution for resource-constrained teams, offering actionable guidance for layer-wise parameter allocation in continued pre-training and hybrid model construction.

Yu-Hang Wu, Qin-Yuan Liu, Qiu-Yang Zhao +3

Nanhu Research Institute of China Electronic Science and Technology · School of Electronic and Electrical Engineering, Shanghai University of Engineering Science

Pretraining Layer-Wise Multi-Stage Training Freeze Traces

May 11, 2026cs.AI

Don't Look at the Numbers: Visual Anchoring Bias and Layer-wise Representation in VLMs

Embedded numeric anchors on images systematically bias Vision-Language Model quality judgments across six VLMs from five architectural families (ANOVA eta^2 = 0.18-0.77, all p < 0.001). Anchor effects are 2.5x larger than severe image quality degradation, confirming bias is not reducible to visual changes. Layer-wise probing reveals consistent dissociation: layers where anchor classification saturates (L12-L34) are suboptimal for quality prediction, with optimal layers deeper (R^2 = 0.69-0.91). Fusion analysis identifies architecture-dependent integration -- instant fusion at L1-L2 in two models versus partial or no fusion in three others. These results establish a causal account of visual anchoring bias, linking behavioral susceptibility to representation dynamics.

M. Shalankin

Layer-Wise Representation Quality

May 11, 2026cs.LG

The Geometric Wall: Manifold Structure Predicts Layerwise Sparse Autoencoder Scaling Laws

Sparse autoencoders (SAEs) operationalise the linear representation hypothesis: they reconstruct model activations as sparse linear combinations of interpretable dictionary atoms, on the implicit assumption that activation space is well approximated by a globally linear structure. Their reconstruction error varies sharply across layers in ways that existing scaling laws, fitted at single layers, do not explain. We argue that this variation is the empirical trace of a geometric mismatch: where the activation manifold is curved and its intrinsic dimension varies across layers, no sparse linear dictionary can match it uniformly, and the SAE's width-sparsity scaling becomes a layer-dependent function of manifold structure rather than a single universal law. We conduct the first cross-layer SAE scaling study, fitting and regressing on 844 residual-stream Gemma Scope SAE checkpoints across 68 layers of Gemma 2 2B and 9B. Stage 1 fits a per-layer scaling-law surface; Stage 2 regresses the fitted parameters and the derived per-layer width exponents on four layerwise geometric summaries. We find that manifold geometry predicts the per-layer width exponent in both models, and that the same regression coefficients learnt on one model predict the other model's per-layer exponents under cross-model transfer, indicating a transferable geometric law. At the showcase layers where richer width grids permit identification of the asymptotic floor, we find that the fitted floor tracks the layerwise geometric ordering: higher curvature and intrinsic dimension correspond to higher floor, consistent with the irreducible second-order residual that any sparse linear approximation of a curved manifold must leave behind. SAEs thus encounter not a finite-resource ceiling but a geometry-dependent wall, set by the manifold they are trying to reconstruct.

Eslam Zaher, Maciej Trzaskowski, Quan Nguyen +1

ARC Training Centre for Information Resilience (CIRES) · School of Mathematics and Physics, University of Queensland · Institute for Molecular Bioscience, University of Queensland +2

Improving Sparse Autoencoders Scaling Laws Layer-Wise

May 9, 2026cs.LG

Sparse Layers are Critical to Scaling Looped Language Models

Looped language models repeat a set of transformer layers through depth, reducing memory costs and providing natural early-exit points at loop boundaries. However, looped models do not scale as favorably as standard transformers with unique layers. We compare standard and Mixture-of-Experts (MoE) transformers, with and without looping, and find two main results. First, we find Looped-MoE models scale better than the standard baseline while dense looped models do not. We trace this to routing divergence between loops: in Looped-MoE models, different experts are activated on each pass through the same shared layers, recovering expressivity without additional parameters. Our second finding is that looped models have better compute-quality trade-offs with early exits than standard models. Because each loop ends with the same layers that produce the final output, loop boundaries are superior exit points, as confirmed by earlier output convergence at these points. In sum, we provide a clear direction for scaling looped models: a Looped-MoE model with early exits can not only beat standard transformers at scale, but also enable significant memory and inference savings with minimal degradation in quality.

Ryan Lee, Jacob Biloki, Edward J. Hu +1

1USC Information Sciences Institute · 2Netflix · 3Independent Researcher

Transformer Architectures Layer-Wise Localized Lora-Moe Mixture-Of-Experts Peak Memory

May 9, 2026cs.LG

A Geometric Perspective on Next-Token Prediction in Large Language Models: Three Emerging Phases

We investigate the geometry of predictive information across the layers of large language models (LLMs). We repurpose representation lenses-learned affine maps trained to predict the next token from intermediate residual streams-as geometric diagnostic tools. Rather than asking what the model predicts at each layer, we ask where predictive information resides and how it evolves across depth. We define at each layer a predictive readout subspace as the dominant k-dimensional singular subspace of such a map on the d-dimensional residual stream (where k is a resolution parameter), and track its trajectory on the Grassmann manifold as a similarity profile across layers. The profile is well described by unimodal distributions exhibiting a rise, near-plateau, and descent; varying k from 1% to 50% of d traces a Pareto frontier between visibility and energy retention, yet the same structure emerges at all scales. Across eight models from two families (Qwen2.5 and OLMo2, 1B-32B), we identify three geometric phases. Updates are approximately orthogonal to the residual stream throughout; what distinguishes the phases is their effect on the effective rank, which expands, stabilizes, and concentrates. In the first, Seeding Multiplexing, feed-forward memories and attention layers seed a candidate set in superposition in family-specific proportions, with the final token rising as leading candidate from 20% to 35% of positions across this phase. In the second, Hoisting Overriding, updates override existing subspaces to concentrate the candidate distribution without expanding the rank. In the third, Focal Convergence, high-energy low-rank updates write the winner into a form aligned with the unembedding direction. Phases 1 and 3 grow slowly with model depth, while Phase 2 expands linearly. The additional capacity of deeper LLMs is largely absorbed by candidate disambiguation.

Gianfranco Lombardo, Giuseppe Trimigno, Stefano Cagnoni

Department of Engineering and Architecture University of Parma Parma, IT 43125

Next-Token Prediction Layer-Wise Residual Stream Feed-Forward Subspace Affine

May 8, 2026cs.LG

Beyond Linear Attention: Softmax Transformers Implement In-Context Reinforcement Learning

In-context reinforcement learning (ICRL) studies agents that, after pretraining, adapt to new tasks by conditioning on additional context without parameter updates. Existing theoretical analyses of ICRL largely rely on linear attention, which replaces the softmax function in the standard attention with an identity mapping. This paper provides the first theoretical understanding of ICRL without making the unrealistic linear attention simplification. In particular, we consider the standard softmax attention used in practice. We show that, with certain parameters, the layerwise forward pass of a Transformer with such softmax attention is equivalent to iterative updates of a weighted softmax temporal difference (TD) learning algorithm. Here, weighted softmax TD is a new RL algorithm that performs policy evaluation in kernel space and adopts both linear TD and tabular TD as special cases. We also prove that under a certain contraction condition, the policy evaluation error decays as the number of layers grows, with the identified parameters above. Finally, we prove that those parameters are a global minimizer of a pretraining loss, explaining their emergence in our numerical experiments.

Zixuan Xie, Xinyu Liu, Claire Chen +3

University of Virginia · California Institute of Technology · Purdue University

In-Context Learning Linear Attention Transformer Architectures Gumbel-Softmax Relaxation Layer-Wise Policy Evaluation

May 8, 2026cs.CV

Amortized-Precision Quantization for Early-Exit Vision Transformers

Vision Transformers (ViTs) achieve strong performance across vision tasks, yet their deployment with low-precision early exiting remains fragile. Existing quantization methods assume static full-depth execution, making them unstable when exit decisions are perturbed by quantization noise, which can amplify errors along dynamic inference paths. In this paper, we introduce Amortized-Precision Quantization (APQ), a utilization-aware formulation that accounts for layer-wise stochastic exposure to quantization noise and reveals depth-precision trade-offs. Building on APQ, we propose Mutual Adaptive Quantization with Early Exiting (MAQEE), a bi-level framework that jointly optimizes exit thresholds and bit-widths under explicit risk control to improve inference stability. MAQEE establishes a superior Pareto frontier in the accuracy-efficiency trade-off, reducing BOPs by up to 95% while maintaining accuracy and outperforming strong baselines by up to 20% across classification, detection, and segmentation tasks.

Rui Fang, Hsi-Wen Chen, Ming-Syan Chen

National Taiwan University

Self-Supervised Vision Transformers Vision Transformer Layer-Wise Transformer Architectures

May 8, 2026cs.CL

Understanding Performance Collapse in Layer-Pruned Large Language Models via Decision Representation Transitions

Layer pruning efficiently reduces Large Language Model (LLM) computational costs but often triggers sudden performance collapse. Existing representation-based analyses struggle to explain this mechanism. We propose studying pruning through decision representation. Focusing on multiple-choice tasks, we introduce two metrics, Decision Margin and Option Frequency, and an Iterative Pruning method to analyze layer-wise decision dynamics. Our findings reveal a sharp decision transition that partitions the network into two stages: a Silent Phase, where the model cannot yet predict the correct answer, and a Decisive Phase, where the correct prediction emerges. We also find that pruning the Decisive Phase has minimal impact, whereas pruning the Silent Phase triggers immediate performance collapse, highlighting its extreme sensitivity to structural changes. Therefore, we conclude that pruning-induced collapse stems from disrupting the Silent Phase, which prevents the critical decision transition from occurring.

Boyu Shi, Chang Liu, ChuanBao Gao +2

School of Computer Science and Engineering, Southeast University, Nanjing, China · Key Laboratory of New Generation Artificial Intelligence Technology and Its Interdisciplinary Applications (Southeast University), Ministry of Education, China

Layer-Wise Large Language Models Fail Representation Quality

May 8, 2026cs.LG

Geometric Asymmetry in MoE Specialization: Functional Decorrelation and Representational Overlap

Mixture-of-Experts (MoE) architectures achieve scalable capacity through sparse routing, yet the geometric structure of expert specialization remains poorly understood. We introduce a unified Jacobian-PCA-Grassmann framework for analyzing MoE layers in both function space and representation space. Across pretrained MoE Transformers (Mistral, Qwen), we find a consistent structural asymmetry: experts exhibit strong functional decorrelation (consistently low, near-zero cross-expert Jacobian alignment) while their routed representations occupy distinct but partially overlapping subspaces. This indicates that functional decorrelation and representation overlap coexist rather than coincide in MoE specialization. Controlled routing experiments further indicate that routing sparsity appears to be a key factor shaping this geometry: top-k routing induces sharper functional separation and larger subspace divergence, whereas fully soft routing yields more entangled expert structure. Together, these results suggest a geometric interpretation in which MoE layers may be viewed as implementing locally decorrelated operators over overlapping submanifolds on a shared representation manifold, and provide a general diagnostic framework for studying conditional computation in modern Transformer architectures.

Feilong Liu

Mixture-Of-Experts Layer-Wise Transformer Architectures Asymmetry Jacobian

May 7, 2026cs.LG

UniPool: Learning Expert-to-Layer Ownership from Brief Global Access

Most Mixture-of-Experts (MoE) transformers preassign each expert to one layer for the whole of training. We study whether a brief global-access phase can learn a compatible expert-to-layer allocation that is then executed privately. UniPool-Lock gives every layer its own router over one global pool, balances aggregate pool usage, and scores experts with a scale-stable NormRouter. After the short ownership-learning phase, it assigns each expert to one layer, locks the disjoint allocation, and continues training as a layer-private MoE. With the same expert-FFN budget and routed expert FLOPs, this recipe lowers held-out loss relative to vanilla MoE by 0.024-0.037 across five dense-equivalent scales from 182M to 1.5B, including -0.0247 at 1.5B after 60B tokens. The ownership-learning phase lasts 2K steps, about 3.3% of training, and post-lock step time is within -0.7% to +2.8% of vanilla MoE in our throughput measurements. Controls locate the gain in full-pool training and in the allocation it produces: a random disjoint allocation fixed at initialization, trained with the same router and losses, matches vanilla, whereas locking the allocation learned during the full-pool phase recovers nearly all of the persistent full-pool gain, and substituting a random allocation at the lock forfeits about half of it. Keeping full-pool access throughout training (UniPool-Full) also improves over vanilla MoE at four scales and outperforms it with only 66.7% (182M) to 50% (469M and 650M) of its expert parameters.

Minbin Huang, Han Shi, Chuanyang Zheng +5

The Chinese University of Hong Kong · Huawei Technologies · The University of Hong Kong

Mixture-Of-Experts Experts Layer-Wise Expert Demonstrations

May 7, 2026cs.LG

Is One Layer Enough? Understanding Inference Dynamics in Tabular Foundation Models

Transformer-based tabular foundation models (TFMs) dominate small to medium tabular predictive benchmark tasks, yet their inference mechanisms remain largely unexplored. We present the first large-scale mechanistic study of layerwise dynamics in 6 state-of-the-art tabular in-context learning models. We explore how predictions emerge across depth, identify distinct stages of inference and reveal latent-space dynamics that differ from those of language models. Our findings indicate substantial depthwise redundancy across multiple models, suggesting iterative refinement with overlapping computations during inference stages. Guided by these insights, we design a proof-of-concept, looped single-layer model that uses only 20% of the original model's parameters while achieving comparable performance. The code is available at https://github.com/amirbalef/is_one_layer_enough.

Amir Rezaei Balef, Mykhailo Koshil, Katharina Eggensperger

TU Dortmund University, Dortmund, Germany · Lamarr Institute for Machine Learning and Artificial Intelligence, Dortmund, Germany · University of Tübingen, Tübingen, Germany

Tabular Foundation Models Transformer Architectures Layer-Wise Foundation Model Inference Dynamics Latent Dynamics

May 6, 2026cs.CL

Rethinking Local Learning: A Cheaper and Faster Recipe for LLM Post-Training

LLM post-training typically propagates task gradients through the full depth of the model. Although this end-to-end structure is simple and general, it couples task adaptation to full-depth activation storage, long-range backward dependencies and direct task-gradient access to pretrained representations. We argue that this full-depth backward coupling can be unnecessarily expensive and intrusive, particularly when post-training supervision is much narrower than pre-training. To this end, we propose \textbf{LoPT}: Local-Learning Post-Training, a simple post-training strategy that makes gradient reach an explicit design choice. LoPT places a single gradient boundary at the transformer midpoint: the second-half block learns from the task objective, while the first-half block is updated by a lightweight feature-reconstruction objective to preserve useful representations and maintain interface compatibility. LoPT shortens the task-induced backward path while limiting direct interference from narrow task gradients on early-layer representations. Extensive experiments demonstrate that LoPT achieves competitive performance with lower memory cost, higher training efficiency and better retention of pretrained capabilities. Our code is available at: https://github.com/HumyuShi/LoPT

Hengyu Shi, Tianyang Han, Peizhe Wang +3

1Independent Researcher · 2D4 Lab · 3Southeast University

Post-Training Layer-Wise Recipe

May 4, 2026cs.LG

Trust, but Verify: Peeling Low-Bit Transformer Networks for Training Monitoring

Understanding whether deep neural networks are effectively optimized remains challenging, as training occurs in highly nonconvex landscapes and standard metrics provide limited visibility into layer-wise learning quality. This challenge is particularly acute for transformer-based language models, where training is expensive, models are often reused in frozen form, and poorly optimized layers can silently degrade performance. We propose a layer-wise peeling framework for monitoring training dynamics, in which each transformer layer is locally optimized against intermediate representations of the trained model. By constructing lightweight, layer-specific reference solutions and projecting layers onto multiple intermediate outputs via different permutations, we obtain achievable baselines that enable fine-grained diagnosis of under-optimized layers. Experiments on decoder-only transformer models show that these layer-wise reference bounds can match or even surpass the trained model at various stages of training, exposing inefficiencies that remain hidden in aggregate loss curves. We further demonstrate that this analysis remains effective under binarization and quantized settings, where training dynamics are particularly fragile. Across all numerical results, the proposed bounds consistently separate apparent convergence from effective optimality, highlighting optimization opportunities that are invisible when relying on training loss alone.

Arian Eamaz, Farhang Yeganegi, Mojtaba Soltanalian

Department of Electrical and Computer Engineering University of Illinois Chicago Chicago, IL, USA

Layer-Wise Transformer Architectures Transformer Encoder AI Trustworthiness

Apr 27, 2026cs.LG

Rethinking Layer Redundancy: Calibration Matters More Than Search in LLM Depth Pruning

Depth pruning improves the inference efficiency of large language models by removing Transformer blocks. Prior work typically treats layer redundancy as an inherent structural property of pretrained networks, emphasizing importance criteria and search algorithms to identify removable layers. In this study, we empirically investigate depth pruning from a functional perspective. Evaluating representative LLM families across diverse calibration configurations and multiple search algorithms, we show that different configurations produce different pruning patterns. Furthermore, under a fixed calibration configuration, complex search algorithms yield marginal performance improvements over simple one-shot methods, converging to similar pruned subsets. Overall, our results suggest that the calibration configuration plays a substantially larger role than the choice of search algorithm in shaping pruning patterns and calibration perplexity, while contributing comparably to variance in downstream reasoning accuracy. This indicates that future pruning efforts may benefit from prioritizing the calibration configuration over search complexity.

Minkyu Kim, Vincent-Daniel Yun, Youngrae Kim +3

Neural Superintelligence Lab, MODULABS, Republic of Korea · University of Southern California, United States · Boston University, United States +2

Language Model Perplexity Layer-Wise Redundancy Downstream Reasoning

Apr 27, 2026cs.CR

Layerwise Convergence Fingerprints for Runtime Misbehavior Detection in Large Language Models

Large language models deployed at runtime can misbehave in ways that clean-data validation cannot anticipate: training-time backdoors lie dormant until triggered, jailbreaks subvert safety alignment, and prompt injections override the deployer's instructions. Existing runtime defenses address these threats one at a time and often assume a clean reference model, trigger knowledge, or editable weights, assumptions that rarely hold for opaque third-party artifacts. We introduce Layerwise Convergence Fingerprinting (LCF), a tuning-free runtime monitor that treats the inter-layer hidden-state trajectory as a health signal: LCF computes a diagonal Mahalanobis distance on every inter-layer difference, aggregates via Ledoit-Wolf shrinkage, and thresholds via leave-one-out calibration on 200 clean examples, with no reference model, trigger knowledge, or retraining. Evaluated on four architectures (Llama-3-8B, Qwen2.5-7B, Gemma-2-9B, Qwen2.5-14B) across backdoors, jailbreaks, and prompt injection (56 backdoor combinations, 3 jailbreak techniques, and BIPIA email + code-QA), LCF reduces mean backdoor attack success rate (ASR) below 1% on Qwen2.5-7B and Gemma-2 and to 1.3% on Qwen2.5-14B, detects 92-100% of DAN jailbreaks (62-100% for GCG and softer role-play), and flags 100% of text-payload injections across all eight (model, domain) cells, at 12-16% backdoor FPR and <0.1% inference overhead. A single aggregation score covers all three threat families without threat-specific tuning, positioning LCF as a general-purpose runtime safety layer for cloud-served and on-device LLMs.

Nay Myat Min, Long H. Pham, Jun Sun

Singapore Management University

Fingerprint Jailbreak Success Rates Runtime Safety Filtering Layer-Wise Runtime

Apr 22, 2026cs.MA

AGNT2: Autonomous Agent Economies on Interaction-Optimized Layer 2 Infrastructure

Current blockchain Layer 2 solutions, including Optimism, Arbitrum, zkSync, and their derivatives, optimize for human-initiated financial transactions. Autonomous AI agents instead generate high-frequency, semantically rich service invocations among mutually untrusting principals. Existing chains treat those interactions as generic calldata, forcing identity, escrow, dependency ordering, and session state to be encoded above the execution layer at the wrong cost point. We present AGNT2, a three-tier stack purpose-built for agent and microservice coordination on-chain. AGNT2 combines: (1) a sidecar deployment pattern that turns any Docker container into an on-chain agent without application-code modification; (2) Layer Top P2P state channels for established bilateral pairs (<100 ms, rough design target 1K-5K TPS per pair, 10M+ aggregate TPS design envelope under endpoint-resource limits), Layer Core as a dependency-aware sequenced rollup for first-contact and multi-party interactions (500 ms-2 s, 300K-500K TPS design target), and Layer Root settlement with computational fraud proofs anchored to any EVM L1; and (3) an agent-native execution environment plus interaction trie that make service invocation, identity, reputation, capabilities, and session context first-class protocol objects. This paper focuses on the execution-layer systems problem: sequencing, state, settlement, and the data-availability (DA) bandwidth gap that bounds all three. Simulation and analytical modeling support the architecture, and prototype measurements validate selected components, but no end-to-end Layer Core implementation exists yet. Practical deployment is currently constrained to roughly 10K-100K TPS by DA throughput, leaving a ~100x gap at the target ceiling. AGNT2 argues that the agent economy requires a dedicated execution layer rather than a general-purpose chain repurposed for agents.

Anbang Ruan, Xing Zhang

NetX Foundation

Blockchain Infrastructure Layer-Wise

Apr 22, 2026cs.CL

LayerTracer: A Joint Task-Particle and Vulnerable-Layer Analysis framework for Arbitrary Large Language Model Architectures

Currently, Large Language Models (LLMs) feature a diversified architectural landscape, including traditional Transformer, GateDeltaNet, and Mamba. However, the evolutionary laws of hierarchical representations, task knowledge formation positions, and network robustness bottleneck mechanisms in various LLM architectures remain unclear, posing core challenges for hybrid architecture design and model optimization. This paper proposes LayerTracer, an architecture-agnostic end-to-end analysis framework compatible with any LLM architecture. By extracting hidden states layer-by-layer and mapping them to vocabulary probability distributions, it achieves joint analysis of task particle localization and layer vulnerability quantification. We define the task particle as the key layer where the target token probability first rises significantly, representing the model's task execution starting point, and the vulnerable layer is defined as the layer with the maximum Jensen-Shannon (JS) divergence between output distributions before and after mask perturbation, reflecting its sensitivity to disturbances. Experiments on models of different parameter scales show that task particles mainly appear in the deep layers of the model regardless of parameter size, while larger-parameter models exhibit stronger hierarchical robustness. LayerTracer provides a scientific basis for layer division, module ratio, and gating switching of hybrid architectures, effectively optimizing model performance. It accurately locates task-effective layers and stability bottlenecks, offering universal support for LLM structure design and interpretability research.

Yuhang Wu, Qinyuan Liu, Qiuyang Zhao +1

China Electronic Technology Nanhu Research Institute, Jiaxing, China

Layer-Wise Frozen Language Model Traces Joint Search

Apr 22, 2026cs.LG

Formalising the Logit Shift Induced by LoRA: A Technical Note

This technical note provides a first-order formalisation of the logit shift and fact-margin change induced by Low-Rank Adaptation (LoRA). Using a first-order Fréchet approximation around the base model trajectory, we show that the multi-layer LoRA effect can be decomposed into a linear summation of layerwise contributions and a higher-order remainder term representing inter-layer coupling.

Xiang Shi, Shuaizhi Cheng, Mingwei Li

Imperial College London · Harbin Institute of Technology · KigLand Learning Lab

Logit Lens Layer-Wise Change Fréchet Inception Distance Documentation

Apr 21, 2026cs.AI

SimDiff: Depth Pruning via Similarity and Difference

Depth pruning improves the deployment efficiency of large language models (LLMs) by identifying and removing redundant layers. A widely accepted standard for this identification process is to measure the similarity between layers using cosine distance. However, we find that methods relying solely on this one-dimensional heuristic can exhibit unpredictable performance and even catastrophic collapse across different architectures. To address this issue, we propose SimDiff, a novel layer importance criterion that jointly evaluates layers from two orthogonal perspectives: representational similarity and transformation difference. The difference is quantified using two distinct metrics: MSSD, which is sensitive to outliers and identifies layers that make decisive corrections, and MASD, which robustly measures a layer's average contribution. Extensive experiments on multiple models ranging from 0.5B to 13B parameters demonstrate that SimDiff significantly outperforms state-of-the-art baselines across various pruning ratios. Notably, our method retains over 91% of LLaMA2-7B's performance at a 25% pruning ratio and achieves up to a 1.49x inference speedup when pruning 12 layers on LLaMA3.1-8B. We also show that pruned models can be effectively recovered with minimal fine-tuning.

Yuli Chen, Shuhao Zhang, Fanshen Meng +4

Unstructured Pruning Large Language Model Compression Layer-Wise Similarity and Metrics Nvidia Isaac Sim

Apr 21, 2026cs.LG

ZC-Swish: Stabilizing Deep BN-Free Networks for Edge and Micro-Batch Applications

Batch Normalization (BN) is a cornerstone of deep learning, yet it fundamentally breaks down in micro-batch regimes (e.g., 3D medical imaging) and non-IID Federated Learning. Removing BN from deep architectures, however, often leads to catastrophic training failures such as vanishing gradients and dying channels. We identify that standard activation functions, like Swish and ReLU, exacerbate this instability in BN-free networks due to their non-zero-centered nature, which causes compounding activation mean-shifts as network depth increases. In this technical communication, we propose Zero-Centered Swish (ZC-Swish), a drop-in activation function parameterized to dynamically anchor activation means near zero. Through targeted stress-testing on BN-free convolutional networks at depths 8, 16, and 32, we demonstrate that while standard Swish collapses to near-random performance at depth 16 and beyond, ZC-Swish maintains stable layer-wise activation dynamics and achieves the highest test accuracy at depth 16 (51.5%) with seed 42. ZC-Swish thus provides a robust, parameter-efficient solution for stabilizing deep networks in memory-constrained and privacy-preserving applications where traditional normalization is unviable.

Suvinava Basak

TU Braunschweig, Universitätspl. 2, 38106 Braunschweig, Germany

Batch Normalization Deep Network Layer-Wise Edge

Apr 21, 2026cs.LG

RDP LoRA: Geometry-Driven Identification for Parameter-Efficient Adaptation in Large Language Models

Fine-tuning Large Language Models (LLMs) remains structurally uncertain despite parameter-efficient methods such as Low-Rank Adaptation (LoRA), as the layer-specific roles of internal representations are poorly understood, leading to heuristic decisions about where adaptation should be applied. We model the evolution of hidden states as a high-dimensional geometric trajectory and propose using the Ramer-Douglas-Peucker (RDP) algorithm, a parameter-free and training-free polygon simplification method that preserves global structural transitions while eliminating locally redundant changes, to identify critical breakpoints along the representation path. Crucially, we use these geometric pivots not merely for analysis, but as a direct decision signal for determining which layers should be adapted during parameter-efficient fine-tuning. By integrating this geometry-aware layer selection strategy into LoRA fine-tuning of Qwen3-8B-Base, we achieve superior performance on MMLU-Math using only 13 RDP-selected layers (81.67%), significantly outperforming both full 36-layer adaptation (79.32%) and random 13-layer selection (75.56%), as well as the baseline Qwen3-8B-Base model (74.25%). These results demonstrate that leveraging the intrinsic geometry of representation trajectories provides a robust, interpretable, and training-free signal for optimizing layer selection during model adaptation.

Yusuf Çelebi, Yağız Asker, Özay Ezerceli +4

Large Language Model Fine-Tuning Parameter-Efficient Adaptation Layer-Wise Geometry-Aware

Apr 21, 2026cs.LG

Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control

Inference-time LLM alignment methods, particularly activation steering, offer an alternative to fine-tuning by directly modifying activations during generation. Existing methods, however, often rely on non-anticipative interventions that ignore how perturbations propagate through transformer layers and lack online error feedback, resulting in suboptimal, open-loop control. To address this, we show empirically that, despite the nonlinear structure of transformer blocks, layer-wise dynamics across multiple LLM architectures and scales are well-approximated by locally-linear models. Exploiting this property, we model LLM inference as a linear time-varying dynamical system and adapt the classical linear quadratic regulator to compute feedback controllers using layer-wise Jacobians, steering activations toward desired semantic setpoints in closed-loop with minimal computational overhead and no offline training. We also derive theoretical bounds on setpoint tracking error, enabling formal guarantees on steering performance. Using a novel adaptive semantic feature setpoint signal, our method yields robust, fine-grained behavior control across models, scales, and tasks, including state-of-the-art modulation of toxicity, truthfulness, refusal, and arbitrary concepts, surpassing baseline steering methods. Our code is available at: https://github.com/trustworthyrobotics/lqr-activation-steering

Julian Skifstad, Xinyue Annie Yang, Glen Chou

1Georgia Institute of Technology, Atlanta, GA, USA. Schools of Electrical and Computer Engineering · 2Computer Science · 3Cybersecurity and Privacy, Aerospace Engineering

Linear Activation Steering Model Activations LLM Inference Optimization Layer-Wise

Apr 20, 2026cs.CL

Probing for Reading Times

Probing has shown that language model representations encode rich linguistic information, but it remains unclear whether they also capture cognitive signals about human processing. In this work, we probe language model representations for human reading times. Using regularized linear regression on two eye-tracking corpora spanning five languages (English, Greek, Hebrew, Russian, and Turkish), we compare the representations from every model layer against scalar predictors -- surprisal, information value, and logit-lens surprisal. We find that the representations from early layers outperform surprisal in predicting early-pass measures such as first fixation and gaze duration. The concentration of predictive power in the early layers suggests that human-like processing signatures are captured by low-level structural or lexical representations, pointing to a functional alignment between model depth and the temporal stages of human reading. In contrast, for late-pass measures such as total reading time, scalar surprisal remains superior, despite its being a much more compressed representation. We also observe performance gains when using both surprisal and early-layer representations. Overall, we find that the best-performing predictor varies strongly depending on the language and eye-tracking measure.

Eleftheria Tsipidi, Samuel Kiegeland, Francesco Ignazio Re +4

ETH Zürich · Toyota Technological Institute at Chicago · University College London

Readability Eye Tracking Layer-Wise Language Modeling Surprisal

Apr 20, 2026cs.IR

Modular Representation Compression: Adapting LLMs for Efficient and Effective Recommendations

Recently, large language models (LLMs) have advanced recommendation systems (RSs), and recent works have begun to explore how to integrate LLMs into industrial RSs. While most approaches deploy LLMs offline to generate and pre-cache augmented representations for RSs, high-dimensional representations from LLMs introduce substantial storage and computational costs. Thus, it is crucial to compress LLM representations effectively. However, we identify a counterintuitive phenomenon during representation compression: Mid-layer Representation Advantage (MRA), where representations from middle layers of LLMs outperform those from final layers in recommendation tasks. This degraded final layer renders existing compression methods, which typically compress on the final layer, suboptimal. We interpret this based on modularity theory that LLMs develop spontaneous internal functional modularity and force the final layer to specialize in the proxy training task. Thus, we propose \underline{M}odul\underline{a}r \underline{R}epresentation \underline{C}ompression (MARC) to explicitly control the modularity of LLMs. First, Modular Adjustment explicitly introduces compression and task adaptation modules, enabling the LLM to operate strictly as a representation-learning module. Next, to ground each module to its specific task, Modular Task Decoupling uses information constraints and different network structures to decouple tasks. Extensive experiments validate that MARC addresses MRA and produces efficient representations. Notably, MARC achieved a 2.82% eCPM lift in an online A/B test within a large-scale commercial search advertising scenario.

Yunjia Xi, Menghui Zhu, Jianghao Lin +4

Shanghai Jiao Tong University Shanghai, China · Huawei Noah’s Ark Lab Shanghai, China · Antai College of Economics and Management, Shanghai Jiao Tong University Shanghai, China

Multimodal Representations Layer-Wise Data Compression Methods Modular Framework

Apr 20, 2026cs.AI

Polysemantic Experts, Monosemantic Paths: Routing as Control in MoEs

An LLM's residual stream is both state and instruction: it encodes the current context and determines the next transformation. We introduce a parameter-free decomposition for Mixture-of-Experts models that splits each layer's hidden state into a control signal that causally drives routing and an orthogonal content channel invisible to the router. Across six MoE architectures, we find that models preserve surface-level features (language, token identity, position) in the content channel, while the control signal encodes an abstract function that rotates from layer to layer. Because each routing decision is low-bandwidth, this hand-off forces compositional specialization across layers. While individual experts remain polysemantic, expert paths become monosemantic, clustering tokens by semantic function across languages and surface forms. The same token (e.g., ":") follows distinct trajectories depending on whether it serves as a type annotation, an introductory colon, or a time separator. Our decomposition identifies the source of this structure: clusters in the control subspace are substantially more monosemantic than those in the full representation. As a result, the natural unit of interpretability in MoEs is not the expert but the trajectory.

Charles Ye, Bo Yuan, Lee Sharkey

Independent · Georgia Institute of Technology · Goodfire

Mixture-Of-Experts Layer-Wise Semantic Representations Sparse Structural Specialization Residual Stream Channel

Apr 19, 2026cs.LG

Decomposing the Depth Profile of Fine-Tuning

Fine-tuning adapts pretrained networks to new objectives. Whether the resulting depth profile of representational change reflects an intrinsic property of the model or the magnitude of gradient flow has not been tested directly. We measure this profile across 240 fine-tuning runs spanning 15 models in four architecture families (encoder and decoder transformers, a state-space model, and an RNN) at scales from 125M to 6.9B parameters. Representational change concentrates in output-proximal layers in every standard-training run except one. We apply a per-layer control that equalizes

\|ΔW\|/\|W\|

across layers after each optimizer step. Under this control, the profile persists in some conditions and collapses in others. At 125M--350M, sequential-block architectures (BERT, OPT, GPT-2) retain the slope across tested objectives while parallel-block architectures (Pythia, CodeGen) retain it only for causal-language-modeling objectives. This architectural distinction narrows at 1.3B--1.4B, where both block types show positive equal-step slopes for CausalLM. Under standard training, profile shape is described by two additional axes: steepness tracks a training-free objective distance at initialization, and profile width is dominated by architecture. We treat the locality gradient, the depthwise slope of representational change, as a composite phenomenon whose components are scale-dependent.

Jayadev Billa

Layer-Wise Model Fine-Tuning Gradient Representational Collapse Transformer Encoder Profile

Apr 17, 2026cs.CL

Beyond Surface Statistics: Robust Conformal Prediction for LLMs via Internal Representations

Large language models are increasingly deployed in settings where reliability matters, yet output-level uncertainty signals such as token probabilities, entropy, and self-consistency can become brittle under calibration--deployment mismatch. Conformal prediction provides finite-sample validity under exchangeability, but its practical usefulness depends on the quality of the nonconformity score. We propose a conformal framework for LLM question answering that uses internal representations rather than output-facing statistics: specifically, we introduce Layer-Wise Information (LI) scores, which measure how conditioning on the input reshapes predictive entropy across model depth, and use them as nonconformity scores within a standard split conformal pipeline. Across closed-ended and open-domain QA benchmarks, with the clearest gains under cross-domain shift, our method achieves a better validity--efficiency trade-off than strong text-level baselines while maintaining competitive in-domain reliability at the same nominal risk level. These results suggest that internal representations can provide more informative conformal scores when surface-level uncertainty is unstable under distribution shift.

Yanli Wang, Peng Kuang, Xiaoyu Han +2

Imperial College London · Zhejiang University · University of Illinois Urbana-Champaign +1

Online Conformal Prediction Layer-Wise

Apr 16, 2026cs.LG

DLink: Distilling Layer-wise and Dominant Knowledge from EEG Foundation Models

EEG foundation models (EFMs) achieve strong cross-subject and cross-task generalization through large-scale pretraining and downstream fine-tuning. Through empirical analysis, we observe that (i) task-adapted EFMs provide strong decoding performance but incur substantial overhead when retained as inference backbones, making knowledge distillation a natural route for optimizing compact students; and (ii) direct distillation from a fixed teacher representation underutilizes EFM knowledge, as task-discriminative information is distributed across intermediate layers rather than concentrated in the final layer. These observations motivate DLink (Distilling Layer-wise and Dominant Knowledge), a spectrally guided distillation framework with input-conditioned layer routing for transferring EFM knowledge into compact students. DLink uses a lightweight router to aggregate teacher layers for each input, and aligns magnitude and phase spectra to mitigate compression-induced spectral distortion in learned representations. The routed teacher knowledge is internalized by a project-then-compress student; the teacher and router are used only during training. Experiments on four EEG benchmarks show that DLink improves matched compact students and remains competitive with lightweight baselines, narrowing the gap to fine-tuned EFMs while substantially reducing parameters, FLOPs, and CPU-only inference latency.

Jingyuan Wang, Zhihao Jia, Chenyu Liu +7

1Xiamen University · 2Nanyang Technological University · Institute of Automation, Chinese Academy of Sciences +1

Electroencephalography Foundation Models Small-Sample Electroencephalogram Datasets Knowledge Distillation Layer-Wise Foundation Model

Apr 16, 2026cs.AI

Intermediate Layers Encode Optimal Biological Representations in Single-Cell Foundation Models

Current single-cell foundation model benchmarks universally extract final layer embeddings, assuming these represent optimal feature spaces. We systematically evaluate layer-wise representations from scFoundation (100M parameters) and Tahoe-X1 (1.3B parameters) across trajectory inference and perturbation response prediction. Our analysis reveals that optimal layers are task-dependent (trajectory peaks at 60% depth, 31% above final layers) and context-dependent (perturbation optima shift 0-96% across T cell activation states). Notably, first-layer embeddings outperform all deeper layers in quiescent cells, challenging assumptions about hierarchical feature abstraction. These findings demonstrate that "where" to extract features matters as much as "what" the model learns, necessitating systematic layer evaluation tailored to biological task and cellular context rather than defaulting to final-layer embeddings.

Vincenzo Yuto Civale, Roberto Semeraro, Andrew David Bagdanov +1

University of Siena · University of di Firenze · University of Firenze

Cells Layer-Wise Biological Single-Cell Foundation Models Trajectory Generation

Mar 16, 2026cs.CL

When Does Sparsity Mitigate the Curse of Depth in LLMs

Recent work has demonstrated the curse of depth in large language models (LLMs), where later layers contribute less to learning and representation than earlier layers. Such under-utilization is linked to the accumulated growth of variance in Pre-Layer Normalization, which can push deep blocks toward near-identity behavior. In this paper, we provide evidence that sparsity-like mechanisms can dampen variance propagation and are associated with improved depth utilization Our investigation covers two sources of sparsity: (i) implicit sparsity, which emerges from training and data conditions, including weight sparsity induced by weight decay and attention sparsity induced by long-context inputs; and (ii) explicit sparsity, which is enforced by architectural design, including key/value-sharing in Grouped-Query Attention and expert-activation sparsity in Mixtureof-Experts. Our claim is thoroughly supported by controlled depth-scaling experiments and targeted layer effectiveness interventions. Across settings, we observe a consistent relationship: mechanisms with reduced effective interaction density tend to exhibit lower output variance and better layer differentiation. We eventually distill our findings into a practical rule-of-thumb recipe for training depth-effective LLMs, yielding a notable 4.6 accuracy improvement on downstream tasks. Our results suggest that sparsity-like design choices are an important and previously underemphasized factor in effective depth scaling for LLMs. Code is available at https://github. com/pUmpKin-Co/SparsityAndCoD.

Dilxat Muhtar, Xinyuan Song, Sebastian Pokutta +4

Max Planck Institute for Intelligent Systems · ELLIS Institute Tübingen · Tübingen AI Center +4

Sparsity Layer-Wise Batch Normalization Variance

Mar 1, 2026cs.IT

Curvature-Weighted Capacity Allocation: A Minimum Description Length Framework for Layer-Adaptive Large Language Model Optimization

Layer-wise capacity in large language models is highly non-uniform: some layers contribute disproportionately to loss reduction, whereas others are nearly redundant. Existing layer-scoring methods provide sensitivity estimates but do not give a principled rule for converting those estimates into allocation or pruning decisions under a global hardware budget. We introduce a curvature-aware, MDL-inspired framework built around the layer gain

ζ_k^2=g_k^\top\widetilde H_{kk}^{-1}g_k

. This quantity equals twice the maximal decrease predicted by the regularized layer-restricted quadratic model and incorporates inverse local curvature; it is therefore a local surrogate for reducible risk, not a universal dominance claim over gradient-norm scores. After normalizing the gains into scores

q_k

, we formulate two convex programs: one allocates expert slots under diminishing returns, and the other assigns layer-wise pruning ratios while protecting high-score layers. Both continuous programs have unique globally optimal solutions characterized by one dual variable and computable in

O(K\log(1/\varepsilon))

time by bisection. We also prove a quadratic transfer-regret bound: when source and target score vectors differ by at most

δ

, the target surrogate cost of the transferred decision is within

O(δ^2)

of the target optimum. Experiments on Mistral-7B and Gemma-7B show clear allocation gains in some settings and competitive, though mixed, pruning performance. The framework therefore replaces an empirical score-to-decision heuristic with a budget-feasible optimization procedure whose guarantees apply to the stated continuous surrogates. Code is available on github repo - TKAI-LAB-Mali/Curvature-Weighted-Capacity-Allocation

Theophilus Amaefuna, Hitesh Vaidya, Anshuman Chhabra +1

1Bellini College of Artificial Intelligence, Cybersecurity and Computing University of South Florida, Tampa, Florida, USA

Layer-Wise Less Data

Feb 4, 2026cs.CL

LEAD: Layer-wise Expert-aligned Decoding for Faithful Radiology Report Generation

Radiology Report Generation aims to produce accurate and coherent diagnostics from medical images. Although large vision-language models improve report fluency and accuracy, they still suffer from hallucinations by generating plausible pathological descriptions that are not supported by the input images. Existing methods primarily rely on external knowledge guidance to facilitate the alignment between generated text and visual information. However, these approaches often ignore the inherent decoding priors and vision-language alignment biases in pretrained models and lack robustness due to reliance on constructed guidance. In this paper, we propose Layer-wise Expert-aligned Decoding, a method that directly intervenes in the internal decoding process of large vision-language models. A pathology-specific expert module is designed to extract discriminative pathological features, which are then injected into each decoder layer through a gated mechanism. This architecture enables the large language model to progressively incorporate expert features during generation through a learned layer-wise gating function, thereby mitigating decoding biases and steering generation toward factual consistency. Experiments on multiple public datasets demonstrate that the proposed method improves clinical accuracy and factual consistency while maintaining competitive report generation quality.

Ruixiao Yang, Yuanhe Tian, Di Dong +3

Beijing Institute of Technology · Zhongguancun Academy · Zhongguancun Institute of Artificial Intelligence +1

Radiology Report Generation Medical Vision-Language Models Vision-Language Alignment Medical Images Report Decoder Layers+2

Jan 14, 2026cs.CV

Attentive multilayer fusion for vision transformers

With the rise of large-scale foundation models, efficiently adapting them to downstream tasks remains a central challenge. Linear probing, which freezes the backbone and trains a lightweight head, is computationally efficient but often restricted to last-layer representations. We show that task-relevant information is distributed across the network hierarchy rather than encoded solely in the last layers. To leverage this distribution of information, we apply an attentive probing mechanism that dynamically fuses representations from all layers of a Vision Transformer. This attentive layer fusion (ALF) learns to identify the most relevant layers for a target task and combines low-level structural cues with high-level semantic abstractions. Across 20 diverse datasets and multiple pretrained foundation models, ALF achieves consistent, substantial gains over standard linear probes. Attention heatmaps further reveal that tasks different from the pre-training domain benefit most from intermediate representations. Overall, our findings underscore the value of intermediate layers and demonstrate a principled, task-aware approach for unlocking their potential for probing-based adaptation.

Laure Ciernik, Marco Morik, Lukas Thede +4

Machine Learning Group, Technische Universität Berlin, Berlin, Germany · Hector Fellow Academy, Karlsruhe, Germany · Berlin Institute for the Foundations of Learning and Data (BIFOLD), Berlin, Germany +7

Self-Supervised Vision Transformers Vision Transformer Progressive Attention Fusion Direct Feature Fusion Layer-Wise Foundation Model+1

Sep 28, 2025cs.CV

LUQ: Layerwise Ultra-Low Bit Quantization for Multimodal Large Language Models

Large Language Models (LLMs) with multimodal capabilities have revolutionized vision-language tasks, but their deployment often requires huge memory and computational resources. Post-training quantization (PTQ) has successfully compressed language models to as low as 1-bit precision, its effectiveness for multimodal LLMs (MLLMs) remains unexplored. In this paper, we present the first method for ultra-low-bit (<4-bit) quantization of MLLMs. Our analysis reveals that multimodal tokens and intermediate layer activations produced by them exhibit significantly higher entropy compared to text tokens, indicating greater functional complexity that makes MLLMs less tolerant to ultra-low bit quantization. However, this entropy varies significantly across layers, with some layers producing lower-entropy activation distributions that we empirically show can better tolerate ultra-low bit quantization. Existing PTQ methods optimize weight quantization within each layer but apply the same target precision uniformly, ignoring this variation in complexity across layers. Building on this insight, we propose LUQ: Layerwise Ultra-Low Bit Quantization, which characterizes each transformer layer's functional complexity via its output activation entropy and selectively applies ultra-low bit quantization to layers encoding simpler, more compressible functions. We also show that multimodal calibration (image and text tokens) boosts VQA performance in the ultra-low bit regime. Evaluated on LLaVA-1.5 and Qwen-2.5-VL across 9 VQA benchmarks, LUQ models use 40% and 31% less memory than their 4-bit counterparts while exhibiting less than 10% degradation on MME.

Shubhang Bhatnagar, Andy Xu, Kar-Han Tan +1

University of Illinois Urbana-Champaign · Work done as an intern at HP Inc. · University of California, Los Angeles +1

Large Language Model Quantization Multimodal Large Language Models Layer-Wise Knowledge-Based Visual Question Answering

Jul 9, 2025cs.CL

On the Effect of Uncertainty on Layer-wise Inference Dynamics

Understanding how large language models (LLMs) internally represent and process their predictions is central to detecting uncertainty and preventing hallucinations. While several studies have shown that models encode uncertainty in their hidden states, it is underexplored how this affects the way they process such hidden states. In this work, we demonstrate that the dynamics of output token probabilities across layers for certain and uncertain outputs are largely aligned, revealing that uncertainty does not seem to affect inference dynamics. Specifically, we use the Tuned Lens, a variant of the Logit Lens, to analyze the layer-wise probability trajectories of final prediction tokens across 11 datasets and 5 models. Using incorrect predictions as those with higher epistemic uncertainty, our results show aligned trajectories for certain and uncertain predictions that both observe abrupt increases in confidence at similar layers. We balance this finding by showing evidence that more competent models may learn to process uncertainty differently. Our findings challenge the feasibility of leveraging simplistic methods for detecting uncertainty at inference. More broadly, our work demonstrates how interpretability methods may be used to investigate the way uncertainty affects inference.

Sunwoo Kim, Haneul Yoo, Alice Oh

School of Computing, KAIST, Daejeon, South Korea.

Large Language Model Uncertainty Uncertainty Layer-Wise LLM Inference Optimization Inference Dynamics Interpretability+1

Oct 16, 2024cs.CL

Tuning Language Models by Mixture-of-Depths Ensemble

Transformer-based Large Language Models (LLMs) traditionally rely on final-layer loss for finetuning and final-layer representations for predictions, potentially overlooking the predictive power embedded in late layers. Interpretability tools such as the logit lens show that late-layer representations already carry largely formed, task-relevant predictions; here we ask whether that observation can be turned into an actionable training signal. We find that focusing tuning effort on these layers can yield losses comparable to those of the final layer, with complementary test-time behaviour. Building on this, we introduce a tuning framework, Mixture-of-Depths Ensemble (MoDE), which treats the late layers as an ensemble that contributes to the final logits through learned routing weights. MoDE can be applied on top of any existing tuning method (e.g., LoRA) and, in our experiments, modestly improves reasoning performance at a small parameter overhead. We present MoDE as a mechanism study showing that late-layer logits can be made directly useful for tuning, and that they can substitute for substantially larger trainable modules with comparable performance.

Haoyan Luo, Lucia Specia

University of Cambridge · Imperial College London

Large Language Model Fine-Tuning Layer-Wise Tuning Transformer Architectures Logit Lens Ensemble