Attention Head Analysis

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11 papers in the last four weeks, against 2 the four weeks before. 0.1% of all new papers.

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Latest papers 53

Oct 6, 2026cs.LG

Finding the Heads and the Neurons Responsible for Network Information Retrieval in Language Models

We ask whether specific attention heads, and more finely specific neurons inside those heads, are responsible for recognizing that a language model's context contains network infrastructure information (a hostname paired with its IP address), and whether that responsibility can be validated causally rather than by correlation alone. At the head level the answer is yes, across five models spanning three architecture families: in every model, a small set of heads (1 to 9 out of 128 to 1152 candidates), found by causal ablation screening and tested for selectivity against matched negative and context-free controls, supports a detector with 99.5--100% held-out accuracy. We then ask whether a head's responsibility concentrates into one neuron or stays spread across its dimensions; this is model-specific. In one model, the top head's signal concentrates into a single neuron, found independently by both a causal intervention and a correlational ranking, which agree exactly (AUC = 1.000, matching the full head). In another, the single clean head works as a whole (AUC = 1.000) but the best causally ranked neuron inside it does not (AUC = 0.665), so the responsibility there is spread across the head. The remaining three models fall in between. On an independent dataset collected by a different institution (reverse-DNS records rather than the discovery data), every model's full-head detector flags 100% of positive records; the single-neuron versions transfer less reliably, and in one model score below chance. Causal head-finding for a specific network-information entity works across models and architectures; how far that finding can be pushed down to individual neurons varies, and needs to be checked for each model.

Md Abdul Kadir, Md Mohasin Hossain, Daniel Sonntag

University of Oldenburg, Oldenburg, Germany · German Research Center for Artificial Intelligence · Saarland University, Saarbrucken, Germany

Attention Head Analysis LLM Interpretability Circuits in Language Models

Oct 5, 2026cs.LG

Spectral Geometry of Attention: From Information Routing to Uncertainty

In this work, we study transformer attention through the lens of spectral geometry and operator theory. We view each attention head as a functional map between Hilbert spaces of functions on the token sequence and derive a Token Difference Operator, whose spectral structure controls how token-space information is routed to the output. We show that standard Euclidean spectra are structurally biased by sinks, conflating mass concentration with genuine routing capacity. By recasting token space in the intrinsic probability geometry induced by attention, the token difference spectrum disentangles sink effects from routing capacity and provides a spectral description of the dimensionality of the head output. This yields a unified framework for analyzing attention maps, explaining sinks, routing collapse, and output dimensionality within a single operator-theoretic framework. In practice, by grounding attention heuristics in spectral geometry, we develop a novel attention-based uncertainty estimator that complements probability-based scores, with the largest gains on long-context inputs.

Giulio Viganò, Simone Melzi, Maks Ovsjanikov

University of Milano-Bicocca Milan, Italy · Ecole Polytechnique · LIX, Ecole Polytechnique IP Paris

Attention Head Analysis Attention Sinks

Sep 30, 2026cs.LG

Attention Function as an Intrinsic Inductive Bias: How Models' Behavior Diverges in Novel Contexts

Developmental psychology holds that certain priors are given to infants prior to experience rather than induced from data, and that the influence of such priors is suppressed under strong, well-constrained conditions but reasserts itself under weak ones. We ask whether an analogous principle holds for the Transformer: can the activation function given to attention heads serve as an intrinsic inductive bias? We propose Mixture of Function Attention (MoFA), a parameter-free modification to multi-head attention that fixes a ratio of softmax and sigmoid heads before training. Across five ratios, a 124M-parameter GPT-2 model, and five seeds, we find that this given ratio has little effect in-distribution -- differences between ratios are statistically negligible for moderate mixtures and remain small even at the extremes -- but its influence re-emerges sharply under zero-shot distribution shift across 15 out-of-distribution domains. Perplexity gaps between ratios widen by more than an order of magnitude on several domains, and the best-performing ratio tracks a single axis of domain structure, separating short, informal text (softmax-favoring) from technical, long-form text (sigmoid-favoring), that explains 78.3% of the variance in domain response. This reorganization is visible at the head level: sigmoid heads show an accelerating drop in attention entropy as their ratio increases, while softmax heads respond more modestly, yielding a consistent division of labor between the two head types. Our results suggest that activation choice functions as a given prior whose influence is masked in-distribution and re-emerges out-of-distribution.

Dong Gyun Kang, Megha Thukral, Kwangsoo Kim

College of Computing, Georgia Institute of Technology · Department of Transdisciplinary Medicine, Seoul National University Hospital

Attention Head Analysis OOD Generalization Attention Mechanisms Hybrid Attention

Sep 30, 2026cs.LG

When Do Attention-Head Ablations Support Causal Claims? Projection-Level Confounds, Floor Effects, and Matched Controls

Attention-head ablation, zeroing a head and measuring the resulting change in task performance, is a common method for inferring which components of a language model are causally responsible for a behavior. We show using GPT-2 small that this inference can be fragile unless the intervention semantics, evaluation metric, and controls are carefully validated. A natural post-projection implementation of "zeroing a head" is nearly uncorrelated with a corrected pre-projection ablation (Pearson r = 0.057) and selects a completely disjoint top-5 set of important heads. We also show that binary accuracy can hide effects at behavioral floors and near ceilings, whereas gold-token log-probability remains graded. Using a discovery/held-out split and 1,000 matched random-head and layer-matched-head control draws, the corrected per-head effect ranking is highly stable across splits (Spearman rho = 0.974), and the top-5 selected heads significantly exceed both control distributions (Monte Carlo p = 0.001). However, evidence for task specificity is not robust on GPT-2. Replication on DistilGPT2 preserves the intervention-semantic and matched-control findings. These results show that single-head ablation does not by itself justify a causal claim; defensible interpretation requires correct intervention placement, a non-saturated continuous metric, and matched held-out controls.

Juli Huang

Stanford University

Attention Head Analysis Causal Interventions in Language Models

Sep 29, 2026cs.AI

Which Attention Heads are like the Human Head? Not the Ones that Compute

Brain-AI alignment is often interpreted as a sign that model and brain perform similar computations. Whether the aligned units are causally involved in model computation is rarely checked. On an abstract pattern-completion task (AAABAAA

\rightarrow

B), we compare LLM attention-head representations with human EEG and test how ablating those heads affects task performance. Alignment and causation dissociate: brain-aligned heads contribute to performance, but their removal is substantially less disruptive than removal of heads selected via attribution patching. We compare two head sets that prior interpretability work defines without reference to the brain: concept vectors (CVs), which represent abstract patterns across formats, and function vectors (FVs), selected for their contribution to correct-answer prediction. Brain alignment shows little association with FV scores, while its association with CV scores varies across models. Among brain-aligned heads, we find recurring attention profiles: one emphasizes distinctive elements (novelty heads), the other repeating elements (repetition heads). The novelty family tracks salience and attends to the same elements that humans look at, yet its removal is less damaging than random ablation on average. Repetition heads contribute modestly to performance and are associated with abstract-pattern representation (CVs). Across 17 models spanning 3B-72B parameters, FV-ranked removal is substantially more disruptive than brain-ranked removal. Brain alignment thus captures how the model reads the stimulus, and only faintly captures how it represents the pattern and solves the task.

Christopher Pinier, Gustaw Opiełka, Hannes Rosenbusch +3

Psychological Methods, University of Amsterdam, Amsterdam, The Netherlands · Princeton Neuroscience Institute, Princeton University, Princeton, NJ, USA

Attention Head Analysis Cross-Modal Alignment Attention Head Specialization

Sep 28, 2026cs.CL

A mechanistic study of language model introspection

Large language models (LLMs) can sometimes report perturbations to their internal activations---even when the input provides no evidence that an intervention occurred. How do models detect and localize such internal changes? We study this question using a controlled task that keeps the input text fixed. We either inject a concept vector into the hidden state at one of ten token positions or apply no intervention. The model is asked to identify the perturbed position or report that no intervention occurred. Across three model families, we identify two small groups of attention heads with distinct roles in introspective reporting. Middle-layer gate heads influence whether the model reports a change, while router heads in a later layer help select the position to report. Interventions on gate heads can suppress position reports even when router heads supply location information. We further examine why reporting accuracy varies across concepts. Concept vectors that are localized more accurately produce stronger attention-score and output responses in gate heads, which is associated with better alignment of the induced key and value changes in their QK and OV computations. Together, these findings identify attention-head mechanisms supporting introspective detection and localization.

Jiahong Zou, Xiangkun Sun, Lingkai Kong +1

Shandong University · Tsinghua University · Northeastern University +1

Attention Head Analysis LLM Interpretability Language Model Introspection Metacognition in Language Models

Sep 28, 2026cs.LG

When Can Attention Heads Be Statically Defined?

Some attention heads learn similar patterns across inputs. Reusing these patterns could reduce training cost by avoiding repeated query-key score computation and softmax. Through controlled pretraining comparisons, we identify Selective Attention Freezing (SAF), which selects heads with low attention-pattern variance and replaces their attention weights with fitted post-softmax means halfway through training. We represent these fixed patterns with absolute-position and relative-distance preferences, reducing storage from quadratic to linear in sequence length. A fused kernel reconstructs the patterns and executes ordinary-attention and replaced heads together. At matched training-token budgets, replacing 25% of attention heads gives 1.056x faster post-replacement optimiser updates at 124M parameters and 4K context, with a 0.77% perplexity increase. At 1B and 8K context, post-replacement updates are 1.068x faster on four GPUs including communication, with a 0.51% perplexity increase. The resulting models also accelerate long-input finetuning and causal prefill. After associative-recall adaptation, the 124M model with 25% replacement generalises to more key-value pairs at a fixed length better than ordinary attention and two pruning controls.

Weixian Waylon Li, Yintao Tai, Marcio Fonseca +1

University of Edinburgh, United Kingdom · Chamber of Deputies, Brazil

Attention Head Analysis Efficient Attention Attention Head Specialization

Sep 27, 2026cs.LG

Rethinking Contextualization by Reinterpreting Attention Head Channels

Contextualization, the core operation of language modeling, transmits information across words to build sentence-specific word representations. Prior works mainly study contextualization, focusing on individual words and attention heads as a growing discrete dictionary, lacking a global view of their general behavior. Therefore, we propose a general principle: Globally, we find and estimate that different words carry different amounts of information, and less-informative words tend to absorb more contextual information. Specifically, these low-information words do not absorb contextual words uniformly, and finer-grained selectivity enables more precise routing to promote information transmission between matched words. Moreover, to find what mechanism causes such processing, we reinterpret attention heads as channels gated by their singular vectors and find that: (1) these singular vectors point to the hidden states of more informative words, allowing such words to write their information to others more strongly to act as information sources, and vice versa; and (2) these singular vectors can be viewed equally as hidden state features, enabling automated interpretation of attention heads beyond prior heuristic head discovery, also embedding heads into a continuous space rather than treating them as discrete, independent dictionary entries.

Hakaze Cho, Haolin Yang, Zhun Sun +3

RIKEN · Tohoku University · New York University +2

Attention Head Analysis Representation Geometry in Language Models Attention Head Specialization

Sep 23, 2026cs.CL

Scaling Attention Head Analysis via Gradient-Based Attribution in Context-Aware Machine Translation

In this paper, we introduce a gradient-based head attribution strategy where the Token-level Max-Margin loss is backpropagated to the attention maps. This framework enables a large-scale causal analysis of attention heads, making it suitable for LLMs. We evaluate our method on the task of disambiguation in Context-aware Machine Translation, where we analyze 50 phenomena across 4 models and 4 language directions. We empirically show the alignment of our method with the effects of increasing the attention scores of token-to-token relations on three models and two language directions, ensuring the robustness of our method. Our analysis reveals the presence of the "general-purpose" attention heads that improve the model's performance when attending to different relations. We find that the average attention a head assigns to a relation does not necessarily relate to the model's performance, which suggests that the models developed redundancies during training in terms of the head functions.

Paweł Mąka, Yusuf Can Semerci, Jan Scholtes +1

Department of Advanced Computing Sciences Maastricht University

Gradient-Based Attribution Attention Head Analysis Causal Interventions in Language Models Machine Translation

Sep 20, 2026cs.AI

Increasing Skill Level Recruits Deeper Attention Layers in a Frozen Chess Transformer

Chess involves complex reasoning in a deterministic environment, which makes it a useful setting for studying the mechanisms of computation inside transformers. The Maia-3 chess transformer takes Elo, a measure of competitive chess skill, as an input to the pre-trained network, so we can vary the skill the network is conditioned on with no change to its weights. Here we investigate how turning this skill dial affects self-attention. Ablating every attention head at every Elo from 700 to 2500, we find 1) increasing skill pushes the causal center of mass of the computation deeper, monotonically, for every chess piece and move type we measured; 2) the depth migration is much greater for specific tactics, especially knight forks, than for other move types; 3) the migration consists of deeper heads getting recruited for more specialized computations while one shared shallow head keeps a roughly constant contribution. These results may shed light on how conditioning inputs redistribute computation in larger transformers.

David Litman

Computational Neurobiology Laboratory, Salk Institute

Transformer Interpretability Attention Head Analysis Self-Attention

Sep 20, 2026cs.LG

Global Ranks Survive, Selected Heads Shift: BOS-Sink Topology under 4-bit Weight-Only Quantization

Sink-aware deployment may identify important first-token attention heads before a model is quantized, then reuse that map at the edge. We test when this shortcut is safe for 4-bit NF4 weight-only post-training quantization (PTQ). Our Sink Topology Consistency (STC) metrics separate global rank preservation, top-

k

set overlap, and layerwise sink-mass shift, and distinguish per-input sensitivity from calibration-map transfer. Across Qwen2.5-0.5B, Qwen2.5-1.5B, and Llama-3.2-1B, global bf16-to-4-bit ranks remain high at 4,096 tokens (

ρ_s \geq 0.980

), yet top-

k

Jaccard overlap is only 0.619-0.793, corresponding to 76.5-88.5% membership retention. The global statistic also masks local failures: terminal Qwen layers shift by 6.2-7.9x their model means, whereas Llama-3.2-1B shows low, nearly uniform drift. Under a C4-to-LongBench shift, cross-domain overlap degrades more than the within-domain precision comparison for both Qwen models, but not for Llama-3.2-1B. Matched-domain 4-bit recalibration reaches 90% of a split-half stability plateau at the smallest tested

n=8

for both Qwen models and

n=32

for Llama-3.2-1B, though not as a sharp threshold; for the two Qwen models, updating only selected layers does not reach the full-map stability criterion. On Jetson Orin NX, the 16-sample workload takes seconds for the two models with valid on-device sink measurements. The practical message is precise: global rankings often transfer, but discrete head sets, layer-local policies, and cross-domain calibration should be revalidated after quantization.

Kuanlin Chen, Chen-Wei Kuo, Cheng-En Ou

Independent Researcher Taoyuan, Taiwan · National Tsing Hua University Hsinchu, Taiwan

Attention Head Analysis 4-Bit Quantization Weight-Only Quantization Attention Sinks Attention Quantization Post-Training Quantization

Sep 14, 2026cs.LG

Attention Mean Fields Predict Average Representation Dynamics and Reveal Context-Specific Computation

A language model's representation geometry is not predetermined; it evolves as the model runs. A faithful account of that geometry must capture that dynamic process, and so cannot be based solely on model-independent statistics such as co-occurrence. Here we introduce a mean-field analysis of attention. The average attention from one token to another defines a kernel that carries representations layer to layer and can be iterated through the network to model how the geometry is transformed. We condition this average two ways. Conditioned on a whole corpus, the kernel predicts the average-case evolution of representation geometry. Conditioned instead on a single context, it predicts the expected geometry for that context. A head's departure from that prediction, its \emph{mean-field deviation}, isolates the context-specific computation that the mean field misses. Under the corpus-conditional reading, the kernel yields an open-loop model: from the input embeddings and the frozen weights alone, we can iterate the kernel and the model's own MLPs over token representations, never consulting a measured deviation at any layer. The resulting prediction is highly accurate. In early training the model and its corpus mean field are indistinguishable. Replace every attention head with its mean field, and the substitution leaves the loss on real text unchanged. Around the onset of induction, the two diverge, and the gap widens as representations become contextualized. Under the context-conditional reading, deviation from the mean field is a task-agnostic measure of context-specific computation. The residual decomposes additively into unusual attention routing and contextualization of the transported values. Across controlled induction and few-shot settings, greater deviation tracks greater reliance on in-context information.

Micah Adler, John W. Byers, Mark Crovella

Department of Computer Science, Boston University · Faculty of Computing & Data Sciences, Boston University

Attention Head Analysis In-Context Learning Mean-Field Theory Representation Geometry in Language Models

Sep 14, 2026cs.CV

Temporal-Attention Head Specialization During Video Diffusion Training

Video diffusion transformers depend on temporal attention to coordinate information across frames, yet nearly everything known about this mechanism comes from analyzing trained models, so when and where temporal-attention structure forms during training remains poorly characterized. Population averages can also hide it, since a few specializing heads and a diffusing majority cancel in the mean. We therefore conduct a checkpoint-resolved census of every temporal-attention head across nine Open-Sora STDiT training runs spanning three model scales (306M to 1.03B parameters), scoring each head with an entropy-normalized measure of cross-frame attention concentration (CFAC) under a preregistered change-point and effect-size selection rule. The census reveals the sparse picture that averages obscure. Aggregate CFAC is flat or decreasing in every run, while a small minority of heads, roughly 4--13% in full-grid runs, develops pronounced concentration. Across seeds, the reproducible signal is positional but block-level. Selected heads repeatedly arise in the first temporal block, whereas individual head coordinates do not reproduce once block membership is accounted for. Among the analyzed 760M selected heads, attention maps converge to a small repertoire of local frame-routing motifs, self-frame diagonals and adjacent-frame bands, even when the responsible coordinates differ across runs. Correlation and ablation analyses do not establish a causal link to generated video quality, and we bound our claims accordingly. Beyond this STDiT family, the study contributes a transferable methodology. Checkpoint-resolved, per-head analysis under fixed selection rules can expose sparse temporal organization in other factorized video diffusion transformers and, with adapted routing metrics, in joint spatio-temporal architectures.

Taewoo Ha, Shafayat Mowla Anik, Dae Yeol Lee +2

Independent Researcher · University of Colorado - Colorado Springs · Dolby Laboratories +1

Video Diffusion Models Attention Head Analysis Temporal Attention Attention Head Specialization

Sep 1, 2026cs.LG

Scaled Idempotence in Transformer Attention: Paired OV Geometry and Shared-Value Algebras

We identify a recurrent algebraic regularity in Transformer attention: a sparse subset of effective OV operators

T=OV^\top

nearly closes under composition,

T^2\approxαT

. Across six pretrained endpoints spanning 2.8B--235B parameters, 3.98--8.00% of heads reach squared closure alignment

\mathcal{P}\geq0.9

, while no matched within-layer O/V mismatch does. An exact principal-coordinate factorization,

T=Q_OKQ_V^\top

and

T^2=Q_O(KDK)Q_V^\top

, separates within-support transport from read--write return geometry. Across all 7,304 heads in nine MHA/GQA models, scrambling only the orientation of

K

while preserving singular values, norms, factor spans, and principal angles reduces median closure from 0.336 to

1.04\times10^{-4}

; trained orientation wins for 98.64% of heads and in every layer. Constructive searches show that high closure is feasible in every surveyed layer, but usually not attained. Retrospective trajectories in three independently trained lineages further separate broadly available capacity from the orientations attained by final strong heads. Under exact value sharing, headwise closure extends to a right-action algebra,

T_iT_j=α_jT_i

. Seven-model experiments verify the approximate law and reveal distinct oblique projections with a shared value-defined kernel. These results characterize scaled idempotence as a sparse trained orientation within broadly available geometric capacity and show how value sharing extends a headwise relation into a local operator algebra.

Jiming Feng, Junliang Li

College of Computer Science, Beijing University of Technology Beijing, China · School of Mathematics, Statistics and Mechanics, Beijing University of Technology Beijing, China

Attention Head Analysis Transformer Attention Attention Mechanisms Multi-Head Attention

Aug 31, 2026cs.LG

No Equivariant Architecture Covers All Equivariant Attention

We give a complete characterization of equivariant multi-head self-attention (MHSA): if an MHSA layer is equivariant to a symmetry group

G

, then

G

can only act by permuting head-clusters, with QK and OV matrices satisfying an equivariance constraint tied to the group action. As a consequence, we prove that any fixed MHSA architecture that achieves exact equivariance by polynomially parameterizing unconstrained MHSA parameters inevitably leads to expressivity loss within the class of equivariant maps: the equivariance locus of unconstrained MHSA forms a union of extremely many Zariski-irreducible components in a reduced parameter space, and any single architecture covers at most one. For

G=D_4

acting on

C

copies of the regular representation as the token feature space, we show that there are

Ω(C^{64})

components for eight attention heads.

Tīkun Ông

Attention Head Analysis Equivariant Neural Networks Equivariant Representation Learning Multi-Head Attention

Aug 7, 2026cs.CL

Autonomy-of-Heads: Data-Free Sparse Attention from Frozen Query-Key Geometry

Long-context LLM inference is bottlenecked by quadratic attention computation and growing KV-cache costs. Existing sparse attention and KV-compression methods typically decide which tokens or heads to preserve from runtime attention scores, observation windows, calibration prompts, or learned gates, making head diagnosis input-dependent and costly to deploy. We propose Autonomy-of-Heads (AoH), a data-free method that identifies retrieval and streaming heads from the spectral geometry of query-key projections. AoH defines the kernel attention operator

M_h = W_K^{h\top}W_Q^h

and uses its effective-rank as a weight-space measure of head function: concentrated spectra indicate a small number of dominant query-key matching directions and are associated with retrieval heads, whereas diffuse spectra indicate the absence of a dominant global matching direction and are associated with streaming heads. We further derive an efficient

d_\text{head}

-dimensional computation that avoids constructing the full

d_\text{model}\times d_\text{model}

matrix. We conducted extensive experiments across models demonstrating that at 50% sparsity, AoH retains 96.5% of Full Attention performance on average while reducing prefill and decode latency by up to 41.4% and 66.0%, respectively, and KV-cache memory by 50.0% at 256K tokens.

Yehan Yang, Junyuan Shang, Yang Li +3

Institute of Computing Technology, Chinese Academy of Sciences · University of Chinese Academy of Sciences · Baidu Inc. +1

Attention Head Analysis LLM Inference Acceleration Sparse Attention Attention Head Specialization

Jul 31, 2026cs.CV

Interpretability-Guided Soft Pruning of Attention Heads in Vision Transformers

Vision foundation models, such as DINOv2, learn highly expressive representations but rely on massive, opaque architectures that demand substantial computational power and memory. To provide an interpretable-guided and efficient solution to this issue, we first propose a spectral analysis and new visualization technique for individual attention heads based on the Laplacian eigenvectors of their attention maps. Building upon recent observations regarding the block structure of Vision Transformers, we perform semantic clustering of attention heads and identify functional redundancies. Leveraging these insights, we introduce SAPER (Soft Attention PrunER), an end-to-end differentiable pruning framework based on the LapSum Soft Top-K approach. Extensive experiments on ImageNet-1K demonstrate that SAPER achieves a highly favorable accuracy-efficiency trade-off, outperforming the competitive RAPTOR baseline in FLOPs reduction while preserving strong classification performance.

Kamil Książek, Piotr Suszyński, Michał Jan Włodarczyk +2

Centre for Credible Artificial Intelligence Warsaw University of Technology Warsaw, Poland · Faculty of Mathematics and Computer Science Jagiellonian University Krakow, Poland · University of Warsaw Warsaw, Poland

Transformer Interpretability Attention Head Analysis Vision Transformer Efficient ViTs Attention Head Pruning Attention Head Specialization

Jul 31, 2026cs.CV

Role-Break in Attention Heads: Understanding and Detecting Hallucinations in VLMs

Despite remarkable progress in vision-language generation, Vision-Language Models (VLMs) remain prone to hallucinations, producing content that is inconsistent with or unsupported by the input image. Existing works largely design detection or mitigation methods around one specific hallucination pattern, such as visual-textual imbalance, but real VLM hallucinations arise from a mixture of multiple patterns, so signals bound to a single pattern struggle to remain stable across models and tasks. Under a unified head-level view, we find that hallucination-induced changes manifest as localized deviations from each head's faithful contextual behavior, a phenomenon we term Role-Break. Detailed analysis reveals that these deviations are systematically organized across attention heads, contextual sources, and deviation directions, and that the resulting signal is linearly readable once head identity is preserved. Based on these findings, we build a lightweight linear detector on top of Role-Break that requires no fine-tuning of the VLM, whose feature dimension stays below 5,000 and reaches an average AUROC of 93.23 across six VLMs and four benchmarks. A small-scale intervention experiment further shows that the detected tokens can be directly acted upon in the discriminative setting.

Mingyu Wang, Weilin Jin, Wenbo Li +5

Peking University, Beijing, China · Joy Future Academy, Beijing, China

Hallucination Detection in VLMs Attention Head Analysis Hallucination Detection VLM Hallucination Faithfulness in VLMs

Jul 25, 2026cs.LG

Through the Bottleneck: How Multi-head Latent Attention Separates Content from Position in Language Models

Multi-head Latent Attention (MLA), introduced in DeepSeek-V2, compresses key-value pairs through a shared low-rank bottleneck (cKV), achieving 81% KV-cache reduction during inference. Despite its adoption in massive production models, no prior work has studied what information this bottleneck preserves or discards, nor how it reshapes internal transformer circuits. We present the first comprehensive mechanistic interpretability study of MLA, training a 114M-parameter transformer (pretrained on a web/code/math mixture, fine-tuned on TinyStories) and analyzing its representations through SVD, attention head taxonomy, linear probing, and a disruption-attribution analysis. Our key findings are: (1) the cKV bottleneck learns a pure content representation, preserving entity identity (98% retention) while discarding positional information, validating MLA's separation of content from position via RoPE; (2) induction heads co-locate at a single layer (Layer 12), unlike their distributed formation in standard MHA; (3) a single "semantic hub" layer (Layer 15) simultaneously exhibits the highest SVD effective rank and strongest disruption-attribution score; and (4) the bottleneck is globally over-provisioned, using only 46% of its capacity on average. These findings suggest MLA does not merely compress attention passively, but reshapes how the model organizes content, position, and circuit structure. We view this as an initial data point and detail scope limitations in Section 5.

Dhruvil S, Fenil Sojitra, Ravirajsinh Chauhan

1Indian Institute of Technology Madras · 2P P Savani University

Transformer Interpretability Low-Rank Attention Attention Head Analysis Attention Mechanisms Representation Geometry in Language Models Multi-Head Attention+1

Jul 22, 2026cs.CL

A Multi-Dimensional Evaluation of Explainability in Media Bias Detection

Detecting media bias automatically is difficult because biased framing is often subtle, yet in domains such as news analysis, accurate predictions alone are insufficient without explanations that reflect the model's underlying reasoning. We present a multi-dimensional evaluation of explainability in encoder-based media bias detection using the Bias Annotations By Experts (BABE) dataset. Specifically, we study BERT and RoBERTa as classifiers (base and large variants) along three complementary axes: predictive performance, explanation plausibility (token-level alignment with expert rationales), and mechanistic faithfulness (whether compact sets of attention heads recover predictive signal under counterfactual rationale masking). To induce variation in plausibility, we additionally investigate attention-supervised finetuning, which incorporates expert rationale annotations as an auxiliary training signal. Attention supervision serves as an intervention on attribution plausibility, while the effectiveness of attribution methods varies substantially across architectures. Circuit analysis further reveals substantial variation in mechanistic recoverability across architectures, suggesting that model scale alone does not determine circuit compressibility. Taken together, our findings suggest that predictive performance, attribution plausibility, and mechanistic faithfulness characterize different aspects of model behavior and should be evaluated separately when studying explainability in media bias detection.

Ting Chen, Raina Zhang, Benjamin M. Ampel +1

Carnegie Mellon University · Indiana University · Georgia State University

Attention Head Analysis Mechanistic Interpretability Explainability Evaluation

Jul 14, 2026cs.SE

Toward Localizing and Repairing Bias in Transformer Attention Heads

Transformer language models are increasingly used as software components, yet biased outputs remain difficult to localize and repair inside the model. Existing fairness testing and repair methods largely operate at the input-output or retraining level, while recent work suggests that bias-related behavior can concentrate in a small set of attention heads. This paper studies whether attention heads can be localized and repaired through a targeted inference-time intervention. We introduce ROBIN, a white-box head-level fairness debugging method that ranks attention heads using sensitivity to fairness probes and removes a small bias subspace from selected head outputs. In a four-model pilot study, ROBIN reduces the measured WinoBias gap across all models while preserving language-modeling quality better than whole-head zeroing. These preliminary results suggest that head-level bias repair should consider not only which heads are selected, but also how selected heads are modified.

Sigma Jahan

Dalhousie University, Canada

Attention Head Analysis Social Bias in Language Models Language Model Bias Evaluation Causal Interventions in Language Models

Jul 7, 2026cs.LG

Fingerprint, Not Blueprint: How Positional Schemes Set the Default Spectral Algebra of Attention

The pre-softmax score of an attention head is a bilinear form

score(i,j) = x_i^T M x_j

in a learned operator

M = W_q^T W_k

. Because M is generally non-symmetric, hence non-normal, it has a complex eigenspectrum and non-orthogonal eigenvectors, the regime where non-Hermitian and random-matrix tools apply. We ask what this spectrum encodes, at three levels for previous-token and induction circuits. Statically, across seven pretrained models spanning three positional schemes, the strongest previous-token heads are spectrally rotational under RoPE and non-rotational, or content-like, where position enters outside QK (learned-absolute and ALiBi); the model-level separation is perfect at every top-k examined (exact permutation

p=0.029

), and zeroing the per-frequency RoPE phase

Im(M_t)

eliminates induction on a pre-identified previous-token head in all three RoPE models. Dynamically, over public Pythia checkpoints every head originates at the random-matrix (Ginibre) null; the rotational signature emerges with the behavior, not before it, and the population-median suppression that yields the final profile follows circuit formation, so the profile is a consolidated fingerprint, not a precursor. Causally, and at toy scale, no spectral channel is necessary: constrained two-layer training reroutes around every ban with capability intact, albeit at a significant formation delay (four pre-registered contrasts,

q_BH <= 0.016

). The cost structure exposes each scheme's default: imposing symmetry slows learned-absolute models by a factor of 2.9, whereas a RoPE head with a fully symmetric static M still routes directionally via the phase channel, impossible under absolute positions. Within the settings examined, the positional scheme sets the default spectral algebra of an attention head's solution: a fingerprint sculpted after function, not a hard constraint upon it.

Li Hengyu

Institute for Solid State Physics, The University of Tokyo

Rotary Positional Embeddings Attention Head Analysis Induction Heads Multi-Head Attention

Jul 1, 2026cs.CL

Logit-Contribution Scoring Identifies Non-Literal Retrieval Heads

In long-context use, large language models frequently synthesize answers from the meaning of a relevant context span rather than literally copy-pasting them. Identifying which attention heads perform this synthesis matters for interpreting long-context model behavior. Yet existing detectors miss these heads by construction: they reward heads whose attended token matches the generated token, a literal-copy criterion that captures where a head reads but not what it writes through its output-value (OV) circuit, the very mechanism that carries non-literal retrieval. We introduce Logit-Contribution Scoring (LOCOS), a write-aware detector that scores each head by the projection of its OV-circuit output onto the answer-token unembedding direction, contrasting needle and off-needle source positions in a single forward pass. Across three model families (Qwen3, Gemma-3, OLMo-3.1), mean-ablating the top LOCOS heads on the NoLiMa non-literal retrieval benchmark collapses ROUGE-L at lower head counts than prior attention-based detections; on Qwen3-8B, ablating 50 heads drives ROUGE-L from 0.401 to 0.000 while the strongest baseline still retains 0.292. The selected heads are retrieval-specific: parametric recall and arithmetic reasoning stay at baseline under the same ablation. On Qwen3-8B, the same ablation also drops MuSiQue from 0.55 to 0.08 and BABI-Long from 0.62 to 0.20, while a random-heads control stays within 0.05 of baseline.

Aryo Pradipta Gema, Beatrice Alex, Pasquale Minervini

QUniversity of Edinburgh · KHeriot-Watt University · V Miniml.AI

Long-Context Retrieval Attention Head Analysis Long-Context Language Model Evaluation Long-Context Language Model Inference LLM Interpretability Multi-Head Attention

Jun 26, 2026cs.CR

Robust Harmful Features Under Jailbreak Attacks: Mechanistic Evidence from Attention Head Specialization in Large Language Models

Jailbreak attacks bypass LLM safety alignment, yet their mechanisms remain poorly understood. We provide evidence that attacks do not comprehensively eliminate safety features, but instead selectively suppress specific attention heads. We identify two functionally differentiated types: Adversarially Compromised Heads (ACHs) concentrated in early layers, which are suppressed under attacks, and Safety-Aligned Heads (SAHs) in mid-layers, which maintain robust activations even when attacks succeed. Ablation studies support the causal role of ACHs and the contribution of SAHs to robust activations: suppressing a small number of ACHs is sufficient to induce jailbreak-like behavior on normally refused inputs, while removing SAHs substantially weakens mid-layer safety activations. Token-level attribution further shows that ACH suppression is driven specifically by attack-template tokens, providing a mechanistic account of why attacks can bypass refusal decisions through ACH suppression while leaving internal safety signals sustained by SAHs -- a phenomenon we term Robust Harmful Features. To validate the practical significance of this robustness, we show that simply reading these persistent activations -- without any training -- yields competitive aggregate detection performance with strong adversarial robustness.

Yanchen Yin, Dongqi Han, Linghui Li

Beijing University of Posts and Telecommunications, Beijing, China.

Attention Head Analysis Jailbreak Attacks LLM Safety Alignment Mechanistic Interpretability Jailbreak Detection

Jun 20, 2026cs.LG

Protein contacts are already in the attention: a single-forward-pass alternative to the Categorical Jacobian

The Categorical Jacobian of Zhang et al. (2024) reads protein contacts from a language model by perturbing every residue with every alternative amino acid, about

19L

forward passes. We show the signal it reconstructs is already concentrated in a small subset of attention heads: averaging the top-

K

contact-relevant heads -- selected on as few as 10 labeled proteins, with no fitted per-pair or per-head weights -- recovers contacts in a single forward pass and matches or beats the Categorical Jacobian for every bidirectional model where it is defined (bar the smallest, 8M). Our primary test is leakage-clean: on a CAMEO split where neither selection nor evaluation touches data the models have plausibly memorized, the head readout beats the Categorical Jacobian on ESM-2-650M by +9pp (

N = 29

,

p < 0.001

), with the within-model margin reproducing across architectures. Ablations localize the gain to labeled head selection, not to averaging: at a matched label budget the unweighted mean ties a supervised

L_1

logistic regression on the same heads. Both methods fall 30-36pp from their in-distribution Zhang numbers to the leakage-clean split, which we read as an upper bound on how much prior numbers reflect pretraining overlap. We additionally introduce representation-CJ, a hidden-state generalization of the Jacobian to architectures without a masked-LM head (the output-head-independent analogue of logit-CJ), agreeing with the Categorical Jacobian where both are defined (per-protein Pearson

r \approx 0.95

); show that the optimal

K

tracks how diffusely a model spreads its contact heads; and find both methods lose the signal on the two causal LMs we test, suggesting attention-encoded pair structure may depend on bidirectional pretraining.

Rome Thorstenson

Independent Researcher

Protein Structure Prediction Attention Head Analysis Protein Language Models Protein Representation Learning Structured Prediction

Jun 19, 2026cs.LG

Does RoPE Prevent or Degrade Retrieval Heads? A Mechanistic Analysis Across Model Families

Retrieval heads, attention heads that copy information from earlier context to the current position, have been proposed as the mechanistic substrate for long-context recall. Rotary position embeddings (RoPE) rotate queries and keys by frequencies decaying with a base hyperparameter theta, and a natural hypothesis is that this rotation either prevents retrieval heads from forming or degrades their function. We test both across four open-weight 7-8B models spanning multi-head and grouped-query attention and a 100x range of theta, using paired-seed needle-in-a-haystack tests, layer-clustered permutation, and causal head-masking. (i) Retrieval heads are causally necessary: masking the 87 detected heads in OLMo-2 collapses recall from 1.00 to 0.00, while masking matched random heads has no effect; this replicates in Qwen. (ii) Higher theta does not reduce retrieval-head count (LLaMA-3.1 at theta=500K has 47 heads vs LLaMA-2 at theta=10K with 42), refuting the prevention hypothesis. (iii) The norm-utility relation is family-specific and significant in opposite directions (Qwen d=-0.49, OLMo d=+0.50, both significant; LLaMA null); since OLMo and LLaMA-3.1 share theta=500K yet differ, the effect is not theta-driven. (iv) Building on Chiang and Yogatama (2025), a controlled patch shows that zeroing the lowest-frequency RoPE dimensions of retrieval heads degrades recall dose-dependently (1.00 to 0.18 when 32 of 128 dimensions are zeroed, vs 0.98 for random dimensions); the effect is head-specific and task-specific. The causal variable is RoPE frequency, not norm-utility. The direction holds in all five models patched (OLMo-2, Qwen2.5-7B/14B, Gemma-2, Mistral) across four lineages and two scales. We do not claim cross-model magnitude. Code and a paired-seed harness are released.

Cengizhan Bayram

Independent Researcher

Rotary Positional Embeddings Long-Context Retrieval Attention Head Analysis LLM Interpretability

Jun 17, 2026cs.LG

Explaining Attention with Program Synthesis

A longstanding goal of research on interpretable deep learning is to replace opaque neural computations with human-meaningful symbolic descriptions. In this paper, we propose an approach for approximating the behavior of components of deep networks with executable programs. We focus on attention heads in transformer language models. For a given head, we first compute its associated attention matrices on a collection of randomly selected training examples. Next, we prompt a pre-trained language model with a summary of these matrices, and instruct it to generate a set of Python programs that can reproduce the associated attention patterns given only text from the input sentence. Finally, we re-rank programs according to how well our final set of programs predict behavior on held-out inputs. We demonstrate that a set of fewer than 1,000 such generated programs can reproduce the attention patterns of heads in GPT-2, TinyLlama-1.1B, and Llama-3B, achieving an average Intersection-over-Union similarity above 75% on TinyStories. Moreover, the best-fit programs can replace neural attention heads without substantially affecting model behavior: replacing 25% of attention heads with programmatic surrogates across the three models incurs only a 16% average perplexity increase, while maintaining performance on a variety of downstream question answering benchmarks. This work contributes a scalable pipeline for reverse-engineering attention heads in transformer models using human-readable, executable code, advancing a path toward symbolic transparency in neural models.

Amiri Hayes, Belinda Z Li, Jacob Andreas

NJIT · MIT EECS

Transformer Interpretability Attention Head Analysis LLM Interpretability Program Synthesis Multi-Head Attention

Jun 13, 2026cs.CL

Rethinking the Role of Efficient Attention in Hybrid Architectures

Modern language models increasingly adopt hybrid architectures that combine full attention with efficient attention modules, such as sliding-window attention (SWA) and recurrent sequence mixers. However, how these efficient modules shape model capabilities remains poorly understood. To address this gap, we conduct a systematic analysis across hybrid architectures from three perspectives: scaling behavior, mechanism analysis, and architecture design. First, from a scaling perspective, we find that efficient-attention design primarily affects how fast long-context capability emerges, while different hybrids eventually converge to comparable long-context performance under sufficient training. Second, mechanistically, we show that long-range retrieval is mainly carried by full attention, whereas efficient attention shapes its optimization trajectory. This explains a counter-intuitive phenomenon we call Large-Window Laziness: larger SWA windows can delay the formation of retrieval heads in full-attention layers. Third, guided by this mechanism, we show that applying NoPE to only the full-attention layers of a small-window SWA hybrid substantially improves long-context performance with negligible impact on short-context performance.

Ziqing Qiao, Yinuo Xu, Chaojun Xiao +6

1Tsinghua University · 2OpenBMB

Attention Head Analysis Long-Context Modeling Efficient Attention Sliding-Window Attention Attention Mechanisms Hybrid Attention

Jun 11, 2026cs.LG

Where Computation Lives Inside TabPFN: Causal Localisation of Attention Head Function

We present the first causal mechanistic analysis of a tabular foundation model, investigating how TabPFN 2.5's feature wise attention heads distribute computation across layers. Using activation patching, ablation, and attention entropy across two synthetic regression datasets, we find clear temporal specialisation: one head's causal necessity dominates that of the others by 2 to 5 times at peak layer, with its dominant layer shifting across tasks of different complexity, while the remaining heads exhibit symmetric late layer profiles. Attention entropy and patching provide convergent evidence for the computationally active layers of the dominant head. We additionally investigate inference time steerability via contrastive activation steering, which fails to transfer across samples. We attribute this result to TabPFN's in context learning mechanism, which encodes task structure through context dependent attention rather than the stable parametric directions that make steering tractable in language models.

Atharva Gupta, Dhruv Kumar, Murari Mandal +1

Department of Computer Science, Birla Institute of Technology and Science, Pilani, India · School of Computer Engineering, Kalinga Institute of Industrial Technology, Bhubaneswar, India · Birla AI Labs, Office of Ananya Birla, Aditya Birla Group, India

Tabular Foundation Models Attention Head Analysis Mechanistic Interpretability Tabular ICL Multi-Head Attention Attention Head Specialization

Jun 8, 2026cs.LG

Closure-Validated Circuit Discovery in Attention Heads: Co-activation Proposes, Ablation Disposes

Interpretability increasingly treats groups of components, not individual units, as the basic object, and proposes to find them by clustering co-activation statistics. We ask whether such a cheap signal actually identifies an attention-head circuit. Adapting a sparse-autoencoder clustering recipe to attention heads -- but validating by causal ablation rather than reconstruction -- we cluster heads and then run a closure test: ablate the discovered community and compare per-example damage to matched-random controls. Across two dense 1B-scale models (Pythia 1B, OLMo 1B) and two input distributions, the communities pass closure. In a Mixture-of-Experts model (OLMoE-1B-7B), route-conditional clustering recovers a statistically real signal that nonetheless does not survive closure -- ablation improves loss, the wrong direction. Extending closure across training, attention-target selectivity and participation ratio decouple from function in both directions. We conclude that a cheap signal is a circuit proposal, not a confirmed circuit; closure is what separates them.

Yongzhong Xu

Transformer Interpretability Circuit Discovery Attention Head Analysis Clustering Multi-Head Attention

Jun 6, 2026cs.AI

Ablation-Reversible Heads Don't Transfer: A Stress Test for Mechanistic Role Claims in Transformers

In mechanistic interpretability, attention heads are commonly elevated to role claims (e.g., "this head represents addition") when they are necessary for a behavior, encode it linearly, and recover that behavior when restored after ablation. We show this evidence is insufficient: across three 7-8B instruction-tuned models and five computation families, heads passing all three checks routinely fail to transfer the computation when their activations are patched into a different prompt under matched controls. We introduce KID (Knowing / Intent / Doing), a role-assignment lens for attention heads, and pair it with a three-stage pipeline: capability-selective screening (CSS), singular value decomposition (SVD), and activation transduction under matched controls. Our results document a preliminary role taxonomy (including prompt-trajectory stabilizers, answer-side logit-bias heads, and soft computation-pattern carriers) and show that the same-answer control (a transduction target sharing the answer string but not the requested computation) is an underused check that exposes broad state transfer masquerading as semantic specificity.

Philip Quirke

Martian

Attention Head Analysis Mechanistic Interpretability Causal Interventions in Language Models Activation Patching Attention Head Specialization

Jun 3, 2026cs.LG

Pattern Selectivity is Not Task-Causal Structure: A Cross-Architecture Mechanistic Study of Composed-Task Circuits in 1B-Class Language Models

We test whether a single screen-and-ablate recipe -- identify attention-head circuits by task-pattern selectivity, then verify by causal ablation against a matched-random null -- produces consistent mechanistic claims across model families. The recipe ports across pipelines; the specific circuit it identifies does not. Across four composed tasks (indirect-object identification, greater-than, successor sequences, variable binding) and three 1B-class language models from distinct training pipelines (Pythia 1B / Pile / dense; OLMo 1B / DCLM / dense; OLMoE 1B-7B / DCLM / mixture-of-experts), we run a unified protocol with the matched-random null sampled across ten seeds per cell. The resulting 12 (task, model) cells contain no two that share the same primary causal screen at comparable effect size: the same task, with the same behavioral capability, is implemented through different attention-pattern types across models. We introduce a five-category screen-outcome taxonomy -- primary cause, secondary cause, correlate, interferer, null -- with quantitative thresholds, and show that all five outcomes appear in the panel. We propose a falsifiable hypothesis: the MoE model in our panel builds composed-task circuits on top of a foundational previous-token positional substrate (the prev-token-circuit ablation is the strongest causal screen on 3 of 4 tasks for OLMoE 1B-7B), with the IOI exception consistent with IOI being a final-position name-copying task whose structure directly probes a different pattern. The hypothesis comes with explicit predictions for other MoE language models. We frame the methodology honestly: the spectral participation-ratio signal from the companion methodology paper is a general indicator of specialized computation; what makes a finding task-specific is the task-pattern screen plus a per-model causal verification.

Yongzhong Xu

Attention Head Analysis Decoder-Only Language Models LLM Interpretability Circuits in Language Models Causal Interventions in Language Models Language Model Probing

Jun 1, 2026cs.LG

When Do Attention Circuits Form? Developmental Trajectories of Capability and Attention-Sink Emergence Across Three 1B-ClassArchitectures

We track the developmental trajectory of attention-head circuit formation across three 1B-class language models spanning two architecture families (dense transformer, mixture-of-experts) and two pretraining corpora (The Pile, DCLM): Pythia 1B, OLMo 1B-0724-hf, and OLMoE 1B-7B-0924. At each of 10 log-spaced revisions per model -- 30 mechanistic-interpretability runs in total -- we apply a participation-ratio (PR) spectral signal and an all-head capability-specific selectivity screen to track induction, previous-token, and BOS-attractor heads as they emerge. Five findings. (F1) Layers 0 and 1 produce zero BOS-classified heads at every revision in every model: the L0/L1 zero-BOS floor is an architectural property, not a learned outcome. (F2) The whole-model BOS-attractor fraction follows three distinct emergence shapes -- a gradual ramp in Pythia 1B, a sharp phase transition in OLMo 1B (7% to 70% between adjacent checkpoints), and a gradual ramp in OLMoE 1B-7B. (F3) In DCLM models, induction-circuit formation precedes BOS-attractor formation by 10-20x in tokens; capability-circuit formation and attention-sink formation are two transitions, not one. (F4) The capability-specific screen converges to the final induction circuit within 0.3-2% of total training tokens -- circuit identification does not require the final model. (F5) For every final-checkpoint induction head sampled across all three models, per-head PR is elevated at or before the first revision at which that head crosses its capability-selectivity threshold. The results refine the induction-phase-transition framing: in 1B-class models trained on DCLM, the induction transition and the attention-sink transition are separated by an order of magnitude in tokens and have qualitatively different shapes.

Yongzhong Xu

Language Model Pretraining Transformer Interpretability Attention Head Analysis Attention Sinks Induction Heads Multi-Head Attention

May 30, 2026cs.CL

Detection vs. Execution: Single-Bucket Probes Miss Half the Mamba-2 State Sink

Mechanistic interpretability often assumes that probes identifying a representational signature also identify the circuit executing the corresponding computation. We show that this assumption can fail systematically in Mamba-2. Studying the state sink (disproportionate Delta-gate activation on boundary tokens, analogous to the attention sink), we find that single-bucket probes recover only a small execution layer while missing a much larger detection layer with the same representational signature. In Mamba-2, the state sink decomposes into two functional head sets. Single-bucket BOS-specialist heads (about 5% of heads at 2.7B) causally support both BOS-context and newline-target predictions across model scales and corpora. Dual heads (27-35% of heads, recovered by multi-class aggregation of the same probe) show stronger BOS-newline representational similarity but substantially weaker causal effects under ablation. Representational similarity does not imply functional equivalence. This distinction matters for downstream behaviour: ablating BOS-specialist heads collapses RULER NIAH retrieval accuracy from 1.00 to 0.00 at 1024 context length in both Mamba-1 2.8B and Mamba-2 2.7B, while size-matched complements preserve baseline performance. A random channel-bucketing control rules out substrate granularity alone, implicating Mamba-2's head-shared Delta projection. Probe-derived specialty can identify execution circuits; at coarse granularity the same probe also recovers detection circuits, and separating them requires class-conditional ablation rather than class-conditional cosine.

Yuhang Jiang

Independent Researcher

Mamba Attention Head Analysis Attention Sinks Language Model Probing Attention Head Specialization

May 29, 2026cs.LG

Positional versus Symbolic Attention Heads: Learning Dynamics, RoPE Geometry, and Length Generalization

Transformer-based language models are widespread in today's society. As such, understanding the mechanisms by which they solve structured tasks and predicting how they may behave in novel scenarios is of great importance for safe deployment. We study the learning dynamics of attention heads in a controlled setting by training a decoder-only Transformer (GPT-J) on two structurally equivalent multi-hop reasoning tasks: a number task requiring positional reasoning and a letter task requiring symbolic reasoning. Using a recently introduced metric that classifies attention-head behavior as positional or symbolic for a given prompt, we show that successful learning is associated with the emergence of pure heads, i.e., heads that express themselves as either positional or symbolic. Despite the tasks' structural equivalence, they impose different mechanistic demands: the number task requires both positional and symbolic heads, whereas the letter task requires only symbolic heads. We then identify the computational roles of these heads, characterize the basic functions they implement, and give theoretical constructions showing how single-layer RoPE-based attention can realize these functions through geometrically interpretable query, key, and value operations. This analysis yields a quantitative separation between positional and symbolic mechanisms in their robustness to longer sequences, formalized through a novel notion of discrepancy. We empirically validate the resulting predictions in both controlled and real-world models, showing that symbolic mechanisms extrapolate more reliably to longer sequences while positional mechanisms face sharper limitations.

Felipe Urrutia, Juan José Alegría, Cinthia Sanchez Macias +3

CENIA & Faculty of Mathematics UC Santiago, Chile · CENIA Santiago, Chile · IMC UC & CENIA Santiago, Chile

Rotary Positional Embeddings Attention Head Analysis Length Generalization Multi-Head Attention Attention Head Specialization

May 27, 2026cs.AI

Revealing Algorithmic Deductive Circuits for Logical Reasoning

Recent studies have shown that Large Language Models (LLMs) can achieve strong reasoning performance by incorporating functional symbolic representations that abstractly describe graph traversal algorithms and step-by-step reasoning in few-shot learning settings. However, it remains unclear how LLMs genuinely understand the abstract meaning of each reasoning step and the overall algorithm from only a limited number of demonstrations. This work aims to localize the attention heads responsible for individual reasoning steps and characterize the types of information transferred among them. We first align constituent reasoning steps with their corresponding token logits under a symbolic-aided Chain-of-Thought (CoT) prompting framework. Our analysis shows that token positions that steer the reasoning process are associated with low confidence scores caused by constraints on satisfying reasoning behavior patterns in demonstrations. We then adopt causal mediation analysis techniques to identify the attention heads responsible for these patterns. In addition, our findings indicate that LLMs retrieve factual and rule-based information for individual sub-reasoning tasks through specialized attention heads (approximately 3% total heads), whereas higher layers predominantly facilitate information integration and the emergence of global reasoning strategies (e.g., graph traversal algorithms) that coordinate multiple intermediate reasoning steps to solve the overall task.

Phuong Minh Nguyen, Tien Huu Dang, Naoya Inoue

Japan Advanced Institute of Science and Technology

Attention Head Analysis LLM Interpretability Mechanistic Interpretability Algorithmic Reasoning LLM Reasoning

May 22, 2026cs.LG

Spectral Probe-Circuits: A Three-Step Recipe for Identifying Attention-Head Circuits in Pretrained Transformers

We present a three-step recipe for identifying attention-head circuits in pretrained transformers. A per-head spectral signal -- the time-integrated participation ratio of each head's attention output -- ranks heads doing sustained content-dependent computation without labels or attribution gradients. A task-pattern screen filters this general indicator into a task-specific candidate circuit, and group ablation against a matched-random control completes the causal claim. We validate across an 8x parameter range (51M to 1B-active / 7B-total), two architecture families (dense, mixture-of-experts), and four pretraining pipelines. The recipe ports: a 2-6 head induction circuit is causally necessary in every model tested, with a 94-100% drop in synthetic-induction top-1 after ablation. The spectral signal is predictive without supervision: on six independent seeds of a 51M-parameter probe model, the same computation identifies the seed-specific circuit on each seed. The fraction of heads doing identifiable specialized computation is conserved at 17-19% across the Pythia family (124M to 410M), while specific induction circuits stay 3-11 heads -- sublinear in total head count. This paper is the methodology anchor of a three-paper program; companion papers extend the recipe to developmental trajectories during pretraining and to composed-task circuits where pattern selectivity decouples from task-causal structure.

Yongzhong Xu

Transformer Interpretability Circuit Discovery Attention Head Analysis Self-Attention Mechanistic Interpretability Induction Heads+2

May 13, 2026cs.LG

Stable Attention Response for Reliable Precipitation Nowcasting

Precipitation nowcasting remains challenging due to the highly localized, rapidly evolving, and heterogeneous nature of atmospheric dynamics. Although recent methods increasingly adopt attention-based architectures in both unimodal and multimodal settings, they mainly emphasize stronger representation learning and prediction capacity, while paying less attention to the stability of attention responses across samples. In this work, we show that cross-sample instability of attention-response energy is an important and previously underexplored source of forecasting unreliability. Empirically, inaccurate forecasts are associated with larger attention-response energy variance across heads and layers. Theoretically, we show that cross-sample variability can propagate through self-attention, and enlarge a lower bound on prediction error. Based on this insight, we propose HARECast, a Head-wise Attention Response Energy-regulated framework for precipitation nowcasting. HARECast explicitly models head-wise attention-response energy and stabilizes it through a group-wise regularization objective that reduces cross-sample fluctuations. The proposed formulation is generic and applicable to both unimodal and multimodal nowcasting architectures. We instantiate HARECast in a standard forecasting pipeline with reconstruction branches and a diffusion-based predictor, and evaluate it on commonly used benchmarks--SEVIR and MeteoNet. Experimental results demonstrate that HARECast achieves state-of-the-art performance.

Penghui Wen, Zexin Hu, Sen Zhang +6

School of Computer Science, The University of Sydney Australia · Independent Researcher Australia · School of Life and Environmental Science, The University of Sydney Australia +3

Precipitation Forecasting Attention Head Analysis Spatiotemporal Forecasting Precipitation Nowcasting

May 12, 2026cs.LG

The Routing and Filtering Structure of Attention

The attention interaction matrix

QK^{\top}

contains two entangled computations: a skew-symmetric component that redistributes information between positions (routing) and a symmetric component that scales mutual relevance (filtering). We decompose 1776 heads across five pretrained transformers and find routing operating at low rank, well below the routing capacity allocated by the weight kernel. We introduce

S

-

D

attention as a diagnostic parameterization that disentangles routing from filtering by construction with guaranteed stability (

\mathrm{Re}(λ) \le 0

) and trains stably without layer normalization. When disentangled and unnormalized, routing self-organizes into a spectral cascade, effective rank

2

at the first layer, expanding with depth across six scales from 7M to 355M parameters. The cascade predicts where attention can be simplified: linearizing the first seven layers of 125M

S

-

D

attention costs

{<}5\%

perplexity, whereas standard attention collapses under the same intervention. The linearizable region widens with depth. Replacing the first four layers with ELU+1 linear attention reaches within

1.4\%

of baseline at full head dimension. Cascade-allocated architectures trade attention parameters for perplexity (

47\%-65\%

fewer attention parameters at

+3.9\%

to

+8.4\%

PPL). The routing-filtering decomposition makes the spectral budget legible; the cascade makes it actionable.

Shafayeth Jamil, Rehan Kapadia

Ming Hsieh Department of Electrical and Computer Engineering University of Southern California Los Angeles, CA 90089

Attention Head Analysis Self-Attention Transformer Attention Efficient Attention Linear Attention Attention Mechanisms+1

May 11, 2026hep-ph

Dissecting Jet-Tagger Through Mechanistic Interpretability

Mechanistic interpretability seeks to reverse engineer a trained neural network by identifying the minimal subset of internal components. We perform a mechanistic interpretability analysis of the Particle Transformer architecture, trained on the Top Quark Tagging reference dataset, with the goal of identifying the computational circuit responsible for jet classification and characterizing the physical content of its internal representations. Combining zero ablation, path patching with two complementary on-manifold corruption strategies and linear probing of the residual stream, we identify a sparse six-head circuit that recovers the great majority of the full model performance while admitting a clean source-relay-readout interpretation. In this circuit, a single early layer head serves as the primary causal source, a cluster of middle-layer heads acts as relays selectively attending to hard pairwise substructure and a single late-layer head reads out the aggregated signal. Linear probes show that the residual stream is preferentially aligned with the energy correlator basis over the

N

-subjettiness basis. Within the energy correlator basis, the model preferentially encodes 2-prong substructure observables over the 3-prong observables. A per-layer trained probe further reveals that the apparent single step commitment of the model to a classification decision in the first class attention block is in fact a basis rotation, with the discriminating signal already saturating in the particle attention stack. These results demonstrate that mechanistic interpretability methods developed for natural language models can be used for jet physics classifiers and indicate that gradient descent may rediscover physically meaningful aspects of jet tagging without supervision.

Saurabh Rai, Sanmay Ganguly

Department of Physics, Indian Institute of Technology, Kanpur. Uttar-Pradesh 208016, India

Transformer Interpretability Attention Head Analysis Jet Tagging Mechanistic Interpretability High-Energy Physics

May 10, 2026cs.AI

A Game Theoretic Free Energy Analysis of Higher Order Synergy in Attention Heads of Large Language Models

Large language models rely on multihead attention, but interactions among heads remain poorly understood. We apply the Game Theoretic Free Energy Principle (GTFEP): a framework casting multiagent systems as distributed variational inference to analyze attention heads as bounded rational agents. According to GTFEP, each head minimizes its variational free energy, and collective behavior follows a Gibbs distribution over coalition structures whose energy is decomposed into Harsanyi dividends. Using a tractable approximation (uniform prior, deterministic dynamics), coalition free energy reduces to joint Shannon entropy of discretized head outputs (argmax key index). Pairwise dividends become mutual information (nonnegative), while triple dividends correspond to interaction information and can be negative. On BERT, GPT2, and Llama with GSM8K, triple dividends are consistently negative, revealing higher order redundancy. The Nash FEP correspondence guarantees that stationary points of collective free energy are epsilon Nash equilibria; thus, heads with negligible contribution can be pruned with minimal performance loss. Pruning heads with low marginal contribution reduces computational cost with minimal performance loss: for example, pruning 20% of heads in GPT2 reduces FLOPs by 18%, increases throughput by 22%, and raises perplexity only modestly (from 28.4 to 33.4 on GSM8K). Our work shows GTFEP provides a principled foundation for analyzing and optimizing transformer architectures.

Djamel Bouchaffra

DAVID Lab, University of Paris-Saclay, UVSQ Campus, 78035 Versailles, France

LLM Pruning Attention Head Analysis Self-Attention Free Energy Principle Neural Network Interpretability Multi-Head Attention

May 9, 2026cs.LG

When and Why Grouping Attention Heads Accelerates Muon Optimization

Muon orthogonalizes matrix updates, but multi-head attention naturally operates at the level of heads. This granularity mismatch raises the question of whether Muon should be applied to the full attention projection, to individual heads, or to intermediate head groups. We study this question through a one-step descent comparison between full-matrix Muon and group-wise Muon. Our analysis reveals a trade-off between the \textbf{group-wise whitening gain} from group-wise updates and the \textbf{grouping-induced norm cost}, an additional update-norm cost caused by replacing full-matrix whitening with group-wise whitening. Motivated by this trade-off, we propose \textbf{Group Muon}, which treats head group size and grouping rule as optimizer hyperparameters. On GPT-2 Small trained on FineWeb, appropriate grouping improves validation loss over both full-QKV Muon and fully head-wise MuonSplit.

Hongtao Zhang, Wenjie Zhou, Wei Chen +1

State Key Laboratory of AI Safety, Institute of Computing Technology, Chinese Academy of Sciences · School of Advanced Interdisciplinary Sciences, University of Chinese Academy of Sciences · University of Chinese Academy of Sciences

Attention Head Analysis Muon Optimizer Transformer Attention Multi-Head Attention

May 9, 2026cs.CL

Architecture, Not Scale: Circuit Localization in Large Language Models

Mechanistic interpretability assumes that circuit analysis becomes harder as models scale. We challenge this assumption by showing that the attention architecture matters more than parameter count. Studying three circuit types across Pythia and Qwen2.5, we find that grouped query attention produces circuits that are far more concentrated and mechanistically stable than standard multi-head attention at comparable scales. The same concentration pattern holds across indirect object identification, induction heads, and factual recall. Within a single architecture family (Qwen2.5), factual recall circuits undergo a discrete phase transition above a critical scale, collapsing to a single bottleneck rather than degrading gradually. These findings suggest that some architectural choices make large models more tractable to study and that interpretability difficulty is not a fixed consequence of model size.

Sohan Venkatesh

Manipal Institute of Technology Bengaluru.

Transformer Interpretability Grouped-Query Attention Circuit Discovery Attention Head Analysis Mechanistic Interpretability Circuits in Language Models

May 6, 2026cs.LG

Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics

When a language model processes a hallucinated response, its attention routing tends to fail in one of two shapes: over-concentrating on a narrow set of positions, or spreading so diffusely that relevance is diluted, and the shape of the failure carries diagnostic signal. We study these shapes as a diagnostic characterization, computed from attention matrices under \emph{forced scoring} of benchmark-labeled responses rather than during live generation. A widely used family of spectral methods analyzes the symmetric component of the degree-normalized attention operator, which governs transport \emph{capacity}; we prove that every transpose-invariant spectral diagnostic of this operator is structurally \emph{orientation-blind} (it cannot distinguish an operator from its transpose, and therefore cannot detect information-flow direction), with a converse to the blindness theorem bounding any Lipschitz diagnostic's transpose sensitivity by the asymmetry coefficient

G

. Pairing this with a closed-form bipartite-Cheeger landscape for canonical causal architectures, we show that uniform causal attention satisfies an

n

-independent floor

φ\ge 1/5

, while window attention pierces the floor as

O(w/n)

; failure modes are shape-different, not just value-different. This floor is an idealized-architecture benchmark, not an empirical attractor: the fraction of real attention heads that pierce it is itself an architectural signature. The resulting two-axis diagnostic (

φ

for capacity,

G

for direction) yields a falsifiable polarity prediction: bottleneck- and diffuse-dominated benchmarks should exhibit opposite polarity. Under length-controlled evaluation, transport features retain interpretable signal (0.62-0.84 LC-AUROC) across the tested decoder-only, encoder-only, and encoder-decoder models, with polarity reversing as predicted between HaluEval and MedHallu.

Dominik Dahlem, Diego Maniloff, Mac Misiura

Red Hat AI

Transformer Interpretability Attention Head Analysis Self-Attention LLM Hallucination Detection Spectral Methods

May 5, 2026cs.LG

Gradient Flow Structure and Quantitative Dynamics of Multi-Head Self-Attention

Transformer self-attention can be interpreted as a gradient flow on the unit sphere, in which tokens evolve under softmax interaction potentials and tend to form clusters. While prior work has established clustering behavior for single-head attention, the multi-head setting remains less understood due to geometric interference between heads, which invalidates standard monotonicity arguments. In this work, we develop a theoretical framework for multi-head self-attention dynamics and resolve several open questions. We show that, under suitable conditions on the score matrices, a natural multi-head energy functional is non-decreasing along both flat and spherical dynamics. We identify the key obstruction to per-head monotonicity as radial shadow terms, which are projections of each head's output onto token directions, persisting even under orthogonality assumptions. We introduce a sufficient condition ensuring monotonicity and establish robustness to approximate orthogonality. In a simplified scalar-head regime with equiangular token configurations, we derive a closed-form expression for the critical inverse temperature governing clustering behavior, and show that heterogeneous heads exhibit super-additive clustering rates. In this regime, we also prove a separation in clustering time between ReLU and softmax attention in the linearized dynamics. Finally, we establish an entropy production identity and show that attention entropy increases monotonically toward equilibrium as clustering progresses. Our results provide a unified perspective on the dynamics of multi-head attention and clarify the mechanisms underlying clustering and stability in transformer models.

Ayan Pendharkar

Softmax Attention Attention Head Analysis Self-Attention Clustering Attention Mechanisms Multi-Head Attention

May 1, 2026cs.LG

Borrowed Geometry: Cross-Distribution Head-Importance Fingerprints of Frozen Pretrained Gemma 4 31B

Frozen Gemma 4 31B weights pretrained exclusively on text, unmodified, transfer through a thin trainable interface to non-text modalities the substrate has never processed. On the L24--L29 slice (192 attention heads), an English-text TxtCopy attention probe (95 sentences) and per-head ablation impact on four non-language token-pattern tasks (binary copy, associative recall, 1D cellular automaton Rule 90, binary addition) jointly classify four heads -- L26.28, L27.28, L27.2, L27.3 -- as top-tier on both signals. The slice-level joint coincidence is significant under hypergeometric null (

P = 0.0013

,

N=192

,

K=38

,

n=4

) and survives multiplicity-aware permutation tests (

P_{V4} = 0.013

). Pretrained Gemma L26 reaches 60.22% on OGBench cube-double-play-task1 vs ~1% for random-init Gemma (

+59

pt at

n=3

); a FrozenRandom-GPT2 control with correct

1/\sqrt{d_k}

scaling also fails. Head-level causal validation: zeroing L26.28 in the trained cube-task1 IQL agent drops success

63.3\% \to 10.0\%

vs

46.7\%

for a layer-matched low-TxtCopy negative control (

3.2\times

specificity at

n=30

;

n=5

paired-

t

p=0.039

). A full L26 sweep places L26.28 at rank 4 of 32. Honest negatives: within-L26 Spearman

ρ(\text{TxtCopy, drop}) = +0.37

(opposite of within-layer causal reading); single-head activation patching does not transfer the matching variable; the 4 named heads alone do not suffice on any task; Walker2d-DT and scene-task1 recruit L24 outside the named slice and show null head-ablation specificity. We frame the contribution as a cross-distribution importance fingerprint at the slice level plus head-level causal evidence on one cross-modality target.

Abay Bektursun

Independent research

Cross-Modal Learning Attention Head Analysis Self-Attention Transfer Learning Causal Interventions in Language Models Multi-Head Attention

Apr 27, 2026cs.IR

Learning to Route Queries to Heads for Attention-based Re-ranking with Large Language Models

Large Language Models (LLMs) have recently been explored as fine-grained zero-shot re-rankers by leveraging attention signals to estimate document relevance. However, existing methods either aggregate attention signals across all heads or rely on a statically selected subset identified by heuristic rules. This solution can be suboptimal because the informative heads can vary across queries or domains. Moreover, naively combining multiple heads can degrade performance due to redundancy or conflicting ranking signals. In this paper, we propose a query-dependent head selection method, RouteHead, for attention-based re-ranking with LLMs. Specifically, we learn a lightweight router that can map each query to an optimal head set, and relevance scores are computed by aggregating attention signals only from these heads. Since query-to-head optimal labels are unavailable, we first construct pseudo labels via an offline search. The router represents each head with a learnable embedding and represents each query using an embedding extracted from the hidden states of the frozen LLM. Then it is trained on the pseudo labels with a sparsity regularizer. Experiments on diverse benchmarks and multiple LLM backbones show that the proposed method consistently outperforms strong baselines.

Yuxing Tian, Fengran Mo, Zhiqi Huang +2

Université de Montréal · Capital One · McGill University & MILA

Attention Head Analysis Learning to Rank LLM Reranking Attention Mechanisms LLM Routing

Apr 19, 2026cs.IR

HeadRank: Decoding-Free Passage Reranking via Preference-Aligned Attention Heads

Decoding-free reranking methods that read relevance signals directly from LLM attention weights offer significant latency advantages over autoregressive approaches, yet suffer from attention score homogenization: middle-context documents receive near-identical scores, destroying the fine-grained distinctions required for ranking. We propose HeadRank, a framework that lifts preference optimization from discrete token space into the continuous attention domain through entropy-regularized head selection, hard adjacent-level preference pairs, and a distribution regularizer that jointly sharpen discriminability in the homogenized middle zone. Depth truncation at the deepest selected layer further reduces inference to

\mathcal{O}(1)

forward passes. Across 14 benchmarks on three Qwen3 scales (0.6B--4B) using only 211 training queries, HeadRank achieves the highest average NDCG@10 at every scale, outperforming both generative and decoding-free baselines on the majority of benchmarks with 100% formatting success. At 4B, 57.4% of relevant middle-zone documents reach the top quartile versus 14.2% for irrelevant ones -- a 43-percentage-point selectivity gap that demonstrates the effectiveness of attention-space preference alignment for listwise reranking.

Juyuan Wang, Chenxing Wang, Yuchen Fang +8

Weixin Group, Tencent, China · 2South China University of Technology, Guangzhou, China

Attention Head Analysis Self-Attention Learning to Rank LLM Reranking Attention Mechanisms Preference Alignment+1

Apr 16, 2026cs.LG

What Is the Minimum Architecture for Prolepsis? Early Irrevocable Commitment Across Tasks in Small Transformers

When do transformers commit to a decision, and what prevents them from correcting it? We introduce \textbf{prolepsis}: a transformer commits early, task-specific attention heads sustain the commitment, and no layer corrects it. Replicating \citeauthor{lindsey2025biology}'s (\citeyear{lindsey2025biology}) planning-site finding on open models (Gemma~~2 2B, Llama~~3.2 1B), we ask five questions. (Q1)~Planning is invisible to six residual-stream methods; CLTs are necessary. (Q2)~The planning-site spike replicates with identical geometry. (Q3)~Specific attention heads route the decision to the output, filling a gap flagged as invisible to attribution graphs. (Q4)~Search requires

{\leq}16

layers; commitment requires more. (Q5)~Factual recall shows the same motif at a different network depth, with zero overlap between recurring planning heads and the factual top-10. Prolepsis is architectural: the template is shared, the routing substrates differ. All experiments run on a single consumer GPU (16,GB VRAM).

Éric Jacopin

Cosmic AI

Transformer Interpretability Attention Head Analysis Transformer LLM Planning Mechanistic Interpretability Attention Mechanisms+1

Feb 11, 2026cs.CL

Compressed Sensing for Capability Localization in Large Language Models

Large language models (LLMs) exhibit a wide range of capabilities, including mathematical reasoning, code generation, and linguistic behaviors. We show that Transformer architectures contain small subsets of attention heads that are necessary for certain capabilities. Zeroing out as few as five task-specific heads can degrade performance by up to

60\%

on standard benchmarks measuring the capability of interest, while largely preserving performance on unrelated tasks. We introduce a compressed sensing-based method that exploits the sparsity of these heads to identify them via strategic knockouts and a small number of model evaluations. We validate these findings across Llama and Qwen models ranging from 1B to 14B parameters and a diverse set of capabilities including mathematical abilities and code generation, revealing a modular organization in which specialized capabilities are dependent on sparse, functionally distinct components. Overall, our results suggest that capability localization is a general organizational principle of Transformer language models, with implications for interpretability, model editing, and AI safety. Code is released at https://github.com/locuslab/llm-components.

Anna Bair, Yixuan Even Xu, Mingjie Sun +1

Carnegie Mellon University

Attention Head Analysis LLM Interpretability Language Modeling Compressed Sensing Attention Mechanisms

Jan 11, 2026cs.CL

Garbage Attention in Large Language Models: BOS Sink Heads and Sink-aware Pruning

Large Language Models (LLMs) are known to contain significant redundancy, yet a systematic explanation for why certain components, particularly in higher layers, are more redundant has remained elusive. In this work, we identify the BOS sink phenomenon as a key mechanism driving this layer-wise sensitivity. We show that attention heads with high BOS sink scores are strongly associated with functional redundancy: such heads, especially in deeper layers, contribute little to predictive performance and effectively serve as dumping grounds for superfluous attention weights. Leveraging this insight, we introduce a simple pruning strategy that removes high-BOS sink heads. Experiments on Gemma-3, Llama-3.1, and Qwen3 demonstrate that this approach identifies redundant transformer components more reliably than weight- and activation-based criteria in terms of downstream task retention, remaining close to dense baselines at low-to-moderate pruning ratios. We further find that high-scoring sink heads sustain their focus on BOS as context length grows. Overall, our results suggest that structural properties of attention offer a more direct basis for model compression than magnitude-based methods.

Jaewon Sok, Jewon Yeom, Seonghyeon Park +2

Department of Rural Systems Engineering, Seoul National University · Graduate School of Data Science, Seoul National University · Department of Aerospace Engineering, Seoul National University

LLM Pruning Attention Head Analysis Self-Attention Transformer Attention Attention Sinks Attention Mechanisms+2

Oct 28, 2025cs.CL

Emergence of Minimal Circuits for Indirect Object Identification in Attention-Only Transformers

Mechanistic interpretability aims to reverse-engineer large language models (LLMs) into human-understandable computational circuits. However, the complexity of pretrained models often obscures the minimal mechanisms required for specific reasoning tasks. In this work, we train small, attention-only transformers from scratch on a symbolic version of the Indirect Object Identification (IOI) task, a benchmark for studying coreference-like reasoning in transformers. Surprisingly, a single-layer model with only two attention heads achieves perfect IOI accuracy, despite lacking MLPs and normalization layers. Through residual stream decomposition, spectral analysis, and embedding interventions, we find that the two heads specialize into additive and contrastive subcircuits that jointly implement IOI resolution. Furthermore, we show that a two-layer, one-head model composes information from the previous layer primarily through query-key interactions. These results demonstrate that task-specific training induces highly interpretable, minimal circuits, offering a controlled testbed for probing the computational foundations of transformer reasoning.

Rabin Adhikari

Saarland University 66123 Saarbrücken

Attention Head Analysis Transformer Mechanistic Interpretability Attention Mechanisms

Oct 4, 2025cs.LG

Performance-Efficiency Tradeoffs in Transformers: An Approximation Theory Perspective

Transformers have achieved remarkable successes across a wide range of applications, yet the theoretical foundation of their model efficiency remains underexplored. In this work, we investigate how the model parameters -- mainly attention heads and head dimensions -- should be allocated across layers to balance expressivity and efficiency. We first provide mathematical analysis on the role of early layers in information extraction from an approximation perspective, with a theoretical characterization on the trade-off between the number of heads and head dimension under a fixed parameter budget. In addition, we uncover and prove the \emph{saturation} behavior of softmax activations: Continuously increasing head dimensions can lead to diminishing returns in learning errors, particularly for long sequences. Supported by both theory and experiments, this saturation pattern suggests that later layers can operate more efficiently with reduced parameters. Combining these insights, we propose principled strategies for allocating attention heads and dimensions across Transformers' layers, shedding light on theoretically-grounded model efficiency of Transformer-based architectures.

Ruoxi Yu, Haotian Jiang, Jingpu Cheng +3

Center for Data Science, Peking University · Institute for Functional Intelligent Materials, National University of Singapore · Department of Mathematics, National University of Singapore +1

Softmax Attention Attention Head Analysis Transformer Attention Mechanisms