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26 papers in the last four weeks, up 44% on the four weeks before. 0.3% of all new papers.

Jul 13Week of Sep 28

Latest papers 351

May 8, 2026cs.LG

Training-Induced Escape from Token Clustering in a Mean-Field Formulation of Transformers

Transformers perform inference by iteratively transforming token representations across layers. This layerwise computation has been studied empirically, and recent mean-field theories of Transformer dynamics explain how attention can drive token distributions toward clustering. However, existing mean-field analyses largely treat model parameters as prescribed, leaving open how training reshapes this clustering picture. We study this question in a noisy mean-field Transformer in which only a parameter-linear FFN is trained under

L^2

regularization. We find and analyze a training-induced phase in the dynamics: after initially following attention-driven clustering, the token distribution can leave the clustered regime near the final layers. Our mathematical analysis is based on an entropy-regularized interaction energy that captures the clustering bias of attention. More broadly, our results point toward a training-aware mean-field theory of Transformer dynamics, in which training and inference dynamics are treated together.

Noboru Isobe, Daisuke Inoue, Masaaki Imaizumi

1RIKEN Center for Advanced Intelligence Project · 2Imperial College London · 3The University of Tokyo +1

Transformer Clustering Transformer Attention Mean-Field Theory Neural Network Training Dynamics

May 8, 2026cs.LO

Encoder-Decoder Transformers: Logical Characterizations and Periodicity

We give logical characterizations of encoder-decoder transformers, the foundational architecture for LLMs that also sees use in various settings that benefit from cross-attention, in the practical setting of floating-point numbers and soft attention. First, we characterize such transformers via a new temporal logic that extends propositional logic with a counting global modality over the encoder input and a past modality over the decoder input, as well as via a type of distributed automata. We consider three frameworks: with and without a final softmax step in the transformer, and in the setting where each model generates tokens via autoregression. Second, we show that both autoregressive transformers and sentences of counting propositional logic - the fragment of the previous logic obtained by omitting the past modality - recognize exactly the commutative star-free languages. Finally, we find that the sequences of tokens the transformers generate are ultimately periodic (and each token appears in the period at most once). This allows us to characterize autoregressive transformers via sentences of counting propositional logic that generate tokens without autoregression, i.e., we can effectively eliminate recursion from the transformers.

Veeti Ahvonen, Damian Heiman, Antti Kuusisto +2

Mathematics Research Centre, Tampere University, Tampere, Finland

Transformer Expressivity Transformer Autoregressive Language Modeling Neural Network Expressivity

May 8, 2026cs.LG

Revisiting Transformer Layer Parameterization Through Causal Energy Minimization

Transformer blocks typically combine multi-head attention (MHA) for token mixing with gated MLPs for token-wise feature transformation, yet many choices in their parameterization remain largely empirical. We introduce Causal Energy Minimization (CEM), a framework that recasts Transformer layers as optimization steps on conditional energy functions while explicitly accounting for layer parameterization. Extending prior energy-based interpretations of attention, CEM shows that weight-tied MHA can be derived as a gradient update on an interaction energy, and that a gated MLP with shared up/down projections can be viewed through an element-wise energy. This perspective identifies a design space for Transformer layers that includes within-layer weight sharing, diagonal-plus-low-rank interactions, lightweight preconditioners, and recursive updates. We evaluate CEM-derived layers in language-modeling experiments at the moderate hundred-million-parameter scale. Despite their constrained parameterizations, these layers train stably and can match corresponding Transformer baselines. Overall, our results suggest that CEM provides a useful lens for understanding Transformer layer parameterization, connecting Transformer architectures to energy-based models and motivating further exploration of energy-guided layer designs.

Jin Xu, Camille Couturier, Victor Rühle +2

Microsoft · Microsoft Research Cambridge

Transformer Energy-Based Models Attention Mechanisms

May 8, 2026cs.CV

Dynamic Mode Decomposition along Depth in Vision Transformers

Recent work has shown that contiguous vision transformer (ViT) blocks (a) can be replaced by a linear map and (b) organize into recurrent phases of computation. We ask whether these observations coincide: does ViT depth implement approximately \textit{autonomous linear} dynamics, admitting a single operator

K

applied recurrently across a contiguous span? We test this using Dynamic Mode Decomposition (DMD), which fits

K

from selected, consecutive hidden-state pairs and predicts

p

steps ahead via

K^p

. On four pretrained DINO ViTs, we study the regularization, rank, and calibration budget required for stable fitting. For short spans (

p \leq 4

),

K^p

tracks an unconstrained endpoint map to within

0.02

cosine similarity on DINOv3-H/16+, while also recovering intermediate activations at each skipped block. At early cut starts, the fitted operators compress to rank

\ll d

with minimal calibration data, and across tokens, \texttt{cls} is most amenable to linearization; both properties decay monotonically with depth. Yet this local fidelity does not transfer downstream. At the final hidden state, after propagating through the remaining blocks, an identity baseline becomes competitive.

Nishant Suresh Aswani, Saif Eddin Jabari

NYU Tandon & NYU Abu Dhabi

Transformer Vision Transformer Dynamic Mode Decomposition

May 8, 2026cs.LG

Approximation Error Upper and Lower Bounds for Hölder Class with Transformers

We explore the expressive power of Transformers by establishing precise approximation error upper and lower bounds for Hölder class. Specifically, a new approximation upper bound is derived for the standard Transformer architecture equipped with Softmax operators, ReLU activation functions, and residual connections. We prove that a Transformer network composed of at most

\mathcal{O}(\varepsilon^{-{d_{0}}/α})

blocks can approximate any bounded Hölder function with

d_{0}

-dimensional input and smoothness

α\in(0,1]

under any accuracy

\varepsilon>0

. In the case of approximation lower bounds, leveraging the VC-dimension upper bound, we are the first to rigorously prove that Transformers demand for at least

Ω(\varepsilon^{-{d_{0}}/({4α})})

blocks to achieve the

\varepsilon

approximation accuracy. As a final step, we extend the derived results for standard Transformers to a general regression task and establish the corresponding excess risk rates demonstrating Transformers' empirical effectiveness in real-world settings.

Xin He, Yuling Jiao, Xiliang Lu +1

School of Mathematics and Statistics, Wuhan University, Wuhan, China · School of Artificial Intelligence, Wuhan University, Wuhan, China · Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, China

Transformer Neural Network Approximation Theory

May 8, 2026stat.ML

Spectrum-Adaptive Generalization Bounds for Trained Deep Transformers

Understanding why trained Transformers generalize well is a fundamental problem in modern machine learning theory, and complexity-based generalization bounds provide a principled way to study this question. While existing norm-based bounds for Transformers remove the explicit polynomial dependence on the hidden dimension, they typically impose fixed norm constraints specified a priori and can exhibit unfavorable exponential dependence on depth. In this paper, we derive spectrum-adaptive post hoc generalization bounds for multi-layer Transformers. Under layerwise spectral norm control, the bounds are expressed in terms of layerwise Schatten quantities of the query-key, value, and feedforward weight matrices. Since the Schatten indices need not be fixed a priori and can instead be selected after training, separately for each matrix type and layer, the bounds adaptively trade off spectral complexity against the dimension- and depth-dependent factors according to the learned singular-value profiles. Empirical comparisons of BERT-adapted proxies for the leading complexity factors suggest that the proxies induced by our bounds grow more slowly with depth and hidden dimension than the corresponding norm-based proxies. Overall, our results provide a complexity-based perspective on how the spectral structure of trained Transformers is reflected in generalization analyses.

Mana Sakai, Masaaki Imaizumi

The University of Tokyo · RIKEN Center for Advanced Intelligence Project · Kyoto University

Transformer Generalization Bounds

May 8, 2026cs.LG

Convergence and Emergence of In-Context Reinforcement Learning with Chain of Thought

In-context reinforcement learning (ICRL) refers to the ability of RL agents to adapt to new tasks at inference time without parameter updates by conditioning on additional context. Recent empirical studies further demonstrate that Chain-of-Thought (CoT) generation can amplify this ICRL capability. This paper is the first to provide a theoretical understanding on how CoT interacts with ICRL. We conduct our analysis in a policy evaluation setup with linear Transformer. We prove that with specific Transformer parameters, the CoT generation process is equivalent to repeatedly executing temporal difference learning updates. Additionally, we provide finite sample convergence analysis showing that the policy evaluation error decreases geometrically with CoT length and eventually saturates at a statistical floor determined by the context length. We also prove that the desired Transformer parameters are a global minimizer of the pretraining loss, providing a theoretical understanding on the empirical emergence of those parameters.

Zixuan Xie, Xinyu Liu, Rohan Chandra +1

University of Virginia

Reinforcement Learning Transformer Transformer-Based RL CoT Reasoning Temporal-Difference Learning In-Context Learning+1

May 8, 2026cs.LG

When Symbol Names Should Not Matter: A Logistic Theory of Fresh-Symbol Classification

Template tasks have emerged as a clean testbed for asking whether transformers reason with abstract symbols rather than concrete token names. We study the fixed-label classification version of this problem, where train and test examples share latent templates but may use disjoint vocabularies. Unlike next-token prediction, the model need not emit unseen symbols; it must learn a decision rule invariant to symbol renaming. We analyze regularized kernel logistic classification in the transformer-kernel regime. Our main result decomposes the learned predictor into an ideal template-level classifier and a finite-sample perturbation caused by accidental token overlaps in the training data. We encode these overlaps by a colored collision graph and prove high-probability margin-transfer guarantees for fresh-symbol classification. This perspective extends template-based analyses to logistic classification and refines scalar diversity conditions: vocabulary size controls the average rate of collisions, but collision geometry controls whether the ideal classification margin is preserved. More broadly, the same perturbation framework applies to abstraction-augmented inputs, yielding a general margin-versus-collision criterion for identifying when prompting strategies improve fresh-symbol generalization. Synthetic template experiments illustrate the predicted roles of regularization, sample size, and transformer-kernel structure.

Wenjie Guan, Jelena Bradic

Department of Statistics and Data Science, Cornell University

Transformer Classification Kernel Methods Invariant Representation Learning Compositional Generalization

May 7, 2026q-bio.GN

A Linear-Transformer Hybrid for SNP-Based Genotype-to-Phenotype Prediction in Grapevine

Robust genotype-to-phenotype (G2P) prediction is essential for accelerating breeding decisions and genetic gain. However, it remains challenging to measure complex traits under variable field conditions and across years. In this study, we propose a linear-Transformer approach, LiT-G2P (Linear-Transformer Genotype-to-Phenotype), an automated predictive framework that integrates additive genetic variance effects with Transformer-based nonlinear interactions using genome-wide single-nucleotide polymorphisms (SNPs) data. We evaluated LiT-G2P on a panel of diverse grape accessions, genotyped with SNP markers and measured for phenotypes across two consecutive years. Target phenotypic traits include leaf hair density and trichome density of grapevines. Across both single-year and cross-year testing scenarios, LiT-G2P consistently improves prediction performance compared with baseline models. For hair density, LiT-G2P achieves the lowest error in both single-year and cross-year evaluations, with RMSEs of 0.469 and 0.454, respectively, while maintaining strong tolerance accuracies of 79.2% and 74.6%, respectively. For trichome density, LiT-G2P also presents the best overall G2P performance. In addition, we extract model-prioritized SNPs from attention weights and apply genotype-stratified analysis to provide interpretable candidate marker for downstream validation. These results demonstrate that integrating stable additive effects with learned interaction patterns can enhance cross-year robustness and support practical SNP-based predictive modeling for genomic selection.

Yibin Wang, Murukarthick Jayakodi, Silvas Kirubakaran +2

Department of Biological and Agricultural Engineering, Texas A&M AgriLife Research, Texas A&M University System, Dallas, TX, 75252, USA · Department of Soil and Crop Sciences, Texas A&M AgriLife Research, Texas A&M University System, Dallas, TX, 75252, USA · USDA-ARS, Grape Genetics Research Unit, 630 West North Street, Geneva, New York 14456, USA

May 7, 2026cs.LG

Beyond Autoregressive RTG: Conditioning via Injection Outside Sequential Modeling in Decision Transformer

Decision Transformer (DT) formulates offline reinforcement learning as autoregressive sequence modeling, achieving promising results by predicting actions from a sequence of Return-to-Go (RTG), state, and action tokens. However, RTG is a scalar that summarizes future rewards, containing far less information than typical state or action vectors, yet it consumes the same computational budget per token. Worse, the self-attention cost of Transformers grows quadratically with sequence length, so including RTG as a separate token adds unnecessary overhead. We propose SlimDT, which removes RTG from the autoregressive sequence. Instead, we inject RTG information into the state representations before the sequential modeling step, allowing the Transformer to process only a compact (state, action) sequence. This reduces the sequence length by one-third, directly improving inference efficiency. On the D4RL benchmark, SlimDT surpasses standard DT across various tasks and achieves performance comparable to existing state-of-the-art methods. Decoupling a sparse conditioning signal from an information-rich sequence thus yields both computational gains and higher task performance.

Yongyi Wang, Hanyu Liu, Lingfeng Li +6

School of Computer Science Peking University Beijing, China 100871

Efficient Transformer Inference Reinforcement Learning Transformer Transformer-Based RL Decision Transformer Offline RL

May 7, 2026cs.LG

The E $Δ$ -MHC-Geo Transformer: Adaptive Geodesic Operations with Guaranteed Orthogonality

We present the E

Δ

-MHC-Geo Transformer, a novel architecture that unifies Manifold-Constrained Hyper-Connections (mHC), Deep Delta Learning (DDL), and the Cayley transform to obtain input-adaptive, unconditionally orthogonal residual connections. Unlike DDL, whose Householder operator is orthogonal only at

β\in \{0,2\}

, our Data-Dependent Cayley rotation

Q(x)=(I+(β/2)A(x))^{-1}(I-(β/2)A(x))

preserves orthogonality for all

β

and all inputs. To handle negation, an eigenvalue

-1

case that Cayley provably excludes, we introduce the E

Δ

-MHC-Geo Hybrid, which combines Cayley rotation with Householder reflection via a learned operator-selection gate

X'=γ(X)Q(X)X+(1-γ(X))H_2(X)X

. A midpoint-collapse regularizer,

4γ(1-γ)

, encourages boundary gate decisions, where each selected component is orthogonal. In matched-parameter comparisons, with approximately 1.79M parameters per model and mean +/- standard deviation over 3 seeds, against four baselines including the concurrent JPmHC, E

Δ

-MHC-Geo achieves the best long-horizon stability, 1.9x over JPmHC and 3.8x over GPT; the best near-

π

rotation loss, 4.5x over JPmHC on single-plane; strong norm preservation, with 0.001 mean deviation; and 0.96 negation cosine alignment in a diagnostic reflection probe, all with 33% fewer layers. While JPmHC's wider representation excels on pure rotation, its finite Cayley residual mixer excludes an exact

λ=-1

operator and has no reflection branch, motivating our hybrid approach for accessing both connected components of

O(n)

.

Arash Shahmansoori

Independent Researcher

Transformer Residual Learning Hyper-Connections Orthogonal Representation Learning

May 7, 2026cs.AI

Large Vision-Language Models Get Lost in Attention

Despite the rapid evolution of training paradigms, the decoder backbone of large vision--language models (LVLMs) remains fundamentally rooted in the residual-connection Transformer architecture. Therefore, deciphering the distinct roles of internal modules is critical for understanding model mechanics and guiding architectural optimization. While prior statistical approaches have provided valuable attribution-based insights, they often lack a unified theoretical basis. To bridge this gap, we propose a unified framework grounded in information theory and geometry to quantify the geometric and entropic nature of residual updates. Applying this unified framework reveals a fundamental functional decoupling: Attention acts as a subspace-preserving operator focused on reconfiguration, whereas FFNs serve as subspace-expanding operators driving semantic innovation. Strikingly, further experiments demonstrate that replacing learned attention weights with predefined values (e.g., Gaussian noise) yields comparable or even superior performance across a majority of datasets relative to vanilla models. These results expose severe misallocation and redundancy in current mechanisms, suggesting that state-of-the-art LVLMs effectively ``get lost in attention'' rather than efficiently leveraging visual context.

Gongli Xi, Ye Tian, Mengyu Yang +5

School of Cyberspace Security, Beijing University of Posts and Telecommunications, Beijing, China · State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, China · School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and Telecommunications, Beijing, China +3

Transformer FFNs Vision-Language Models Transformer Self-Attention Large Vision-Language Models VLM Interpretability+1

May 6, 2026cs.CC

Average Attention Transformers and Arithmetic Circuits

We analyse the computational power of transformer encoders as sequence-to-sequence functions on vectors. We show that average hard attention can be used to simulate arithmetic circuits if they are given as an input to an encoder. The circuit families that can be simulated this way have constant depth while using unbounded addition, binary multiplication and sign gates. The transformers we use have arithmetic circuits instead of feed-forward networks. With typical average attention the functions they compute are also computed by the same class of circuit families. Our results hold for transformers over the reals, rationals and any ring in between the two.

Lena Ehrmuth, Laura Strieker

Institute for Theoretical Computer Science, Leibniz University Hanover, Hanover, Germany

Transformer Expressivity Transformer Attention Mechanisms Neural Network Expressivity

May 6, 2026cs.LG

FLUID: Continuous-Time Hyperconnected Sparse Transformer for Sink-Free Learning

Continuous-time (CT) Transformers improve irregular and long-range modeling over CT-RNNs by exploiting inputs or outputs embeddings with continuous dynamics. However, the core scaled-dot-product-attention (SDPA) mechanism remains inherently discrete. We propose FLUID (Flexible Unified Information Dynamics), a CT Transformer that incorporates continuous dynamics directly into the attention computation by replacing it with Liquid Attention Network (LAN). LAN reinterprets attention logits as continuous dynamical system and reformulates them as the solution to a linear ODE modulated by input-dependent nonlinear recurrent gates. Theoretically, we establish stability guarantees for LAN dynamics and show that it serves as an interpolating middle ground between SDPA and CT-RNNs, recovering each as special case under well-defined parameterization of its gating functions. LAN also introduces an explicit attention-sink gate to eliminate disproportionate attention mass on uninformative nodes. FLUID replaces standard residual connections with input-dependent Liquid Hyper-Connections to adaptively regulate interlayer information flow. Empirically, we evaluate FLUID on a broad set of learning tasks, including (i) irregular time-series, (ii) long-range modeling, (iii) lane-keeping control of autonomous vehicles, and (iv) learning physical dynamics under a scarce data regime. Across all the tasks, FLUID consistently matches or outperforms CT baselines, achieving improvements of up to 47% in certain scenarios and enhancing generalization under distributional shifts. Additionally, FLUID demonstrates superior noise robustness and a self-correcting inductive bias in autonomous vehicle control. We also provide a detailed analysis of key hyperparameters to guide tuning and show that FLUID occupies an intermediate position among competing approaches in terms of runtime and memory efficiency.

Waleed Razzaq, Yun-Bo Zhao

School of Automation University of Science and Technology China Hefei, Anhui

Transformer Transformer Attention Attention Mechanisms Time Series Transformers

May 5, 2026eess.SP

Domain-Adaptive Arrhythmia Classification Using a Hybrid Transformer on Wearable Heart Signals

Cardiovascular disease remains the leading cause of death globally, underscoring the need for effective, accessible monitoring solutions, particularly through wearable devices that enable continuous, real-time tracking of heart rhythms in home settings. However, deploying deep learning models trained on clinical electrocardiogram (ECG) datasets to wearable devices remains challenging, as differences in recording equipment, signal quality, and patient populations introduce domain shifts that degrade model performance. We propose a hybrid transformer model that processes continuous ECG signals alongside seven heart rate variability (HRV) features, where the raw signal path captures beat-level morphological patterns and the HRV path encodes rhythm regularity statistics, allowing the model to jointly leverage complementary information from both representations. To enhance the model's ability to generalize across domains, we employ representation learning techniques, including Maximum Mean Discrepancy (MMD), a non-parametric kernel-based metric that quantifies the distance between feature distributions of different domains, to align feature distributions between source and target domains, addressing the challenge of domain shifts between public datasets and wearable device data. By leveraging five public ECG datasets for training, the model learns robust, generalized representations that mitigate domain-specific biases. When tested on wearable device data with an unseen domain, the model achieved an F1-macro 95% and balanced accuracy of 96.15%. These results demonstrate minimal performance degradation, with only a 2% drop in F1-macro compared to seen-domain evaluation, highlighting the model's generalization capabilities and its potential for reliable, real-time heart monitoring applications in home and ambulatory settings.

Maedeh H. Toosi, Siamak Mohammadi

School of Electrical and Computer Engineering, University of Tehran, Tehran, Iran

Transformer Domain Adaptation Electrocardiogram Classification Wearable Health Monitoring

May 5, 2026cs.CL

Feature-Augmented Transformers for Robust AI-Text Detection Across Domains and Generators

AI-generated text is nowadays produced at scale across domains and heterogeneous generation pipelines, making robustness to distribution shift a central requirement for supervised binary detectors. We train transformer-based detectors on HC3 PLUS and calibrate a single decision threshold by maximising balanced accuracy on held-out validation; this threshold is then kept fixed for all downstream test distributions, revealing domain- and generator-dependent error asymmetries under shift. We evaluate in-domain on HC3 PLUS, under cross-dataset transfer to the multi-domain, multi-generator M4 benchmark, and on the external AI-Text-Detection-Pile. Although base models achieve near-ceiling in-domain performance (up to 99.5% balanced accuracy), performance under shift is brittle and strongly model-dependent. Feature augmentation via attention-based linguistic feature fusion improves transfer, with our best model (DeBERTa-v3-base+FeatAttn) achieving 85.9% balanced accuracy on M4. Multi-seed experiments confirm high stability. Under the same fixed-threshold protocol, our model outperforms strong zero-shot baselines by up to +7.22 points. Category-level ablations further show that readability and vocabulary features contribute most to robustness under shift. Overall, these results demonstrate that feature augmentation and a modern DeBERTa backbone significantly outperform earlier BERT/RoBERTa models, while the fixed-threshold protocol provides a more realistic and informative assessment of practical detector robustness.

Mohamed Mady, Johannes Reschke, Björn Schuller

Chair of Health Informatics, Technical University of Munich (TUM), Germany · OTH Regensburg, Germany · GLAM – Group on Language, Audio & Music, Imperial College London, United Kingdom

AI-Generated Text Detection Transformer Cross-Domain Generalization Robustness of Machine-Generated Text Detection

May 5, 2026cs.LG

Transformers with Selective Access to Early Representations

Several recent Transformer architectures expose later layers to representations computed in the earliest layers, motivated by the observation that low-level features can become harder to recover as the residual stream is repeatedly transformed through depth. The cheapest among these methods add static value residuals: learned mixing coefficients that expose the first-layer value projection V_1 uniformly across tokens and heads. More expressive dense or dynamic alternatives recover finer-grained access, but at higher memory cost and lower throughput. The usefulness of V_1 is unlikely to be constant across tokens, heads, and contexts; different positions plausibly require different amounts of access to early lexical or semantic information. We therefore treat early-representation reuse as a retrieval problem rather than a connectivity problem, and introduce Selective Access Transformer (SATFormer), which preserves the first-layer value pathway while controlling access with a context-dependent gate. Across models from 130M to 1.3B parameters, SATFormer consistently improves validation loss and zero-shot accuracy over the static value-residual and Transformer baselines. Its strongest gains appear on retrieval-intensive benchmarks, where it improves over static value residuals by approximately 1.5 average points, while maintaining throughput and memory usage close to the baseline Transformer. Gate analyses suggest sparse, depth-dependent, head-specific, and category-sensitive access patterns, supporting the interpretation that SATFormer learns selective reuse of early representations rather than uniform residual copying. Our code is available at https://github.com/SkyeGunasekaran/SATFormer.

Skye Gunasekaran, Téa Wright, Rui-Jie Zhu +1

UC Santa Cruz · UC Berkeley

Transformer Residual Learning Transformer Attention

May 4, 2026cs.CL

A Systematic Benchmark of Machine Transliteration Models for the Tajik-Farsi Language Pair: A Comparative Study from Rule-Based to Transformer Architectures

This paper presents the first comprehensive comparative analysis of modern machine learning architectures for transliteration between Tajik (Cyrillic script) and Persian (Arabic script). A key contribution is the creation and validation of a unique parallel corpus aggregated from multiple heterogeneous sources, including crowdsourced projects, lexicographic pairs, parallel texts of "Shahnameh", diplomatic articles, texts of "Masnavi-i Ma'navi", official terminology lists, and transliterated correspondences. The initial dataset comprised 328,253 sentence pairs; a representative subset of 40,000 pairs was formed using stratified random sampling. The experiment compared six classes of models: rule-based baseline, LSTM with attention, character-level Transformer, G2P Transformer (trained from scratch), pre-trained multilingual models (mBART, mT5 with LoRA), and byte-level ByT5. Results demonstrate the overwhelming superiority of ByT5 (chrF++ 87.4 for Tajik to Farsi, 80.1 for reverse). The G2P Transformer significantly outperformed mBART (72.3 vs. 62.2 chrF++) despite limited data. Models using subword tokenization (mT5) failed completely (chrF++ less than 18.5). The findings demonstrate that for accurate transliteration of the Tajik-Farsi pair, architectures operating at the byte or character level are unequivocally more effective than traditional multilingual Seq2Seq models relying on subword tokenization.

Mullosharaf K. Arabov

Institute of Computational Mathematics and Information Technologies Kazan Federal University Kazan, Russia

Multilingual Language Models Transformer Byte-Level Language Model

May 4, 2026cs.LG

Projection-Free Transformers via Gaussian Kernel Attention

Self-attention in Transformers is typically implemented as

\mathrm{softmax}(QK^\top/\sqrt{d})V

, where

Q=XW_Q

,

K=XW_K

, and

V=XW_V

are learned linear projections of the input

X

. We ask whether these learned projections are necessary, or whether they can be replaced by a simpler similarity-based diffusion operator. We introduce \textbf{Gaussian Kernel Attention} (GKA), a drop-in replacement for dot-product attention that computes token affinities directly using a Gaussian radial basis function (RBF) kernel applied to per-head token features. Each head learns only a bandwidth parameter

σ_h

, while a single output projection

W_O

preserves compatibility with the standard Transformer interface. GKA can be interpreted as normalized kernel regression over tokens, linking modern Transformer architectures to classical non-local filtering and kernel smoothing methods. We evaluate GKA in both vision and language modeling settings. For autoregressive language modeling within the \texttt{nanochat} framework, we implement causal masking and sliding-window constraints by masking and renormalizing the Gaussian kernel. At depth 20, a GKA model with

0.42\times

the parameters and

0.49\times

the total training FLOPs of a standard attention baseline trains stably, exhibits a near-zero train-validation gap, and demonstrates competitive behavior on standard benchmarks, albeit with higher bits-per-byte (BPB) at this compute scale. Overall, GKA provides a minimal, interpretable attention mechanism with an explicit locality scale, offering a dimension in the accuracy-efficiency trade-off for Transformer design.

Debarshi Kundu, Archisman Ghosh, Swaroop Ghosh +1

The Pennsylvania State University, University Park, USA

Transformer Self-Attention Transformer Attention Attention Mechanisms

May 3, 2026cs.CV

Linear-Time Global Visual Modeling without Explicit Attention

Existing research largely attributes the global sequence modeling capability of Transformers to the explicit computation of attention weights, a process that inherently incurs quadratic computational complexity. In this work, we offer a novel perspective: we demonstrate that attention can be mathematically reframed as a Multi-Layer Perceptron (MLP) equipped with dynamically predicted parameters. Through this lens, we explain attention's global modeling power not as explicit token-wise aggregation, but as an implicit process where dynamically generated parameters act as a compressed representation of the global context. Inspired by this insight, we investigate a fundamental question: can we achieve Transformer-level sequence global modeling entirely through dynamic parameterization while maintaining linear complexity, effectively replacing explicit attention? To explore this, we design various dynamic parameter prediction strategies and integrate them into standard network layers. Extensive empirical studies on vision models demonstrate that dynamic parameterization can indeed serve as a highly effective, linear-complexity alternative to explicit attention, opening new pathways for efficient sequence modeling. Code is available at https://github.com/LeapLabTHU/WeightFormer.

Ruize He, Dongchen Han, Gao Huang

Tsinghua University

Transformer Transformer Attention Efficient ViTs Conditional Computation

May 1, 2026cs.CL

Characterizing the Expressivity of Local Attention in Transformers

The transformer is the most popular neural architecture for language modeling. The cornerstone of the transformer is its global attention mechanism, which lets the model aggregate information from all preceding tokens before generating the next token. One common variant of attention is called local attention, which restricts each token to aggregating information from a bounded window of predecessors, reducing the quadratic cost of global attention to linear. Although this restriction is usually motivated by efficiency, it has also been found to improve model quality, a phenomenon that has so far lacked a satisfactory explanation. We provide a formal account of this phenomenon in terms of recognizer expressivity. It has been shown that fixed-precision transformers with global attention correspond to a fragment of linear temporal logic containing a single past operator. We additionally prove that adding local attention introduces a second temporal operator, strictly enlarging the class of recognizable regular languages. Moreover, global and local attention are expressively complementary: neither subsumes the other, and combining them yields the richest fragment. Experiments on formal language recognition and natural language modeling corroborate the theory, showing that hybrid global--local transformers outperform their global-only counterparts.

Jiaoda Li, Ryan Cotterell

Transformer Expressivity Transformer Autoregressive Language Modeling Local Attention Attention Mechanisms Neural Network Expressivity

Apr 30, 2026cs.RO

E $^2$ DT: Efficient and Effective Decision Transformer with Experience-Aware Sampling for Robotic Manipulation

In reinforcement learning (RL) for robotic manipulation, the Decision Transformer (DT) has emerged as an effective framework for addressing long-horizon tasks. However, DT's performance depends heavily on the coverage of collected experiences. Without an active exploration mechanism, standard DT relies on uniform replay, which leads to poor sample efficiency, limited exploration, and reduced overall effectiveness. At the same time, while excessive exploration can help avoid local optima, it often delays policy convergence and leads to degraded efficiency. To address these limitations, we propose E

^2

DT, a DT-guided k-Determinantal Point Process sampling framework that enables the model to actively shape its own experience selection. Our framework is experience-aware, allowing E

^2

DT to be both efficient, by prioritizing sampling quality, such as high-return, high-uncertainty, and underrepresented trajectories, and effective, by ensuring diversity across trajectory windows to preserve policy optimality. Specifically, DT's internal latent embeddings measure diversity across trajectory windows, while quality is quantified through a composite metric that integrates return-to-go (RTG) quantiles, predictive uncertainty, and stage coverage based on inverse frequency. These two dimensions are integrated into a novel quality-diversity joint kernel that prioritizes the most informative experiences, thereby enabling learning that is both efficient and effective. We evaluate E

^2

DT on challenging robotic manipulation benchmarks in both simulation and real-robot settings. Results show that it consistently outperforms prior methods. These findings demonstrate that coupling policy learning with experience-aware sampling provides a principled path toward robust long-horizon robotic learning.

Kaiyan Zhao, Borong Zhang, Yiming Wang +4

School of Computer Science, Wuhan University, Wuhan 430072, China · State Key Lab of Internet of Things for Smart City and Department of Computer Information Science, University of Macau, Macao 999078, China

Long-Horizon Robotic Manipulation Transformer Decision Transformer Experience Replay Determinantal Point Process Robotic RL+1

Apr 30, 2026cs.SE

Hierarchical Fault Detection and Diagnosis for Transformer Architectures

Transformers now underpin critical AI systems across industry and research. Yet their faults can silently alter model behavior without runtime errors, and existing techniques offer little support for tracing these failures to their component and root cause. Such faults evade detection because loss and numerical values stay normal, and the visible symptom rarely identifies the component responsible. We present DEFault++, a hierarchical learning-based technique that first detects a fault, then identifies the affected component, and finally the cause within it, helping developers effectively debug transformer models. DEFault++ organizes component-level runtime measurements with a Fault Propagation Graph (FPG), a structural prior over the architecture's dependency paths, and reports the evidence behind each diagnosis. To train and evaluate it, we construct DEFault-bench, a benchmark of 5,556 labeled runs from mutation testing across seven models, nine tasks, and both encoder and decoder architectures. DEFault++ improves fault detection over four prior techniques, reaching an F1 of 0.826--0.909, and in a developer study with 21 participants, it raises repair accuracy from 57.1% to 83.3%. These results show that transformer fault diagnosis benefits from component-level measurements and architecture-aware reasoning rather than model-level behavior alone, and DEFault-bench provides a foundation for further research on transformer fault diagnosis.

Sigma Jahan, Saurabh Singh Rajput, Tushar Sharma +1

Dalhousie University, Halifax, Canada

Software Engineering Automated Software Testing Transformer Fault Detection Fault Diagnosis

Apr 30, 2026cond-mat.dis-nn

Sampling two-dimensional spin systems with transformers

Autoregressive Neural Networks based on dense or convolutional layers have recently been shown to be a viable strategy for generating classical spin systems. Unlike these methods, sampling with transformers is commonly considered to be computationally inefficient. In this work, we propose a novel approach to transformer-based neural samplers in which we generate not a single spin per step but groups of spins. As an additional improvement, we construct a model of approximated probabilities, further improving the efficiency of the algorithm. Despite our approach being computationally heavier than dense networks or CNN-based approaches, we were able to sample larger systems of up to

180 \times 180

spins in case of the Ising model. The Effective Sample Size of our sampler is

\sim 20

times larger than that of the previous state-of-the-art neural sampler when trained for the

128 \times 128

Ising model at critical temperature. Finally, we also test our algorithm on the 2D Edwards-Anderson model, where we train

64\times 64

spin systems.

Piotr Białas, Piotr Korcyl, Tomasz Stebel +2

Institute of Applied Computer Science, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland · Institute of Theoretical Physics, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland · Doctoral School of Exact and Natural Sciences, Jagiellonian University, ul. Łojasiewicza 11, 30-348 Kraków, Poland

Transformer Ising Model Autoregressive Modeling

Apr 30, 2026cs.LG

PINN-Cast: Exploring the Role of Continuous-Depth NODE in Transformers and Physics Informed Loss as Soft Physical Constraints in Short-term Weather Forecasting

Operational weather prediction has long relied on physics-based numerical weather prediction (NWP), whose accuracy comes at the cost of substantial compute and complex simulation workflows. Recent transformer-based forecasters offer efficient data-driven alternatives, however transformers are physics-agnostic models. Additionally, standard transformer encoders evolve representations through discrete layer updates that may be less suited to modeling smooth latent dynamics. In this work, we propose a continuous-depth transformer encoder for weather forecasting that integrates Neural Ordinary Differential Equation (Neural ODE) dynamics within each encoder block. Specifically, we replace discrete residual updates with ODE-based updates solved using adaptive numerical integration. We also introduce a two-branch attention module that combines conventional patch-wise self-attention with an auxiliary branch that applies a derivative operator to attention logits, providing an additional change-sensitive interaction signal. To further align forecasts with governing principles, we propose a customized physics-informed training objective that enforces physical consistency as a soft constraint. We evaluate the proposed method against a standard discrete transformer baseline and an existing continuous-time Neural ODE forecasting variant, demonstrating the importance of PINN-Cast in short term weather forecasting.

Hira Saleem, Flora Salim, Cormac Purcell

University of New South Wales, Sydney, NSW, Australia

Transformer Physics-Informed ML Spatiotemporal Forecasting Neural ODEs Weather Forecasting

Apr 29, 2026cs.LG

Learning Rate Transfer in Normalized Transformers

The Normalized Transformer, or nGPT (arXiv:2410.01131) achieves impressive training speedups and does not require weight decay or learning rate warmup. However, despite having hyperparameters that explicitly scale with model size, we observe that nGPT does not exhibit learning rate transfer across model dimension and token horizon. To rectify this, we combine numerical experiments with a principled use of alignment exponents (arXiv:2407.05872) to revisit and modify the

μ

P approach to hyperparameter transfer (arXiv:2011.14522). The result is a novel nGPT parameterization we call

ν

GPT. Through extensive empirical validation, we find

ν

GPT exhibits learning rate transfer across width, depth, and token horizon.

Boris Shigida, Boris Hanin, Andrey Gromov

Meta Superintelligence Labs · Princeton University

Transformer Hyperparameter Transfer

Apr 29, 2026math.PR

Stochastic Scaling Limits and Synchronization by Noise in Deep Transformer Models

We prove pathwise convergence of the layerwise evolution of tokens in a finite-depth, finite-width transformer model with MultiLayer Perceptron (MLP) blocks to a continuous-time stochastic interacting particle system. We also identify the stochastic partial differential equation describing the evolution of the tokens' distribution in this limit and prove propagation of chaos when the number of such tokens is large. The bounds we establish are quantitative and the limits we consider commute. We further prove that the limiting stochastic model displays synchronization by noise and establish exponential dissipation of the interaction energy on average, provided that the common noise is sufficiently coercive relative to the deterministic self-attention drift. We finally characterize the activation functions satisfying the former condition.

Andrea Agazzi, Giuseppe Bruno, Eloy Mosig García +2

Department of Mathematics and Statistics, University of Bern (CH) · Department of Mathematics, University of Pisa (IT)

Dynamical Systems Transformer Transformer Attention

Apr 29, 2026cs.LG

Exploring the Potential of Probabilistic Transformer for Time Series Modeling: A Report on the ST-PT Framework

The Probabilistic Transformer (PT) establishes that the Transformer's self-attention plus its feed-forward block is mathematically equivalent to Mean-Field Variational Inference (MFVI) on a Conditional Random Field (CRF). Under this equivalence the Transformer ceases to be a black-box neural network and becomes a programmable factor graph: graph topology, factor potentials, and the message-passing schedule are all explicit and inspectable primitives that can be engineered. PT was originally developed for natural language and in this report we investigate its potential for time series. We first lift PT into the Spatial-Temporal Probabilistic Transformer (ST-PT) to repair PT's missing channel axis and weak per-step semantics, and adopt ST-PT as a shared cornerstone backbone. We then identify three distinct properties that PT/ST-PT offers as a factor-graph model and derive three Research Questions, one per property, that probe how each property can be exploited in time series: RQ1. The graph topology and potentials are direct programmable primitives. Can this be used to inject symbolic time-series priors into ST-PT through structural graph modifications, especially under data scarcity and noise? RQ2. The CRF's factor matrices are the operator's potentials. Can an external condition program these factor matrices on a per-sample basis, so that conditional generation becomes structural rather than feature-level modulation of a fixed one? RQ3. Each MFVI iteration is a Bayesian posterior update on the factor graph. Can this turn the latent transition of latent-space AutoRegressive (AR) forecasting from an opaque MLP into a principled posterior update, and can a CRF teacher distill its latents into the AR student to counter cumulative error? We give one empirical study per question. Together, these three studies position ST-PT as a programmable framework for time-series modeling.

Zhangzhi Xiong, Haoyi Wu, You Wu +3

School of Information Science and Technology, ShanghaiTech University

Transformer Conditional Random Fields Time Series Forecasting Time Series Generation Variational Inference

Apr 29, 2026cs.CL

Folding Tensor and Sequence Parallelism for Memory-Efficient Transformer Training & Inference

We present tensor and sequence parallelism (TSP), a parallel execution strategy that folds tensor parallelism and sequence parallelism onto a single device axis. In conventional multi-dimensional parallelism layouts, tensor parallelism (TP) shards model weights while sequence parallelism (SP) shards tokens, reducing per-device parameter or activation memory, respectively. Traditionally, each scheme is assigned its own mesh dimension. TSP instead assigns each rank both a weight shard and a sequence shard, reducing both parameter and activation memory along the same device axis. We implement this design with two runtime schedules. For attention, ranks iterate over broadcast parameter shards and reconstruct context through a sequence-wise key/value exchange. For gated MLPs, weight shards circulate in a ring while partial outputs accumulate locally. By sharding both weights and activations across the same devices, TSP trades additional communication volume for reduced memory overhead. We provide a theoretical communication and memory analysis, describe our implementation of TSP attention and gated MLP blocks, and benchmark TSP against TP, SP, and TP+SP. These results position TSP as a hardware-aware alternative for long-context and memory-constrained model training, and as a viable axis of parallelism in concert with existing parallelism schemes such as pipeline and expert parallelism for dense and mixture-of-expert models.

Vasu Shyam, Anna Golubeva, Quentin Anthony

Zyphra

Transformer Inference Transformer Tensor Parallelism Memory-Efficient Inference

Apr 29, 2026cs.LG

Efficient and Interpretable Transformer for Counterfactual Fairness

The growing reliance of machine learning models in high-stakes, highly regulated domains such as finance and insurance has created a growing tension between predictive performance, interpretability, and regulatory fairness requirements. In these settings, models are expected not only to deliver reliable predictions but also to provide transparent decision rationales and comply with strict fairness requirements. Attention-based transformers offer powerful mechanisms for modeling complex data relationships as demonstrated in various language tasks, yet their attention mechanisms alone do not ensure counterfactually fair predictions, even when combined with fairness-aware techniques. To address these limitations, we propose the Feature Correlation Transformer (FCorrTransformer), an attention-light architecture tailored for tabular data. In this design, the attention matrix admits a direct statistical interpretation as pairwise feature dependencies, enhancing both interpretability and efficiency. Leveraging this structure, we introduce Counterfactual Attention Regularization (CAR), a framework that enforces group-invariant fair representations of sensitive features at the attention level, promoting counterfactually fair predictions without relying on explicit causal assumptions. Empirical evaluations on imbalanced classification and regression benchmarks demonstrate that FCorrTransformer combined with CAR achieves strong counterfactual fairness while maintaining competitive predictive performance and substantially reducing model complexity compared with standard transformer-based baselines. Overall, this work bridges a critical gap between fairness theory and machine learning models, offering a practical framework for responsible AI in regulatory-sensitive domains.

Panyi Dong, Zhiyu Quan

Acturial and Risk Mangament Sciences, University of Illinois Urbana-Champaign, Champaign, Illinois, USA.

Transformer Interpretability Transformer Algorithmic Fairness Counterfactual Fairness