Transformer

Follow this topic Ask about this topic

Momentum

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 16, 2026cs.CL

Response-free item difficulty modelling for multiple-choice items with fine-tuned transformers: Component-wise representation and multi-task learning

Item difficulty must often be estimated before test administration, when no responses are yet available for calibration. While most response-free difficulty modelling approaches derive item-text features by hand for a separate statistical model, we fine-tune a transformer end-to-end on the wording, avoiding the theory-based feature design and the preprocessing that discards information. We address reading-comprehension multiple-choice items, whose difficulty depends on inferential demands spanning passage, question, and options, yet the simplest model sees one undifferentiated sequence and is trained on difficulty alone. We introduce and investigate two extensions to the joint-encoding baseline: a component-wise variant, which encodes the wording parts separately, and a multi-task variant, which adds an auxiliary task of question answering. We compare the methods across three training-set sizes sampled from a corpus of nearly 30,000 items whose labels approximate response-based Rasch difficulty. At the smallest training size, both extensions improve on the baseline, the multi-task variant across every metric, and component-wise encoding in rank ordering. Further research may ground the auxiliary supervision in observed responses and extend the approach to other item types.

Jan Netík, Patrícia Martinková

Faculty of Education, Charles University, Prague, Czech Republic · Institute of Computer Science of the Czech Academy of Sciences, Prague, Czech Republic

Transformer Educational Assessment Multi-Task Learning Item Response Theory

May 16, 2026cs.LG

Propagation of Chaos in Contextual Flow Maps

We develop a quantitative statistical theory of transformers in the large-context regime by adopting the abstraction of contextual flow maps (CFMs): dynamical systems that evolve a distinguished token in the presence of a contextual measure across a stack of attention blocks. Within this framework, the finite-context model approximates an idealized infinite-context system in which the contextual measure is replaced by its underlying population, so that the context length

n

becomes a statistical resource. Exploiting the McKean--Vlasov structure of the dynamics and the classical machinery of propagation of chaos, we establish a forward bound controlling the deviation between the finite- and infinite-context CFMs uniformly along depth, and a backward bound controlling the deviation between the corresponding training trajectories uniformly across iterations of online gradient descent. Both bounds achieve the optimal Wasserstein rate

n^{-1/d}

for general CFMs and parametric rate

n^{-1/2}

for a restricted class of CFMs that includes transformers as a special case. The analysis rests on a new Eulerian adjoint formulation of the loss gradient and stability estimates for the resulting forward--adjoint system, both of which may be of independent interest.

Shi Chen, Zhengjiang Lin, Kaizhao Liu +1

Transformer Gradient Descent Dynamics

May 15, 2026cs.LG

Learning How to Cube

Despite the effectiveness of Cube-and-Conquer (C&C) for solving challenging Boolean Satisfiability (SAT) problems, no prior work has shown that transformer-based models can learn effective cubing heuristics. We introduce a neuro-symbolic post-training framework for this task. We design an MCTS-based data curation pipeline that uses symbolic heuristics to explore splitting decisions over SAT competition formulas, producing preference data grounded in solver statistics and augmented with reasoning traces from a teacher model. Our two-stage post-training, supervised fine-tuning (SFT) followed by direct preference optimization (DPO), enables a 4B-parameter model to achieve a pass@5 score of 53 on 100 SAT competition benchmarks, surpassing frontier LLMs such as Claude-Sonnet-4 (50) and matching the best symbolic heuristic (53). Ablations show that SFT alone improves pass@5 from 46 to 51, with DPO adding 2 additional benchmarks; an entropy/agreement ablation on realized first-cube decisions further shows that SFT, not DPO, accounts for the root-level decision diversity that produces complementary per-run coverage over deterministic symbolic methods. This demonstrates that transformers can be trained to make effective cubing decisions in a domain traditionally dominated by symbolic methods.

Ferhat Erata, Sam Kouteili, Thanos Typaldos +4

Yale University · AWS Agentic AI

Transformer Constraint Satisfaction Neurosymbolic Learning

May 15, 2026cs.LG

No Free Swap: Protocol-Dependent Layer Redundancy in Transformers

When researchers ask whether two transformer layers are "equivalent" for compression, they often conflate distinct tests. Replacement asks whether one layer's map can substitute for another's in place; interchange asks whether two layers approximately commute when their positions are swapped. Both are output-grounded swap-KL probes, but they need not agree: on pretrained transformers the protocol gap can change which layers look safe to prune by several-fold under the same evaluator, especially when replacement distances are high. We measure both protocols across checkpoints and architectures. On a Pythia training trajectory (410M and 1.4B), the replacement-interchange gap grows from initialization to convergence. Under one matched WikiText-2 contract at 8B scale, Qwen3-8B enters a divergent regime: interchange-guided removal is several-fold safer than replacement-guided at the same layer budgets, while Llama-3.1-8B ties the two protocols for pruning cost even though interchange KL is lower, showing metric gaps need not map one-to-one to removal. Before layer removal or merging, score both swap-KLs on the target checkpoint; the diagnostic requires only unlabeled forward passes.

Gabriel Garcia

Independent Researcher

Transformer Neural Network Pruning

May 15, 2026cs.LG

Multi-Headed Transformer Architectures as Time-dependent Wasserstein Gradient Flows

In recent years, transformer architectures have revolutionized the field of language processing, opening the door to previously unforeseen possibilities. However, from a theoretical point of view, the mathematical models proposed in the literature often lack direct contact with the actual architectures and depend on strong simplifying assumptions. In this paper, we reduce this gap by modelling the data flow in multi-headed transformer architectures as time-dependent gradient flows for a suitable interaction energy capturing the design of the attention mechanism. The explicit dependence on time allows us to consider different weights for each head and for each layer, without imposing constraints on the initialization method. Moreover, we prove that, under a suitable integrability assumption on the evolution of the weights, each element of the

ω

-limit set of the gradient flows is a stationary point of the interaction energy at a limiting weight distribution. Finally, we analyse the stability of the gradient flows considering perturbations of both the initial data and the weights. Specifically, on the one hand, we study the robustness of the proposed models with respect to noisy inputs, establishing a continuous dependence of the gradient flows on the initial data and uniqueness of the flows. On the other hand, we prove the

Γ

-convergence of the perturbed interaction energy to the unperturbed one, leading to the convergence of the corresponding gradient flows. We complement these theoretical results with numerical experiments that confirm the predicted energy-dissipation identity and clarify the asymptotic behavior of the dynamics in both the autonomous-like (Ornstein--Uhlenbeck) and the genuinely non-autonomous (oscillating-weights) regimes.

Alex Massucco, Leonardo Del Grande, Marcello Carioni +2

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK · Department of Mathematics, University of Twente, Enschede, Netherlands

Transformer Wasserstein Gradient Flows Transformer Attention Multi-Head Attention

May 15, 2026cs.LG

A Retrieval-Enhanced Transformer for Multi-Step Port-of-Call Sequence Prediction in Global Liner Shipping

Accurate multi-step port-of-call sequence prediction is vital for tactical resource orchestration and logistical efficiency. However, existing methods struggle with unreliable voyage schedules and the inability of AIS data to provide visibility beyond the immediate next port. To address this, this study proposes a Connectivity-Constrained and Retrieval-Enhanced (CCRE) deep learning framework. Inspired by Retrieval-Augmented Generation, CCRE introduces a retrieval-enhanced historical encoder that queries a global maritime database for contextually similar navigational precedents. Transforming these scenarios into candidate-level semantic representations compensates for data sparsity in long-tail routes and resolves routing ambiguities. Integrating this with a Transformer-based trajectory encoder, the architecture executes adaptive "middle fusion" via cross-attention. This dynamically shifts predictive reliance from real-time kinematics for short-term accuracy to historical context for long-term strategic stability. To ensure sequence-level coherence, forecasting is formulated as a joint sequence generation problem using an autoregressive Transformer decoder enriched with Scheduled Sampling and Gumbel-Softmax relaxation. This mitigates error accumulation, while topology masks strictly enforce maritime network reachability to eliminate operationally infeasible routes. Evaluated on a global dataset, CCRE achieves a 72.3% first-destination accuracy and a 61.4% average three-step accuracy, outperforming baselines like CatBoost and LSTM by average margins of 12.6% and 11.3%, respectively. Case studies further corroborate the model's scalability and ability to capture complex routing patterns across diverse international trade lanes.

Yanzhao Su, Fang He, Yineng Wang

Department of Industrial Engineering, Tsinghua University, Beijing 100084, P.R. China · Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hong Kong

Transformer Vessel Trajectory Prediction Trajectory Prediction

May 15, 2026cs.LG

AOT-POT: Adaptive Operator Transformation for Large-Scale PDE Pre-training

Pre-training neural operators on diverse partial differential equation (PDE) datasets has emerged as a promising direction for building general-purpose surrogate models in scientific machine learning. However, the inherent complexity and structural diversity of PDE solution operators make multi-PDE pre-training fundamentally challenging. Existing methods mainly address this by increasing model capacity, while leaving the target solution operators unchanged. Inspired by classical numerical analysis, we instead propose to transform complex and diverse solution operators into simpler, better-aligned forms that are easier to model jointly. Since the optimal transformation varies across PDE types, it must be adaptive and input-dependent, allowing a single neural operator to approximate an entire family of operators. We instantiate this idea as AOT-POT (adaptive operator-transformation for pre-training operator transformer), which expands hidden representations into multiple parallel streams, adaptively aggregates and redistributes them before and after each sub-layer, and mixes streams through Sinkhorn-projected doubly stochastic matrices for stable training. These mechanisms together reshape diverse solution operators into a unified form that can be effectively modeled by a single architecture. Empirically, AOT-POT achieves state-of-the-art performance on 12 PDE benchmarks with only 3% additional parameters, reducing relative L2 error by up to 77.6% (40.9% on average). Fine-tuning AOT-POT further reduces L2 error by up to 92% on in-domain PDEs and 89% on out-of-domain PDEs (unseen types during pre-training), demonstrating that adaptive operator transformation is an effective and complementary direction for advancing PDE foundation models beyond simply scaling model capacity.

Qitan Lv, Hong Wang, Zhongkai Hao +5

University of Science and Technology of China · 2Shanghai AI Laboratory · Department of Electronic Engineering, Tsinghua University, China

Transformer PDE Operator Learning Neural Operators

May 15, 2026cs.LG

Grokking as Structural Inference: Transformers Need Bayesian Lottery Tickets

Why does a Transformer that has memorized its training set wait thousands of steps before it generalizes? Existing accounts locate this delay in norm minimization, feature emergence, or the late discovery of sparse subnetworks. These explanations capture important parts of the transition, but ignore a constraint unique to attention-based models: if attention discards an informative token, no bounded downstream computation can recover it. We formalize attention as an implicit Bayesian posterior over the task dependency graph and prove that generalization requires two separable conditions: a familiar Goldilocks bound on MLP capacity, coinciding with norm-based theories of grokking, and a novel Bayesian structural condition requiring attention to place sufficient mass on every informative token. This decoupling explains delayed generalization as delayed structural inference. Early in training, the MLP memorizes through unaligned features, drives the cross-entropy loss near zero, and thereby starves attention of structural gradient. Weight decay must then erode memorization before the missing graph becomes learnable, yielding the known inverse-weight-decay delay, which we derive as a structural waiting time. We then prove that this explaining-away delay can be bypassed by a KL-based structural intervention, yielding an inverse-intervention-strength scaling law for the grokking time. Experiments on algorithmic sequence tasks isolate structure from capacity and show that this Bayesian ticket matches or outperforms lottery-ticket transfer.

Kai Hidajat, Solden Stoll, Joseph An

Department of Computer Science University of Washington Seattle, WA 98195

Neural Network Generalization Transformer Self-Attention Attention Mechanisms Grokking

May 15, 2026cs.CL

GiLT: Augmenting Transformer Language Models with Dependency Graphs

Augmenting Transformers with linguistic structures effectively enhances the syntactic generalization performance of language models. Previous work in this direction focuses on syntactic tree structures of languages, in particular constituency tree structures. We propose Graph-Infused Layers Transformer Language Model (GiLT) which leverages dependency graphs for augmenting Transformer language models. Unlike most previous work, GiLT does not insert extra structural tokens in language modeling; instead, it injects structural information into language modeling by modulating attention weights in the Transformer with features extracted from the dependency graph that is incrementally constructed along with token prediction. In our experiments, GiLT with semantic dependency graphs achieves better syntactic generalization while maintaining competitive perplexity in comparison with Transformer language model baselines. In addition, GiLT can be finetuned from a pretrained language model to achieve improved downstream task performance. Our code is released at https://github.com/cookie-pie-oops/GiLT-LM.

Tianyu Huang, Yida Zhao, Chuyan Zhou +1

School of Information Science and Technology, ShanghaiTech University · Shanghai Engineering Research Center of Intelligent Vision and Imaging

Transformer Language Modeling Compositional Generalization

May 14, 2026cs.GR

WorldParticle: Unified World Simulation of Lagrangian Particle Dynamics via Transformer

A unified simulator that can model diverse physical phenomena without solver-specific redesign is a long-standing goal across simulation science. We present a learning-based particle simulator built on a single transformer architecture to model cloth, elastic solds, Newtonian and non-Newtonian fluids, granular materials, and molecular dynamics. Our model follows a prediction-correction design on a shared Lagrangian particle representation. An explicit predictor first advances particles under the known external forces, producing an intermediate state that captures externally driven motion but not inter-particle interactions. A learned corrector then predicts the residual position and velocity updates through three stages: a particle tokenizer that encodes local particle-particle, particle-boundary, and topology-guided interactions; a super-token encoder that hierarchically merges particle tokens into a compact set of super tokens via alternating self-attention and token merging; and a super-token decoder that lifts these super tokens back to particle resolution through cross-attention to predict per-particle position and velocity corrections. Progressive token merging reduces the attention cost at successive encoder layers by halving the token count at each level, and the decoder communicates through the compact super-token set rather than full particle-to-particle attention. Across the six dynamics categories, the same architecture generalizes to unseen materials, boundary configurations, initial conditions, and external forces. We further demonstrate downstream interactive control, inverse design, and learning from real-world manipulation data, reducing the need for per-phenomenon solver engineering.

Caoliwen Wang, Minghao Guo, Siyuan Chen +13

University of British Columbia, Canada · MIT CSAIL, USA · Georgia Institute of Technology, USA +7

Neural Surrogate Modeling Transformer Physics-Based Simulation Deformable Object Simulation

May 14, 2026cs.CL

Ideology Prediction of German Political Texts

Elections represent a crucial milestone in a nation's ongoing development. To better understand the political rhetoric from various movements, ranging from left to right, we propose a transformer-based model capable of projecting the political orientation of a text on a continuous left-to-right spectrum, represented by a normalized scalar d between -1 and 1. This approach enables analysts to focus on specific segments of the political landscape, such as conservatives, while excluding liberal and far-right movements. Such a task can only be achieved with multiclass classifiers, provided that the desired orientation is incorporated within one of their predefined classes. To determine the most suitable foundation model among 13 candidate transformers for this task, we constructed four distinct corpora. One corpus comprised annotated plenary notes from the German Bundestag, while another was based on an official online decision-making tool, Wahl-O-Mat. The third corpus consisted of articles from 33 newspapers, each identified by its political orientation, and the fourth included 535,200 tweets from 597 members of the 20th and 21st German Bundestag. To mitigate overfitting, we used two distinct corpora for training and two for testing, respectively. For in-domain performance, DeBERTa-large achieved the highest F1 score F1=0.844 as well as for the X (Twitter) out-of-domain test ACC=0.864. Regarding the newspaper out-of-domain test, Gemma2-2B excelled (MAE = 0.172). This study demonstrates that transformer models can recognize political framing in German news at the level of public opinion polls. Our findings suggest that both the model architecture and the availability of domain-specific training data can be as influential as model size for estimating political bias. We discuss methodological limitations and outline directions for improving the robustness of bias measurement.

Sinclair Schneider, Florian Steuber, Joao A. G. Schneider +1

Bundeswehr University Munich · Research Institute CODE · Carl-Wery-Straße 22 +1

Transformer Political Discourse Analysis Text Classification

May 14, 2026cs.LG

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

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

Jesseba Fernando, Grigori Guitchounts

Network Science Institute, Northeastern University · Flagship Pioneering

Dynamical Systems Transformer LLM Interpretability Spectral Methods Neural Network Training Dynamics

May 13, 2026cs.CL

Exploiting Pre-trained Encoder-Decoder Transformers for Sequence-to-Sequence Constituent Parsing

To achieve deep natural language understanding, syntactic constituent parsing plays a crucial role and is widely required by many artificial intelligence systems for processing both text and speech. A recent approach involves using standard sequence-to-sequence models to handle constituent parsing as a machine translation problem, moving away from traditional task-specific parsers. These models are typically initialized with pre-trained encoder-only language models like BERT or RoBERTa. However, the use of pre-trained encoder-decoder language models for constituency parsing has not been thoroughly explored. To bridge this gap, we extend the sequence-to-sequence framework by investigating parsers built on pre-trained encoder-decoder architectures, including BART, mBART, and T5. We fine-tune them to generate linearized parse trees and extensively evaluate them on different linearization strategies across both continuous treebanks and more complex discontinuous benchmarks. Our results demonstrate that our approach outperforms all prior sequence-to-sequence models and performs competitively with leading task-specific constituent parsers on continuous constituent parsing.

Daniel Fernández-González, Cristina Outeiriño Cid

Universidade de Vigo, Departamento de Informática, Campus As Lagoas s/n, Ourense, 32004,, Spain

May 13, 2026cs.LG

Chem-GMNet: A Sphere-Native Geometric Transformer for Molecular Property Prediction

Modern SMILES-based chemical language models obtain strong MoleculeNet performance by treating SMILES as generic text and compensating with multi-million-molecule self-supervised pretraining. We ask: when a domain carries structural priors as rich as chemistry's, does it warrant a domain-native transformer rather than a generic one rescued by scale? We answer affirmatively with \textbf{GM-Net} (Geometric Measure Network), a transformer family in which every module is replaced by a sphere-native counterpart, and instantiate it as \textbf{Chem-GMNet}. Three blocks follow: SH-Embedding (tokens as learnable directions on

S^{k-1}

lifted through a Gegenbauer feature map); DualSKA (a per-head fusion of a linear-time gated Sphere-Flow recurrence whose persistent state we prove is the truncated multipole expansion of the input distribution, and a softmax Sphere-Kernel branch over the same Schoenberg-valid kernel); and SH-FFN (sphere projection

\to

Gegenbauer lift

\to

moment readout). On canonical DeepChem scaffold splits, against same-shape ChemBERTa-2 baselines under the chemberta3-faithful protocol: (i) random-initialised, Chem-GMNet wins on 7 of 10 MoleculeNet endpoints at

\sim\!35\%

fewer parameters; (ii) pretrained on the same 10M-SMILES ZINC corpus as ChemBERTa-2 MLM-10M, it matches or beats the public release on 6 of 8 shared endpoints (5/7 excluding a known ClinTox release anomaly). A

(k,L)

ablation shows that increasing the sphere dimension from

k\!=\!8

to

k\!=\!10

at fixed

L\!=\!3

lowers ESOL RMSE to

0.938

at scratch, beating pretrained ChemBERTa-2 MLM-10M on this endpoint without any pretraining at all.

Deepak Warrier, Raja Sekhar Pappala

MSTACK AI

Transformer Geometric Representation Learning Molecular Property Prediction Molecular Representation Learning

May 12, 2026cs.LG

Precision Tracked Transformer via Kalman Filtering, Kriging and Process Noise

The Transformer is the foundational building block of modern AI, yet offers no principled handling of \emph{uncertainty}, which is prevalent in real applications: cold-start tokens with sparse histories in sequential recommendation, heterogeneous signal quality in language models, and attention sinks induced by unconstrained softmax. Every token is treated with uniform confidence. We show this uniformity is a degenerate case of our \emph{Bayesian Filtering Transformer} (BFT): attention becomes precision-weighted kriging, the residual connection becomes a Kalman update with adaptive gain, and the FFN becomes a dynamics model propagating precision via a Jacobian--plus--process-noise rule. Observation precision comes from a parameter-free Restricted Maximum Likelihood (REML) estimator with a conjugate Bayesian prior. BFT replaces any Transformer layer with negligible overhead. On sequential recommendation, BFT applied to three major architectures yields significant gains on six benchmarks, with the largest improvements on cold-start users and rare items where uncertainty is highest. On supervised fine-tuning of large language models with noisy data, BFT improves robustness in two regimes: noisy supervision (token-label corruption in question answering) and noisy context (retrieval-augmented QA with real RAG distractors). A single principled modification -- restoring precision -- unlocks substantial headroom across both classical sequence-modeling and modern LLM regimes.

Bo Long, Deepak Agarwal, Jelena Markovic-Voronov +2

LinkedIn Core AI

Bayesian Filtering Transformer Attention Mechanisms Language Model Robustness

May 12, 2026cs.LG

Emergence of Frontier Superposition: Möbius attractor and Cascade Supervision

Superposition allows Transformers to reason in depth, carrying an entire reasoning frontier in parallel through a bounded-depth forward pass instead of unrolling serial chain-of-thought tokens. While Zhu et al. (2025) hand-crafted an equal-weight breadth-first frontier in a single residual stream for graph reachability, it remained open whether gradient descent could ever find this target amidst permutation-symmetric saddles. We close this gap on Reachability-by-Superposition over Erdős-Rényi graphs by isolating architectural and supervisional contributions. Architecturally, we identify a Möbius attractor: under

S_n

-symmetry in the tree regime, layerwise dynamics reduce to a 1D Möbius map whose zero set is a codimension-one manifold of global optima containing the equal-weight superposition state. On the supervision side, we identify Cascade Supervision: a loss class whose backward pass simultaneously delivers (A) selectivity bootstrap, (B) gradient persistence across depth, and (C) per-step discrimination (e.g., \mathcal{L}{sup} and \mathcal{L}{node}). End-to-end supervision fails condition (B) and is provably insufficient: internal gradients at layer c decay as (np)^{-(D-c-2)/2} in the graph fan-out and stall before the manifold is reached. Our thesis: Möbius attractor + Cascade Supervision = emergence of superposition reasoning. The parameter-free decay law predicts a final-step cosine of 0.35 vs. 0.71 (end-to-end vs. cascade) at depth D=3; experiments confirm 0.37 vs. 0.69, matching within 0.02 at every step.

Hongyu Gu, Jingwen Fu

University of Science and Technology of China · Zhongguancun Academy

Transformer Process Supervision

May 11, 2026math.AP

Quantifying Concentration Phenomena of Mean-Field Transformers in the Low-Temperature Regime

Transformers with self-attention modules as their core components have become an integral architecture in modern large language and foundation models. In this paper, we study the evolution of tokens in deep encoder-only transformers at inference time which is described in the large-token limit by a mean-field continuity equation. Leveraging ideas from the convergence analysis of interacting multi-particle systems, with particles corresponding to tokens, we prove that the token distribution rapidly concentrates onto the push-forward of the initial distribution under a projection map induced by the key, query, and value matrices, and remains metastable for moderate times. Specifically, we show that the Wasserstein distance of the two distributions scales like

\sqrt{{\log(β+1)}/β}\exp(Ct)+\exp(-ct)

in terms of the temperature parameter

β^{-1}\to 0

and inference time

t\geq 0

. For the proof, we establish Lyapunov-type estimates for the zero-temperature equation, identify its limit as

t\to\infty

, and employ a stability estimate in Wasserstein space together with a quantitative Laplace principle to couple the two equations. Our result implies that for time scales of order

\logβ

the token distribution concentrates at the identified limiting distribution. Numerical experiments confirm this and, beyond that, complement our theory by showing that for finite

β

and large

t

the dynamics enter a different terminal phase, dominated by the spectrum of the value matrix.

Albert Alcalde, Leon Bungert, Konstantin Riedl +1

Department of Mathematics Friedrich-Alexander-University Erlangen-Nürnberg · Institute of Mathematics CAIDAS University of Würzburg · Mathematical Institute University of Oxford Reuben College +1

Transformer Inference Transformer Transformer Attention Mean-Field Theory

May 11, 2026cs.CV

Masked Generative Transformer Is What You Need for Image Editing

Diffusion models dominate image editing, yet their global denoising mechanism entangles edited regions with surrounding context, causing modifications to propagate into areas that should remain intact. We propose a fundamentally different approach by leveraging Masked Generative Transformers (MGTs), whose localized token-prediction paradigm naturally confines changes to intended regions. We present EditMGT, an MGT-based editing framework that is the first of its kind. Our approach employs multi-layer attention consolidation to aggregate cross-attention maps into precise edit localization signals, and region-hold sampling to explicitly prevent token flipping in non-target areas. To support training, we construct CrispEdit-2M, a 2M-sample high-resolution (>1024) editing dataset spanning seven categories. With only 960M parameters, EditMGT achieves state-of-the-art image similarity on multiple benchmarks while delivering 6x faster editing, demonstrating that MGTs offer a compelling alternative to diffusion-based editing.

Wei Chow, Linfeng Li, Xian Sun +14

1ByteDance · 2National University of Singapore · 3Duke University +2

Transformer Text-Guided Image Editing Image Editing

May 11, 2026stat.ML

Uniform Scaling Limits in AdamW-Trained Transformers

We study the large-depth limit of transformers trained with AdamW, by modelling the hidden-state dynamics as an interacting particle system (IPS) coupled through the attention mechanism. Under appropriate scaling of the attention heads, we prove that the joint dynamics of the hidden states and backpropagated variables converge in

L^2

, uniformly over the initial condition, to the solution of a forward--backward system of ODEs at rate

\mathcal O(L^{-1}+L^{-1/3}H^{-1/2})

. Here,

L

and

H

denote the depth and number of heads of the transformer, respectively. The limiting system of ODEs can be identified with a McKean--Vlasov ODE (MVODE) when the attention heads do not incorporate causal masking. By using the flow maps associated with this MVODE and applying concentration of measure techniques, we obtain bounds on the difference between the discrete and continuous models that are uniform over compact sets of initial conditions. As this is achieved without resorting to a covering argument, the constants in our bounds are independent of the number of tokens. Furthermore, under a suitable adaptation to AdamW, the bounds become independent of the token embedding dimension.

William Gibson, Christoph Reisinger

Mathematical Institute · University of Oxford · Oxford, OX2 6GG, UK

Transformer Self-Attention Neural Network Training Dynamics

May 11, 2026cs.CR

DRIFT: Drift-Resilient Invariant-Feature Transformer for DGA Detection

Domain Generation Algorithms (DGAs) evolve continuously to evade botnet detection, posing a persistent challenge for dependable network defense. While deep learning-based detectors achieve strong performance under static conditions, they suffer severe degradation when facing temporal drift. Through a 9-year longitudinal study (2017-2025), we empirically show that state-of-the-art character- and word-based DGA classifiers rapidly lose effectiveness as new DGA variants emerge. To address this problem, we propose a drift-resilient Transformer-based framework that learns invariant representations through a hybrid tokenization strategy and multi-task self-supervised pre-training. The model integrates (i) character-level encoding to capture stochastic morphological patterns and (ii) subword-level encoding for word-based DGAs. Three pre-training tasks enable the model to learn robust structural and contextual features prior to supervised fine-tuning. Comprehensive evaluations demonstrate that our method significantly mitigates temporal degradation and consistently outperforms state-of-the-art baselines in forward-chaining experiments. The proposed approach offers a dependable foundation for long-term DGA defense in evolving threat landscapes. Our code is available at: https://github.com/snsec-net/2026-DSN-DRIFT.

Chaeyoung Lee, Chaeri Jung, Seonghoon Jeong

Division of Artificial Intelligence Engineering Sookmyung Women’s University Seoul, Republic of Korea

Transformer Concept Drift Invariant Representation Learning

May 11, 2026cs.LG

Rethinking Random Transformers as Adaptive Sequence Smoothers for Sleep Staging

Automatic sleep staging commonly adopts Transformers under the assumption that they learn complex long-range dependencies. We challenge this view by revealing a neglected property of sleep sequences: strong local temporal continuity. We show that a randomly initialized Transformer, without any training, substantially improves sleep staging performance and consistently outperforms heuristic smoothing. We formalize this effect via a Random Attention Prior Kernel (RAPK), showing that random self-attention acts as an adaptive smoother by balancing global averaging and content-based similarity while preserving stage transitions. Using two metrics, the Local Smoothness Influence Index (LSII) and the Weighted Transition Entropy (WTE), we provide evidence that most performance gains in Transformer-based sleep staging arise from architectural inductive bias rather than parameter learning. Our results suggest that sleep staging can be effectively addressed with structure-driven smoothing mechanisms rather than complex dependency modeling, enabling more efficient and edge-deployable healthcare systems for large-scale physiological monitoring.

Guisong Liu, Xin Gao, Martin Dresler +2

School of Biological Science and Medical Engineering Southeast University Nanjing, China · University of Bath Bath, England · Donders Institute for Brain, Cognition and Behaviour Radboud University Medical Center Nijmegen, The Netherlands +1

Sleep Stage Classification Transformer Transformer Attention Time Series Transformers

May 11, 2026cs.LG

Continuous Latent Contexts Enable Efficient Online Learning in Transformers

Large language models (LLMs) exhibit a strong capacity for in-context learning: Given labeled examples, they can generate good predictions without parameter updates. However, many interactive settings go beyond static prediction to online decision-making, in which effective behavior demands adaptation over long multi-turn horizons in response to feedback, and efficient algorithms in these domains must use compact representations of what they have learned. Recently, continuous transformer architectures with latent chain of thought have shown promise for offline iterative tasks such as directed graph-reachability. Motivated by this, we study whether continuous latent context tokens equip transformers to more effectively realize online learning. We give explicit constructions of constant-depth transformers that implement two foundational online decision-making procedures -- the weighted majority algorithm and

Q

-learning -- by storing their algorithmic state as linear combinations of feature embeddings, using a small number of latent context tokens. We further train a small GPT-2-style transformer with latent contexts using a multi-curriculum objective that does not directly supervise the latent states. On long synthetic online prediction sequences, this model outperforms larger and more complex LLMs, including Qwen-3-14B and DeepSeek-V3. Our results suggest that continuous latent contexts provide a simple and effective persistent state for transformers to implement online learning algorithms.

Emile Anand, Abdullah Ateyeh, Xinyuan Cao +1

Georgia Institute of Technology · University of California, Berkeley · Columbia University

Transformer Sequential Decision Making Online Learning

May 11, 2026cs.CV

Probing Routing-Conditional Calibration in Attention-Residual Transformers

Post-hoc calibration is usually evaluated as a function of logits or softmax confidence alone, even as routing-augmented architectures increasingly accompany predictions with sample-specific internal routing traces and pair them with claims of calibration-relevant uncertainty. We ask a basic question: do these traces provide stable routing-specific evidence for post-hoc calibration beyond confidence? We study this in Attention-Residual transformers (Kimi Team, 2026) through a matched-confidence diagnostic suite that stratifies examples by routing-derived state, compares subgroup gaps against within-bin routing-permutation nulls, and evaluates matched post-hoc probes differing only in their auxiliary feature. Across our completed AR runs, scalar routing summaries do not provide stable evidence of routing-conditional miscalibration: weighted gaps remain small or seed-sensitive, and only

1

of

30

within-bin permutation tests rejects the conditional-null at

α=0.05

(only on one seed; not stable across seeds in that cell). AR-CondCal, a minimal

2

-D Nadaraya--Watson probe on confidence and routing-depth variance, lies within the seed-variance band of matched confidence-only and predictive-entropy controls and does not reliably improve worst-routing-tertile ECE; bandwidth-sensitivity checks (Scott multiples, CV-NLL, global-ECE oracle) do not change this. A full-vector MLP over

(c, H_1, \ldots, H_L)

can appear to improve over a linear confidence baseline, but the apparent gain disappears once a capacity-matched confidence-only MLP is included as a control, and shuffled routing profiles achieve comparable performance. Apparent routing-aware calibration gains in this AR setting should not be read as internal-state calibration until matched-confidence, bandwidth, capacity, and permutation controls rule out common confounds.

Wenhao Liang, Lin Yue, Wei Emma Zhang +4

Adelaide University · Australian Institute for Machine Learning (AIML), Adelaide University · The University of Queensland

Post-Hoc Calibration Transformer

May 10, 2026cs.LG

One for All: A Non-Linear Transformer can Enable Cross-Domain Generalization for In-Context Reinforcement Learning

A central challenge in reinforcement learning (RL) is to learn models that generalize beyond the tasks on which they are trained, a goal traditionally pursued through multi-task and meta RL. Recently, transformer architectures have emerged as a promising approach, enabling adaptation to new tasks via in-context learning without explicit parameter updates. From a functional perspective, a transformer can be viewed as a functional operator that maps a context to a task-specific function. It is thus fundamental to understand and design this operator to support stronger generalization in RL. In this work, we address this resulting question of generalization from a kernel-based perspective by establishing a connection between non-linear transformers and kernel-based temporal difference learning. By interpreting the transformer as performing regression in a Reproducing Kernel Hilbert Space (RKHS), we show that value functions from different domains can be represented using a shared set of weights, provided they lie within the same RKHS. Experiments on multiple MetaWorld domains support this interpretation, demonstrating convergence of the temporal-difference objective.

Bowen He, Juncheng Dong, Lin Lin +1

Duke University, Durham, U.S.A.

Reinforcement Learning Transformer Transformer-Based RL Temporal-Difference Learning Cross-Domain Generalization In-Context Learning+2

May 10, 2026cs.LG

Spectral Transformer Neural Processes

Time series, spatial data, and images are natural applications of Neural Processes. However, when such data exhibit strong periodicity and quasi-periodicity, existing methods often suffer from underfitting and generalise poorly beyond the training distribution. In this work, we propose Spectral Transformer Neural Processes (STNPs), a frequency-aware extension of Transformer Neural Processes (TNPs). STNPs introduce a Spectral Aggregator that estimates an empirical context spectrum, compresses it into a spectral mixture, samples task-adaptive spectral features, and concatenates them with time-domain embeddings, thereby injecting a spectral-mixture-kernel bias into TNPs. This design reshapes the similarity geometry, allowing inputs that are distant in Euclidean space to remain close in an induced periodic manifold while enhancing time-frequency interactions. Extensive experiments on synthetic regression tasks, real-world time-series datasets, and an image dataset demonstrate that STNPs consistently improve predictive performance over existing baselines, extending Neural Processes beyond translation equivariance towards effective modelling of periodicity and quasi-periodicity.

Xianhe Chen, Hao Chen, Yingzhen Li

University of Cambridge · Tencent · Imperial College London

Transformer Neural Processes Frequency-Domain Feature Learning Time Series Forecasting Time Series Transformers

May 10, 2026cs.LG

The Transformer as a Polar State Estimator

We show that the core components of the Transformer---attention, residual connections, and normalization---arise naturally from a single geometric state estimation problem. Modeling the latent state in polar coordinates naturally separates radial and hyperspherical dynamics, yielding a precision-weighted filtering procedure in which normalization enforces the hyperspherical constraint, attention aggregates directional evidence, and the residual connection implements an incremental state update. The standard Transformer block with rotary positional encodings is recovered by discarding the geometric correction terms of the resulting state estimator, showing that its architecture follows from the underlying estimation problem rather than from independent design choices. The proposed \textit{Polar Transformer} retains these geometric corrections.

Peter Racioppo

Independent Researcher Los Angeles, CA

Transformer Layer Normalization Attention Mechanisms

May 10, 2026cs.LG

Sparsity Moves Computation: How FFN Architecture Reshapes Attention in Small Transformers

Architectural choices inside the Transformer feedforward network (FFN) block do not merely affect the block itself; they reshape the computations learned by the rest of the model. We study this effect in one-layer Transformers trained on digit addition with carry, modular arithmetic, and histogram counting. Comparing dense FFNs, gated linear units (GLUs), mixture-of-experts (MoE), and MoE-GLUs, we find that sparse MoE routing can shift computation from FFN to attention, with the strongest ablation-visible effect on carry-based addition. We decompose this redistribution into reduced per-token FFN capacity and sparse partitioning across experts. Critically, frozen random routing nearly matches learned routing, suggesting that redistribution is driven largely by architectural sparsity rather than router-learned specialization. As a secondary finding, GLU-style multiplicative gating rotates task-relevant Fourier structure out of the per-neuron basis and into distributed subspaces, making neuron-level interpretability less informative while preserving structured computation. We validate these conclusions with random-routing, narrow-FFN, and top-2 MoE controls, plus parameter-matching, activation-function, and width-scaling analyses. Together, these results show that local FFN design choices can have nonlocal consequences for Transformer computation.

Gabriel Smithline, Chris Mascioli

University of Michigan

Transformer FFNs Transformer Mixture of Experts Attention Mechanisms

May 9, 2026cs.LG

VORT: Adaptive Power-Law Memory for NLP Transformers

Standard Transformers impose near-exponential decay on the influence of distant tokens, conflicting with the power-law structure of long-range dependencies in natural language. We introduce the \emph{Variable-Order Retention Transformer} (\VORT{}), a memory architecture in which each ingested token is assigned a learnable fractional order α_i\in[δ,1] that governs a Grünwald--Letnikov power-law retention kernel. Because the fractional weighted sum is non-Markovian, we approximate it through a sum-of-exponentials (SOE) decomposition computed by Gauss--Laguerre quadrature on a Laplace-type integral representation of the kernel weights. Each exponential component admits a one-step Markovian recurrence at O(Sd_v) per step, where S=O(\log(T/\varepsilon)) terms suffice for \varepsilon-uniform accuracy on horizon [1,T]. Retrieval is keyed and associative via a linear-attention accumulator with an exact O(KSd_φd_v) -per-step recurrence. Four results are established: (i) an SOE approximation theorem with geometric convergence rate from the analyticity of the integrand after a log-change of variables; (ii) a quantisation bound valid on [δ,1] with correct analysis near α=0; (iii) a direct L^2 energy argument (Proposition) showing that for α>1/2 any mixture with fixed minimum decay rate Λ>0 incurs L^2([1,T]) error at least N_α(T)-C(Λ)\to\infty, with the Λ-dependence made explicit; and (iv) linear convergence of a gradient plasticity rule under the Polyak--Łojasiewicz condition. Two synthetic experiments confirm the architectural advantage: a Zipf-distributed retrieval benchmark and an entity label-copy task with uniform lag distribution, the latter ruling out prior-matching as an explanation for the power-law kernel's advantage.

Nabil Mlaiki

Department of Mathematics and Sciences, Prince Sultan University, Riyadh, Saudi Arabia

Memory-Augmented Language Models Transformer Long-Context Language Modeling Persistent Memory for Language Models

May 9, 2026stat.ML

Learning Theory of Transformers: Local-to-Global Approximation via Softmax Partition of Unity

This paper investigates the learning theory of Transformer networks for regression tasks on the compact Euclidean domain

[0,1]^d

and

d

-dimensional compact Riemannian manifolds. We propose a novel constructive approximation framework for Transformers that builds local approximations of the target function and aggregates them into a global approximation via softmax partition of unity. This approach leverages the attention mechanism to achieve spatial localization through affine transformations of the input. The softmax activation plays a crucial role in aggregating local approximations to a global output. From an approximation perspective, we prove that a dense Transformer equipped with only two encoder blocks and standard single-hidden-layer point-wise feed-forward networks can achieve a uniform

\varepsilon

-approximation error for

α

-Hölder continuous functions with

α\in (0,1]

using

\mathcal{O}(\varepsilon^{-d/α})

total parameters. Building upon this approximation guarantee, we establish a near minimax-optimal generalization error bound of order

\mathcal{O}\big(n^{-\frac{2α}{2α+d}} \log n\big)

for the empirical risk minimizer, where

n

is the training data size. The Transformer architecture studied in this paper is dense, shallow and wide, and employs softmax activation and sinusoidal positional encodings, closely reflecting practical implementations.

Zhongjie Shi, Wenjing Liao

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States

Neural Network Generalization Transformer Neural Network Approximation Theory Statistical Learning Theory

May 9, 2026cs.LG

Probing the Impact of Scale on Data-Efficient, Generalist Transformer World Models for Atari

Developing generalist systems that retain human-like data efficiency is a central challenge. While world models (WMs) offer a promising path, existing research often conflates architectural mechanisms with the independent impact of model \emph{scale}. In this work, we use a minimalist transformer world model to analyze scaling behaviors on the Atari 100k benchmark, using fixed offline datasets derived from a presupposed expert policy. Our results reveal that environments fundamentally fall into distinct scaling regimes, even when constrained by identical offline data budgets and model capacities. For individual tasks, some environments naturally allow models to pass the interpolation threshold, yielding monotonic improvements in the overparameterized regime, while others remain trapped in the classical regime, where larger world models degrade fidelity. In the unified setting, i.e., a single transformer trained on a suite of 26 Atari environments, we uncover that joint training stabilizes scaling dynamics, ensuring monotonic gains across all environments, regardless of their distinct inherent scaling regimes. Finally, we demonstrate that improved fidelity translates directly to downstream control, with policies learned entirely within the simulated dynamics achieving a median expert-random-normalized score of 0.770. Our findings suggest that future progress lies as much in precise scaling strategies as in architectural innovation.

Jooyeon Kim

Graduate School of Artificial Intelligence UNIST

World Model Learning Transformer World Models Data-Efficient Learning