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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

Sep 21, 2026cs.LG

Enhancing Transformer Representations of Symbolic ODE Expressions

Existing approaches to solving differential equations, such as symbolic regression, physics informed neural networks, and neural operators, typically focus on numerical approximations or blind symbolic search via fitting to numerical data. Less attention has been paid to learning structured representations of mathematical expressions that preserve commutative properties and could support mathematical reasoning in symbolic forms. Transformer models have shown strong capabilities in solving symbolic differential equations. However, standard positional embeddings in transformers are designed for sequence data. Symbolic differential equations are naturally represented by expression trees, so these positional embeddings may not efficiently capture their hierarchical structures. We investigate existing tree positional embeddings in symbolic ordinary differential equation (ODE) tasks. We systematically study their effectiveness under different settings. Our results show that tree positional embeddings aid learning in early epochs and continue to improve performance throughout, ultimately yielding consistent advantages across various data sizes and tasks. Based on learned structural representations, we apply contrastive learning to support the commutative property in mathematics. Ablation studies provide insight into how these methods interact in modelling symbolic mathematical structures.

Xiyue Fan, Adam Prugel-Bennett, Stuart E. Middleton

University of Southampton

Transformer Positional Encoding

Sep 17, 2026cs.CL

Design of the IBM Granite 5.0 TurboCTC ASR Model

We describe the architecture, training methodology and inference speedups of Granite 5.0 Turbo CTC, a 470 million parameter encoder-only model with an excellent speed-accuracy tradeoff. The architecture uses pyramidal temporal subsampling within Conformer blocks using strided depthwise convolutions, block-diagonal (chunk-wise) self-attention, and conditioning on intermediate predictions from the middle layer. Training highlights are the use of only publicly available data, the novel use of a Muon optimizer, and balanced data sampling. Inference speedups include replacing 1 x 1 convolutions with linear layers and optimizing the attention computation in the Conformer blocks. Collectively, these result in a model that is on the speed-accuracy Pareto frontier of the Open ASR leaderboard for English short-form ASR while being twice as fast as the fastest competitor. The model can be used under a permissive license and downloaded from https://huggingface.co/ibm-granite/granite-speech-5.0-470m-turboctc.

Brian Kingsbury, George Saon, Masayuki Suzuki +5

IBM Research

Transformer Automatic Speech Recognition

Sep 15, 2026cs.RO

TIO-Former: Ultra-Lightweight 6-Directional ToF-Inertial Odometry for Nano-UAVs via a Streaming Causal Transformer

Autonomous nano-UAV navigation requires accurate ego-motion estimation under stringent size, weight, power, and computing (SWaP-C) constraints, where visual sensors and LiDARs exceed payload limits, optical flow degrades in low-texture scenes, and inertial-only state estimation is susceptible to accumulated drift. While multi-zone time-of-flight (ToF) arrays provide a lightweight metric complement, 6-DoF estimation from merely 384 ranges per frame is challenged by invalid returns, anisotropic observability, and temporal computational scaling. We propose TIO-FORMER, a camera-free, optical-flow-free, and mapless range-inertial odometry framework driven by an IMU and an ultra-lightweight (15 g) payload of six orthogonal 8 x 8 ToF arrays. Our frontend pairs consecutive range grids with a bilateral gated difference, while IMU-guided cross-attention dynamically routes directional features conditioned on platform kinematics. A Streaming Causal Transformer couples an uncompressed Local KV cache with compressed Chunk-FIFO memory, maintaining bounded inference cost and memory footprint independent of flight duration. In real-flight evaluations, TIO-FORMER reduces open-loop position error by 54.4% compared to nano-UAV optical flow and by 66.4%-89.1% over learned inertial baselines. We also evaluate performance across multiple environments and robustness under severe sensing degradation. Deployed on an edge RISC-V companion computer, TIO-FORMER achieves a P95 latency of 10.466 ms and peak resident memory of 6.324 MiB (less than 5 percent system RAM), demonstrating that sparse range sensing provides practical geometric anchoring for resource-constrained micro-aerial robots. Code is available at https://github.com/Ly041021/TIO-Former.

Yang Liu, Yifan He, Wenhao Zhao +9

Zhejiang University, Hangzhou, China · Differential Robotics, Hangzhou, China

Inertial Odometry Transformer UAV Navigation Robot State Estimation Multimodal Sensor Fusion

Sep 14, 2026cs.CV

Investigating Temporal Motion Features for Pose-to-Text Indian Sign Language Translation

We investigate the effect of pretrained T5 model scale and explicit motion features on pose-to-text Indian Sign Language Translation (SLT) for the WSLP 2026 Shared Task. Pose sequences are projected into the embedding space of T5 through a lightweight pose encoder, with the complete model fine-tuned to generate English text. The shared task data used for this work consists of a test set with 5,334 examples and a validation set with 5,257 examples. We compare T5-small, T5-base, and T5-large, and additionally introduce a motion-augmented variant, T5-small + Motion, that adds explicit frame-to-frame pose differences to the input representation. T5-small achieves the best BLEU and ROUGE scores among the spatial-only models, while T5-large obtains the highest chrF score. Augmenting T5-small with motion features yields the largest single improvement observed in our study, substantially improving BLEU over the spatial-only baseline and making it the strongest model overall on this metric. Our submitted system ranked 5th on the official WSLP 2026 SLT testing leaderboard. The source code and trained models are publicly available on GitHub and HuggingFace.

Manav Dhamecha, Praveen Kumar Chandaliya, Pruthwik Mishra

Sardar Vallabhbhai National Institute of Technology, Surat, India

Sign Language Translation Transformer Motion Representation Learning

Sep 14, 2026cs.CL

Type Diversity Enables Transformers to Generalise Compositionally

Compositional generalisation has been divided into lexical and structural generalisation. Previous work has found that structural generalisation is harder than lexical for Transformers. We propose that this difference is not inherent to Transformers, but due to the high diversity of lexical types and low diversity of structural types in the specific datasets of these previous works. By type diversity we mean the number of different constructors of that type, instead of, for example, the specific word combinations that might populate the structure. To test this, we vary the amounts of type diversity of lexical and structural types in previously published datasets. We create linguistically diverse variants of the COGS and SLOG datasets using Grammatical Framework. We find that type diversity correlates with compositional generalisation equally in lexical and structural test cases, supporting our hypothesis. We note a contradiction with the proposition in previous work that compound divergence explains the difficulty in compositional generalisation tasks. We further investigate the effects of other dataset properties on compositional generalisation, such as the diversity of types other than the novel test structure, and surface properties of the logical semantics format.

Anssi Moisio, Mathias Creutz, Mikko Kurimo

Aalto University · University of Helsinki

Transformer Semantic Parsing Compositional Generalization

Sep 12, 2026cs.SD

A New Transformer-Based Approach for Audio-Based Kinship Verification and a New Uncontrolled Mandarin Kinship Speech Dataset

Kinship verification is a task involving determining whether two individuals share a first-order kin relation. To tackle this task, we propose CONVTRAP-TN, a new architecture for audio-based kinship verification, and conduct an ablation study on the proposed model. To the best of our knowledge, we are the first to apply the successful transformer architecture to the task of audio-based kinship verification. Furthermore, we also collect a custom speech dataset, ARKIN, which accurately reflects everyday recording conditions. We do this because only a few speech datasets with kinship labels currently exist, all of which either source extremely noisy in-the-wild data from the internet, or instruct speakers to record in specific environments. These settings fail to reflect real-world scenarios where users record on personal devices under unrestrained conditions. Additionally, we perform a series of preliminary baseline experiments on the collected dataset, including speaker verification and recognition, speech recognition, age estimation, and kinship verification, as well as cross-dataset kinship verification experiments to show that existing methods are not robust across datasets.

Qiyang Sun, Langqing Zhang, Yupei Li +1

Department of Computing Imperial College London London, United Kingdom · Chair of Health Informatics TUM University Hospital Munich, Germany

Sep 8, 2026hep-ex

"Transforming" LHCb: self-supervised maps of heavy-flavour decays

Decays of beauty and charm hadrons provide sensitive probes of physics beyond the standard model, including decays with invisible particles, in which part of the final state leaves no reconstructed detector signature. The large heavy-flavour data samples recorded by the LHCb experiment at the CERN LHC, together with its precise tracking, displaced vertex reconstruction, and particle identification, make it particularly well suited to learning a map of reconstructed heavy-hadron decay environments directly from data. We propose to bring recent advances in jet flavour tagging at ATLAS and CMS to significantly improve on the performance of the current LHCb taggers and extend them to the reconstruction of heavy-flavour decays with several invisible particles in the final state. To achieve this, we introduce a self-supervised transformer architecture that learns the decay maps without flavour or exclusive-decay labels by inferring masked particle identification information and completing jets from which constituents have been removed. Across five classification tasks in simulated LHCb Open Data, the self-supervised model outperforms an otherwise identical transformer with random weights, and performs comparably to a fully supervised transformer. We achieve a tagging power of about 10%. In addition, removing constituents from reconstructed exclusive decays also systematically increases the model anomaly score relative to random removals from the same heavy hadrons. We confirm this behaviour directly in 2017 LHCb proton-proton collision Open Data: the score increases for all eight studied heavy-flavour channels, and the signal region response exceeds that in the adjacent sidebands. These studies provide a proof of principle that mapping heavy-flavour decay environments through jets can transform flavour tagging in LHCb and extend the discovery reach for incomplete or otherwise unusual decays.

Marko Stamenkovic, Greg Landsberg

Department of Physics, Brown University, Providence, Rhode Island 02912, U.S.A.

Transformer Self-Supervised Learning Jet Tagging High-Energy Physics Unsupervised Anomaly Detection

Sep 8, 2026cs.SD

Disentangled Global-Local Feature Learning with E-Branchformer for Audio Deepfake Detection

The rapid advancement of voice synthesis technologies such as text-to-speech and voice conversion poses significant threats to speech-based authentication systems, necessitating robust deepfake detection methods. In this work, we propose a novel E-Branchformer-based architecture that effectively leverages self-supervised speech representations for audio deepfake detection. Our model employs parallel branches to simultaneously capture global contextual dependencies through multi-head self-attention and local temporal patterns through convolutional processing. To enhance discriminative capability, we integrate depthwise convolution and Squeeze-and-Excitation modules that enrich the classification token with refined patch token information after feature merging. Extensive experiments on ASVspoof 2021 LA, DF, and In-the-Wild datasets demonstrate state-of-the-art performance with equal error rates of 0.88%, 1.85%, and 6.30% respectively, substantially outperforming existing methods. Comprehensive ablation studies validate that the dual-branch architecture provides complementary discriminative information, Squeeze-and-Excitation Aggregation significantly improves SSL feature integration, and the combination of DWConv and SE modules is critical for effective class token enhancement. The superior performance on real-world scenarios demonstrates strong generalization capability to diverse acoustic conditions and unseen spoofing attacks.

Phuong Tuan Dat, Ho Bao Thu, Nguyen Tran Trung +2

Department of Electrical and Computer Engineering, National University of Singapore · School of Communication and Information Technology, Hanoi University of Science and Technology

Audio Deepfake Detection Transformer ASVspoof

Sep 8, 2026cs.LG

Length Generalization for Transformers via Compression

Recent advancements in transformer length generalization theory enable us to reliably predict when a transformer can learn to solve a task. In particular, the C-RASP hypothesis (a formalized version of the so-called RASP-l conjecture) posits that transformers length-generalize on a task if and only if a solution is expressible in the C-RASP language. While this hypothesis has strong empirical validation, theoretical problems arise from the fact that no computable length generalization bounds exist for C-RASP, alongside the discovery of seemingly contradictory experiments. To address these problems, we refine the C-RASP hypothesis utilizing the recently-proposed fragments C-RASP+ and C-RASP1. These fragments have computable length generalization bounds, though in the worst case requiring an extremely large (double exponential) sample size. It is an open question whether these sample size bounds are tight. In this paper, we resolve this open question by providing an exponentially tighter bound. In doing so, we show a polynomial length generalization bound for transformers if we adopt compressed strings, via a novel connection to power words. As an application, we show how this yields a fine-grained analysis of the C-RASP conjecture that resolves contradicting experimental evidence against it.

Georg Zetzsche, Hongjian Jiang, Andy Yang +4

Max Planck Institute for Software Systems (MPI-SWS) · RPTU Kaiserslautern-Landau · University of Notre Dame

Transformer Expressivity Transformer Length Generalization Generalization Bounds

Sep 8, 2026cs.CL

Global Divergence, Local Convergence: Representation Geometry in SSMs and Transformers

Recent state-space models (SSMs) such as Mamba achieve language modeling performance comparable to transformers despite relying on fundamentally different architectures. This raises an important question: how do these structural differences influence the geometry and functional nature of their internal representations? We study this question through a multi-scale analysis of representations in transformers, SSMs, and hybrid architecture. First, we find that SSMs distribute their representational information evenly across all dimensions, whereas transformer representations are heavily dominated by a single principal direction. By evaluating hybrid architectures, we observe that the representation space becomes increasingly skewed toward a single dominant direction after each attention layer. Next, we explore how the different geometric spread of representations impacts representational capacity through compressibility. Surprisingly, we find that despite their contrasting geometric structures, both architectures exhibit tightly matched effective capacities. We further investigate whether this skewed geometry affects how concepts are encoded. Using rank-constrained probes, we demonstrate that both architectures encode concepts in subspaces of surprisingly similar dimensionality. Furthermore, we demonstrate that the transformers' dominant principal direction does not inherently encode more conceptual information. Finally, we zoom in and examine the alignment between manifolds, either by analyzing representations of specific topics or by looking at the nearest neighborhoods of tokens, and find that they are highly aligned. Ultimately, our analysis suggests that while transformers and SSMs induce different usage of latent space, they display a striking functional convergence at the level of local semantic manifolds.

Amit Ben-Artzy, Roy Schwartz

Computer Science, The Hebrew University of Jerusalem

Transformer Representation Geometry in Language Models State Space Models

Sep 8, 2026q-bio.GN

A Transformer-Based Delta Expression Encoder for Psilocybin Transcriptional Response: Architecture, Representations, and Biological Validation

Understanding why individuals respond differently to psilocybin requires modeling the drug's transcriptional perturbation signature at the cell-type level. I present a Transformer-based delta expression encoder that learns to classify differential gene expression status - upregulated, downregulated, or neutral - from single-nucleus RNA-sequencing data, without supervision from pathway annotations or prior biological knowledge. The model is trained on pseudobulk profiles from 623 examples spanning 18 cell types, 2 drug conditions, and 6 timepoints derived from the Liao et al. 2025 dataset, and achieves 69.4% weighted classification accuracy. Three principal findings are reported, alongside one direct test of a published hypothesis that returned a result inconsistent with that hypothesis. First, per-cell-type classification accuracy ranges from 28.3% (L2/3 IT, a primary HTR2A-expressing psilocybin target) to 99.6% (endothelial cells), consistent with known psilocybin response biology. Second, psilocybin-induced transcriptional downregulation is significantly more stereotyped across individuals than upregulation (Mann-Whitney U=18615.0, p<0.0001), a novel finding with a cortical depth gradient across excitatory subtypes. Third, attention-guided gene co-regulation analysis recovers drug-specific modules without pathway supervision. Separately, a direct test of whether baseline HTR2A expression predicts drug-response separability across cell types found a significant negative correlation (Spearman r = -0.7088, p = 0.0021), the opposite of what a simple HTR2A-gating account would predict.

Sai Jayakumar

Stanford School of Medicine, Biomedical Data Science Program, Stanford, CA

Transformer Single-Cell Perturbation Modeling

Sep 2, 2026cs.LG

Graph Machine: Towards Better Pretraining via Edges

We introduce the Graph Machine (GM), an architecture that maintains an

O(n)

-sized state and accesses it through sparse, dynamic routing. Unlike methods with fixed-size states or sparse but static routing, GM preserves

O(n)

complexity in its sparse layers without restricting the potentially accessible state size to

O(1)

. Instead, GM uses edges - pointer-like objects updated differentiably by a referral mechanism resembling pointer chasing. We replace 75% of the dense Transformer layers in Qwen3-0.6B with GM sparse layers and pretrain from scratch on 15.7B tokens. With only 2 of 4,096 tokens retrieved per KV head in each sparse layer, loss degrades only slightly; with 4, the best model marginally improves loss.

Lintai Hou

Iter Labs

Transformer Autoregressive Language Modeling

Sep 2, 2026cs.CL

oHC: Orthogonal Hyper-Connections on SO(4) via Quaternions

Hyper-Connections (HC) replace the single residual stream of a Transformer with

n

parallel ones, mixing them at every layer with a learned

n \times n

residual matrix. Leaving that matrix unconstrained places no limit on the factor by which the mixing step rescales the residual streams, and that factor compounds across layers, which destabilizes training. Manifold-constrained Hyper-Connections (mHC) address this by restricting the matrix to the doubly stochastic matrices. That caps the factor at one, so the mixing can no longer amplify any direction, but nothing bounds it from below. We prove that inside this set the mixing step can reduce the norm of the residual streams only by shrinking the differences between the streams, while their mean is left unchanged; and since the reduction accumulates over layers, the streams grow more alike and their diversity is spent with depth. We therefore propose Orthogonal Hyper-Connections (oHC), restricting the residual matrix to the rotation group

SO(n)

, so that the mixing step can neither amplify nor attenuate the residual streams in any direction, which keeps training stable and no longer forces the differences between the streams to contract. Specifically, at the four streams used by recent HC models we parameterize the group in closed form by a pair of unit quaternions, which adds no parameters, replaces the iterative projection with a fixed pattern of signed additions, and can be constructed faster than mHC. We evaluate oHC across a comprehensive set of downstream tasks, where it outperforms the single-stream residual baseline, mHC and iHC, which fixes the residual matrix to the identity.

Haoqiang Guo, Xuyi Chen, Bo Ke +5

The Hong Kong University of Science and Technology · Baidu Inc.

Hyper-Connections Transformer Residual Learning

Sep 2, 2026cs.LG

AGI Maze Prediction Datasets: A Compact Benchmark for Learning World Dynamics with Transformers

World modeling requires a predictive model to maintain and update an internal state adequate for reasoning about the consequences of actions. We introduce the AGI Maze Prediction Datasets and Benchmark, a lightweight controlled testbed for studying this capability in Transformers and other predictive models. Derived from procedurally generated, stateful grid worlds, the benchmark comprises per-step transition prediction, fixed-horizon state prediction, and sequential textual-observation prediction. Source-maze-disjoint training and validation splits, together with greedy exact-match evaluation, distinguish learning transferable action-conditioned dynamics from memorizing transitions in familiar layouts. We establish from-scratch byte-level Transformer baselines and compare them with two working-memory-augmented architectures. A generic auxiliary latent-memory Transformer can fit some training sets perfectly but does not consistently improve held-out performance. In contrast, a pseudo-video spatial-memory Transformer initializes a two-dimensional latent workspace from the input map and updates it from action history without receiving intermediate maps, positions, or state labels. Under the same data, objectives, and evaluation protocol, this model reaches perfect validation accuracy on selected fixed-horizon tasks where the byte and unstructured-memory baselines do not, and substantially improves sequential text-trace prediction. These results suggest that structured, task-aligned working memory can be more useful than additional latent capacity alone. More broadly, we argue that language grounding is mediated by persistent data structures and computations over them; the benchmark offers a compact setting for testing architectures that couple textual interfaces to learned structured state.

Alexey Potapov

SingularityNET Foundation

World Models Action-Conditioned World Models Transformer

Sep 2, 2026cs.CV

If It Moves, Radar Knows: A Physics-Aware Radar Transformer for Class-Agnostic Moving-Object Detection

Detectors trained on closed-set annotations can miss rare moving objects outside the training taxonomy. Automotive radar provides category-independent Doppler motion cues and is less affected by adverse illumination and weather, but sparse, noisy returns hinder class-aware 3D box detection. Surface location and velocity remain useful for motion reasoning and collision avoidance when full box geometry is difficult to recover. We present the Physics-Aware Radar Transformer (PART), a fully sparse radar-only detector that predicts existence confidence, a representative surface point, and 2D ground-plane velocity for each moving-object hypothesis. Doppler-Aware Query Initialization (DAQI) replaces scene-independent learned queries with input-dependent proposals by clustering radar returns in position and velocity, easing query-object assignment in sparse scenes. Physics-Guided Cross-Attention (PGCA) incorporates radial-Doppler consistency and radar cross section (RCS) into query-point association. Uncertainty-aware supervision randomly masks ground-truth objects and assigns soft existence targets to ambiguous radar-supported queries, reducing reliance on exhaustive annotations. With only 1.1 million parameters, PART achieves a class-agnostic average precision (CA-AP) of 0.8827, a mean average surface translation error (mASTE) of 0.3188 m, and a mean average velocity error (mAVE) of 0.8084 m/s on nuScenes. It attains 0.9203 recall on rare and safety-relevant categories excluded from the standard evaluation and remains effective at night, in rain, and under severe occlusion. Inspection of apparent false positives shows that some predictions correspond to moving objects absent from the nuScenes annotations. Code and pretrained model weights will be publicly available at https://github.com/sunyinghao-uestc/PART.

Yinghao Sun, Shuguang Li, Jinliang Shao +1

School of Automation Engineering of the University of Electronic Science and Technology of China (UESTC), Chengdu, Sichuan, P. R. China

Object Detection Autonomous Driving Transformer

Sep 1, 2026cs.LG

OR-Transformer: Scaling Real-Time Decision-Making to 1,000 Items

Modern supply chain operations can require coordinating replenishment across thousands of heterogeneous items under correlated stochastic demand, heterogeneous lead times, and shared fixed ordering costs, yielding observation spaces exceeding

10^4

dimensions. At this scale, rolling-horizon stochastic mixed-integer linear programs (MILPs) become prohibitively slow, while standard reinforcement learning (RL) methods face increasingly challenging credit assignment in high-dimensional action spaces. We introduce OR-Transformer, a deep reinforcement learning framework for joint replenishment under stochastic demand, with an item-permutation-equivariant Transformer architecture and pathwise-gradient training through the inventory dynamics. Across problem sizes up to 1,024 inventory items, OR-Transformer increasingly outperforms learning-based and rolling-horizon MILP baselines as scale grows. It also reduces online decision-making time by over 4 million times relative to MILP solvers, enabling real-time, large-scale deep RL in supply chain operations.

Shuze Daniel Liu, David Simchi-Levi, Claire Chen +2

Massachusetts Institute of Technology · Purdue University · California Institute of Technology +1

Inventory Control Transformer Supply Chain Management RL for Combinatorial Optimization

Sep 1, 2026cs.LG

One-Layer Transformer Provably Learns Multiclass One-Nearest Neighbor in Context

We extend recent work establishing an equivalence between one-layer transformers and nearest-neighbor classifiers in the binary setting to the multiclass case. By leveraging the simplex encoding, we show that one-layer transformers with an argmax classification head behave identically to a one-nearest-neighbor classifier in the multiclass setting. This closes a gap left by prior work, whose multiclass result relied on a non-standard rounding-based approach rather than the typical argmax head used in practice.

Skanda Athreya, Yutong Wang

James B. Conant High School · Hoffman Estates, IL · Illinois Institute of Technology +1

Transformer In-Context Learning Multiclass Classification Classification k-Nearest Neighbors

Sep 1, 2026cs.CL

Measuring Optimal Transport in Transformer Depth

A transformer carries each token's state from layer to layer, and the whole vocabulary carried together forms a cloud that moves with depth. We ask whether a trained network moves this cloud the way optimal transport would: at the cheapest cost, and along the map that pairs each token with its optimal destination. We measure both on Pythia-160m and Pythia-410m, with an exact assignment between consecutive layer clouds, a measured sampling floor, calibration on couplings known to be optimal, and a split of the cost into the common shift of the cloud and the token-specific moves. At the last layer, both models move their tokens where the optimal-transport map sends them, at the optimal cost for Pythia-410m and slightly above it for Pythia-160m. At the first layer they do not. In between, single layers can be judged on cost at only two of ten transitions, and blocks of several layers move the cloud at close to the optimal cost. The agreement at the last layer is much weaker at initialisation (0.64 against 0.86) and grows with training.

Alexandre Quemy

Hother Labs

Transformer Neural Network Training Dynamics Representation Geometry in Language Models Optimal Transport

Aug 31, 2026cs.LG

Can LLMs Use Relational Transformer Embeddings?

Injecting frozen relational-encoder embeddings as soft tokens into a large language model (LLM) is a conceptually appealing fusion strategy: the encoder handles multi-table structure, the LLM handles language and reasoning, and no lossy text serialization is required. We test this hypothesis concretely by injecting embeddings from a frozen Relational Transformer (RT) into Qwen3.5-4B via a learned MLP projection and LoRA adaptation, trained first with supervised fine-tuning (SFT) on chain-of-thought reasoning traces and then with group-based reinforcement learning (GSPO). We evaluate across 10 binary classification tasks on 6 relational databases from RelBench, under four supervision regimes: single-task (ST), within-dataset (WD), cross-dataset (CD), and all-task (ALL). The hybrid model does not consistently outperform standalone RT: it is frequently below random, highly sensitive to serialization format and relational-token budget, and unstable under RL training. We report these negative results and analyze the failure modes, arguing that soft-token fusion requires stronger alignment objectives and schema-aware design before it can serve as a reliable route to relational prediction.

Francisco Galuppo Azevedo, Clarissa Lima Loures

Kunumi Institute, Brazil · Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil.

Transformer LLM Fine-Tuning Relational Deep Learning

Aug 30, 2026math.OC

Transformer-Based Flow Shop Scheduling Using MILP-Generated Training Data

Advances in machine learning (ML) have created new opportunities to complement traditional operations research (OR) methods. In particular, transformer models can capture complex interactions in token sequences by mapping tokens into a high-dimensional embedding space and propagating contextual information via attention. This makes them a candidate to model non-permutation flow shop scheduling with secondary resources as a next-token prediction task, where tokens represent job-machine-secondary resource tuples. For training, mixed-integer linear programming (MILP)-generated schedules are tokenized and used as next-token prediction data. During inference, partial token sequences (prefixes) are randomly generated and completed by the trained transformer through constrained decoding. A computational study is conducted on a flow shop with 8 jobs, 4 machines, and 3 secondary resources, where jobs are selected from a fixed pool of 20 jobs that is sampled during training and provides the candidates during prefix completion. The transformer achieves better solution quality (smaller makespans) compared to a genetic algorithm (GA), the NEH heuristic, and random search. It is outperformed only by the MILP model and the iterated greedy (IG) heuristic. The study concludes that transformer models can, to some extent, learn patterns from MILP-optimized non-permutation flow shop schedules and that transformer-based scheduling represents an interesting direction for future research, particularly in settings with a fixed, recurring job set.

Roderich Wallrath

University of Twente, Faculty of Science and Technology, Sustainable Process Technology, Process Design and Optimization, Drienerlolaan 5, 7522 NB Enschede, The Netherlands

Transformer Combinatorial Optimization Neural Combinatorial Optimization

Aug 22, 2026cs.LG

TANGO: Treating Tokens as Operators

Transformers separate cross-token mixing in self-attention from token-wise transformation in feed-forward networks. We ask whether combining these operations can lower predictive loss under fixed data and parameter budgets. To do so, we introduce the Token-Aggregated Nonlinear Gating Operator (TANGO) model. TANGO computes a nonlinear feature-wise gate at each source token. Attention averages these gates for each destination. The average modulates a linear projection of the destination and forms the diagonal core of a source-conditioned linear operator. We test this proposal by comparing full-prefix and windowed TANGO with looped and untied Transformers, the Gated Attention Unit (GAU), and Fast Linear Attention with a Single Head (FLASH) on web text, Lean formal mathematics, DeepMind Mathematics, and code. The comparison uses two parameter scales, two depths, and three seeds. Checkpoints are selected on development data and evaluated on held-out test data. At matched parameters and training data, full-prefix TANGO has the lowest mean test negative log-likelihood in all 16 settings. In eight additional combinations of size and dataset, its development loss never increases as depth rises from 4 to 8 to 16, whereas the looped Transformer's loss increases in four. Full-prefix TANGO is computationally expensive because it averages wide gates over every visible source. To reduce this cost, we evaluate a variant with three narrower gated-projection sets assigned to the first, middle, and last applications. Across four FineWeb-Edu settings, this variant achieves 3.26 to 3.45 times the throughput of TANGO and 75% to 96% that of the looped Transformer. Its mean development negative log-likelihood is lower than TANGO's in three settings and 0.023 higher in the fourth, while remaining lower than both Transformer baselines in all four.

Joshua Nunley

Department of Informatics Luddy School of Informatics, Computing, and Engineering Cognitive Science Program Indiana University Bloomington

Transformer FFNs Transformer Self-Attention Autoregressive Language Modeling

Aug 13, 2026cs.FL

Algebraic Decomposition Theory for Transformer Length Generalization

Transformer-based language models are known to sometimes generalize to sequences longer than seen during training, but we lack a precise characterization of which tasks admit length generalization. It is not even known which regular languages transformers length-generalize on -- and this is a foundational class of languages. Our contributions are to establish the first complete characterization of which regular languages transformers length-generalize on and provide a decision algorithm running in polynomial time in the size of the language's syntactic monoid. These results rely on an effective characterization of the regular languages in C-RASP, a recently-established formalism that expresses which languages transformers length-generalize on. This characterization is challenging because classical tools like Krohn-Rhodes decomposition theory for finite semigroups are insufficient for C-RASP. Firstly, the basic building blocks of Krohn-Rhodes theory -- flip-flop and simple groups -- are not expressible in C-RASP. Secondly, the basic building block of C-RASP (unbounded counting) is not expressible by the finite semigroups of Krohn-Rhodes theory. Thus, length generalization on regular languages is controlled by an algebraic property that is invisible to classical finite decomposition theory. We generalize classical decomposition theory from finite semigroups to the infinite additive group on the integers, allowing us to characterize C-RASP in terms of iterated wreath products of the integers and derive a provable polynomial-time decision algorithm for regular language membership. Experiments across a broad test suite of regular languages confirm that our theory captures transformers' length-generalization behavior more accurately than existing classifications.

Andy Yang, Blerta Veseli, Corentin Barloy +5

University of Notre Dame · 2Saarland University · 3Ruhr University Bochum +4

Transformer Length Generalization

Aug 13, 2026cs.AI

Rethinking Normalization Placement for LLMs: Post-Norm under Curriculum Depth Growing

Pre-norm is the standard normalization placement in modern Transformers because it facilitates joint optimization of full-depth models. We ask whether this preference persists when depth is introduced through a curriculum. In curriculum depth growth, each appended block receives the boundary representation produced by a trained prefix, making normalization placement relevant to forward conditioning. We therefore test whether placement and training curriculum interact. In a controlled distillation study with a Qwen3-8B teacher and a nine-layer student, pre-norm and post-norm are indistinguishable under joint training, differing by

0.0004

validation CE, while post-norm improves over pre-norm by

0.0328

under curriculum growth, an order of magnitude larger. A post-joint control matched by student active-layer tokens remains worse than post-grow, which rules out compute as the sole explanation. The ranking crosses over during the curriculum: post-norm takes the lead once blocks are appended. Single-block and freeze controls localize the ranking change to block appending rather than shallow-block quality or retraining. Boundary diagnostics associate post-norm with stable residual scales and pre-norm with structural-token scale drift; on a fixed batch, the final pre-grow block is also nearly identity-mapped. Together with the phase-wise crossover, these observations are consistent with boundary-scale conditioning after new blocks are appended. The results motivate treating normalization placement and training curriculum as coupled design choices in this distillation setting.

Sheng Ren, Yadong Wang, Naiqiang Tan +7

Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China · Didichuxing Co. Ltd, Beijing, China

Transformer Layer Normalization

Aug 13, 2026cs.CV

Paths: Prompt-aware Spatio-temporal Transformer with Hierarchical Multi-modal Fusion for RGB-Event Video Person Re-Identification

RGB-Event Video Person Re-Identification (RE-VReID) aims to retrieve specific person across non-overlapping cameras with complementary RGB videos and event streams. However, existing methods often decouple spatial and temporal modeling, which limits their interaction. In addition, global-level RGB-Event fusion fails to fully exploit fine-grained discriminative cues. To address these issues, we propose Paths, a unified framework with spatio-temporal modeling and hierarchical multi-modal fusion for RE-VReID. Specifically, we first design a Memory-Augmented Backbone (MAB) to maintain modality-specific identity prototypes for stable intra-modal representation learning. Then, we propose a Prompt-aware Spatio-temporal Transformer (PST) to jointly model spatial and temporal cues within a unified Transformer. Finally, we introduce a Hierarchical Multi-modal Fusion (HMF) to integrate RGB and event features at global and local levels. With these modules, our framework can learn robust and discriminative representations for RE-VReID. Extensive experiments on three public RE-VReID benchmarks including EvReID, MARS and iLIDS-VID, demonstrate the effectiveness of our proposed method. The code is available at https://github.com/Reflection0427/Paths.

Yakun Huo, Yingquan Wang, Yangyang Liu +4

Dalian University of Technology Dalian, China

Cross-Modal Representation Learning Transformer Multimodal Fusion Person Re-Identification

Aug 12, 2026cs.LG

Geometric and Behavioral Stratification in Transformer Residual Streams

Trained transformer models develop privileged bases: coordinate axes whose statistics differ from the rest of the residual stream. But what kind of direction does such a basis select? We investigate the prediction direction, the unembedding direction of the token a model currently predicts, and find that it functions as a content-defined privileged anchor. Measured with respect to this anchor, residual-stream variation is geometrically and behaviorally stratified by proximity to the prediction. The stratification holds in all eighteen models tested (dense and mixture-of-experts, 7B-120B, base and instruction-tuned). A narrow, scale-invariant prediction interface concentrates readout-relevant structure, while the vast prediction-distal complement expands with model scale. Because the prediction direction sits nearly orthogonal to the principal variance axes, variance-based analyses recover this organization only partly, and the shortfall grows with prompt heterogeneity. Anchoring reveals a steep geometric gradient: prediction-proximal regions are highly structured and cluster related prompts, while the complement is flatter and anti-discriminates among prompt groups. The interface is a narrow slice but functionally decisive. Disrupting the variance directions closest to the prediction causes immediate divergence and frequent task-frame shifts; disrupting the next level down delays divergence and preserves framing. The complement is weakly readout-aligned per direction yet causally and temporally load-bearing, and behavior is driven by direction rather than magnitude. These results establish the prediction direction as a privileged anchor distinct from previously described coordinate axes, and give a geometric account of how high-dimensional computation coexists with linear readout.

Nelson Guda

Transformer Interpretability Transformer Representation Geometry in Language Models

Aug 10, 2026cs.CL

Cracks in the Foundation: Seemingly Minor Architectural Choices Impact Long Context Extension

One might imagine that architectural variations within the dense transformer paradigm have a limited effect on accuracy. However, we demonstrate that this is not the case in the long context setting. Specifically, we show that a set of four minor architectural decisions --- all made by at least one of the Olmo, Llama, and Qwen dense model families --- have a compoundingly negative effect on long context extensibility. Any one of these choices alone has a minor impact on long context performance, but combining three or more can drop the performance downstream by up to 47%. Furthermore, these differences are not detectable from short-context loss or validation datasets. We show that much of the variation in long context ability across model families is driven by these architectural features and detectable from applying context extension early in pretraining. We demonstrate this with controlled ablations that hold data, tokenizer, and extension recipe fixed while varying normalization, GQA, pretraining context length, and sliding window attention. After over 170,000 GPU hours of training, we release the resulting set of models as OlmPool, a set of 26 comparable 7B models with checkpoints before and after long-context extension. This pool includes several architectures that outperform the Llama 3 architecture on long context extensibility. In an analysis of our ablation models, we identify patterns in attention sink behavior and attention distributions across context that are attributable to specific architectural differences.

Amanda Bertsch, Luca Soldaini, Matthew R. Gormley +4

Ai2 · Carnegie Mellon University · University of Washington

Transformer Long-Context Language Modeling

Aug 10, 2026cs.LG

Training-Free Universal Approximation by Prompting Random Transformers

How expressive is prompting a transformer? Answering this question is important for separating the roles of prompting, architecture, and pretraining in transformer models, and for determining whether task-specific behavior must be stored in model weights or can instead be induced at inference time through the prompt. We show, in an approximation-theoretic sense, that pretraining is optional: a single-layer softmax attention network with random, untrained weights can approximate any Hölder function on a compact manifold when steered by an appropriate soft prompt. Guided by the connection between softmax attention and kernel methods, we construct explicit soft prompts (a prompt per target function, independent of the query) as solutions to linear systems matching attention logits to Gaussian kernel exponents, under which the frozen transformer emulates the classical Nadaraya-Watson kernel estimator. The construction requires only a mild rank condition on the weights, which we show holds almost surely under Gaussian initialization. The prompted network inherits the theoretical guarantees of kernel regression, leading to universal approximation theorems with minimax-optimal rates that depend on the intrinsic dimension. We further quantify the cost of prompting, exposing a tradeoff between the norm of the constructed soft prompt tokens, prompt length, and hidden dimension. Numerical experiments corroborate the constructions and predicted rates.

Alexander Hsu, Rongjie Lai

Department of Mathematics, Purdue University

Transformer Expressivity Prompt Learning Transformer Neural Network Approximation Theory

Aug 10, 2026cs.LG

MixFormer: Linear Transformer with Mixture of Memory Experts

State Space Models (SSMs), as a mainstream research direction of linear Transformers, aim to achieve higher efficiency than standard Transformers in long-context modeling. However, existing SSMs suffer from limited input adaptivity and constrained memory capacity, leading to information loss when modeling ultra-long sequences. To address these limitations, we propose MixFormer, a novel linear Transformer that integrates a Mixture-of-Memory-Experts (MoE) mechanism. Specifically, the model maintains differentiated memory states through multiple collaborating memory experts and employs a novel Time-Aware Linear Attention (TALA) mechanism, which leverages learnable exponential decay functions and positional biases to dynamically update memory. This design enables the model to selectively reinforce important historical information while effectively mitigating memory dilution, substantially improving long-range dependency modeling. Experiments on long-sequence text and image generation tasks demonstrate that MixFormer not only achieves significant performance gains but also provides a more sustainable computational backbone for the next generation of web infrastructure.

Yu Guo, Lei Duan

School of Computer Science, Sichuan University Chengdu, China · School of Artificial Intelligence, Sichuan University Chengdu, China

Memory-Augmented Neural Networks Transformer Long-Context Modeling Linear Attention Mixture-of-Experts Models

Aug 10, 2026cs.LG

Why Post-Norm Transformers Collapse: Attention Amplification and Gradient Repair Failure

Deep decoder-only Transformers often replace the original Post-Norm architecture with Pre-Norm variants because Post-Norm training is highly sensitive to warmup and learning rate under conventional initialization schemes. Although prior work has identified rank collapse and gradient vanishing as related symptoms, it remains poorly understood how causal attention creates high-similarity representations and why training dynamics fail to repair them. We give a two-stage analysis of Post-Norm rank collapse using token similarity as a scalar state variable. First, at initialization, causal attention acts approximately as a prefix-averaging operator that increases token similarity across depth, while the SwiGLU branch contributes only a smaller damping effect. Second, once training enters a high-similarity regime, growth of pre-normalization residual norms makes the RMSNorm backward factor contractive; under mild conditions, gradients to earlier layers decay geometrically. As a complementary result, we characterize the properties of a collapsed network: its best predictor is frequency distribution with relatively high loss floor, and gradients in collapsed layers vanish at frequency distribution. Experiments on 48-layer decoder-only Transformers trained on C4 dataset match the predicted initialization-time similarity growth and collapse-time gradient contraction, and show that collapsed runs stay near the predicted frequency loss. Together, these results distinguish the forward similarity amplification and backward repair incapacity in Post-Norm collapse, while also characterizing the behavior of collapsed networks.

Xingjian Wang, Qingyu Han, Xiaodong Luo +1

The Chinese University of Hong Kong, Shenzhen · Shenzhen Research Institute of Big Data

Transformer Self-Attention Decoder-Only Language Models Layer Normalization

Aug 7, 2026cs.AI

Post-Grokking Collapse at the Representation-Readout Interface in Muon-Trained Transformers

Muon-trained modular-arithmetic transformers can lose accuracy while retaining linearly decodable task information. Adjacent swaps localize five captured unnormalized failures to AdamW readout updates. Multiplying the actual readout displacement by the large feature mean produces a class-dependent logit offset shared across inputs that nearly reproduces each failure. Training-only decoders recover 98.20-100% held-out accuracy. Correcting cross-entropy derivative errors stabilizes five matched branches through step 100,000; four prospective accurate-CE RMS runs fail through embedding updates.

Ali Janati, Kaoutar El Maghraoui, Anass Belfatmi

Data Science Institute, Columbia University, New York, NY, USA · Department of Computer Science, Columbia University, New York, NY, USA · CentraleSupélec, Gif-sur-Yvette, France

Transformer Muon Optimizer Modular Arithmetic Grokking Gradient Descent Dynamics