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

Aug 6, 2026cs.LG

Cryptanalytic Extraction of Isolated Bias-Free GLU Feed-Forward Blocks by Antipodal Separation

Cryptanalytic extraction has been demonstrated for ReLU networks, for networks using componentwise activations such as GELU or SiLU, and for a Transformer's final projection matrix. These methods do not recover the bias-free Gated Linear Unit (GLU) feed-forward blocks used in many modern language models. Such a block multiplies an activated linear projection by a second learned linear projection within each hidden unit, a two-branch structure absent from the network classes and final-layer setting addressed by those methods. We give a constructive, multi-stage forward-query recovery primitive for isolated bias-free GLU blocks. Finite-difference curvature supplies gate-direction candidates, and paired observations at x and -x separate gate magnitude, orientation, and value-branch coupling. Across high-precision targets, six Qwen layers, an 8,192-unit Llama subproblem, and a full-dimensional Gemma block all reach sub-percent median validation error. Four finite-precision configurations remain below 5 percent median error, but none reproduces every stored weight. These isolated-block experiments are not an end-to-end model-API attack: deriving the required internal block responses from final model outputs remains unsolved.

Chunhui Shi, Xinwen Fu

Transformer FFNs Model Extraction Attacks Transformer

Aug 4, 2026cs.SD

Equivariant Music Transformer

Humans recognize a musical passage even when it is shifted in time or transposed in pitch, indicating a notion of equivariance in the representation space. Our analysis, however, shows that standard music transformers map such time-shifted or pitch-transposed inputs onto uncorrelated representations: these models become progressively less equivariant as they scale in size or train longer. This suggests that in standard music transformers, additional model capacity is allocated to memorizing absolute patterns rather than capturing shared musical structures. In this paper, we propose the Equivariant Music Transformer (EMT), which enforces equivariance through self-distillation by jointly optimizing a next-token-prediction and an auxiliary equivariance regularization loss. We find that the additional equivariance loss acts as a beneficial regularizer, simultaneously improving next-token prediction and producing equivariant latent representations. Through both objective and subjective evaluations, EMT demonstrates superior equivariance and generative capability compared to data augmentation, feature engineering, and state-of-the-art (SOTA) baselines. More broadly, our findings reveal that standard language modeling methods alone do not capture music's translational symmetries, and dedicated inductive biases are required to produce better music representations. The code, weights and demos are available online.

Zixun Guo, Simon Dixon

Centre for Digital Music, Queen Mary University of London, United Kingdom

Representation Learning Transformer Symbolic Music Generation Equivariant Neural Networks Equivariant Representation Learning

Aug 4, 2026cs.CL

Probing Character-level Transformers for the Spanish L-shaped Morphome

When a transformer learns an irregular morphological pattern, what has it learned? Our test case is the Spanish \emph{L-shaped morphome}, a complex irregular pattern in which the verb's stem alternates in exactly the first-person singular indicative and all subjunctive forms, and whose membership no phonological, semantic, or syntactic feature predicts. Prior studies have shown that character-level transformers can reproduce this pattern, but that evidence describes what models produce, not what they represent. Probing five architectures, twelve trained models each, under lemma-disjoint cross-validation with controls and surface baselines, we show that the models encode the L-shaped class itself, not just its visible alternations. It is decodable above every surface baseline, survives instances in which every form shows the same stem, and probes trained on alternating instances still classify non-alternating ones. The encoding is localized where the stem choice is made, at the stem-final consonant position of the middle decoder, before the alternant is read. And it is item-specific: which verbs a model learned matters far more than which architecture it is. The models store the morphome as an item-specific lexical abstraction, sufficient to reproduce the pattern but not to generalize it as humans do.

Akhilesh Kakolu Ramarao, Kevin Tang, Wiebke Petersen +1

Department of English Language and Linguistics, Heinrich Heine University Düsseldorf · Department of Linguistics, College of Liberal Arts and Sciences, University of Florida · Institute of Linguistics and Information Science, Heinrich Heine University Düsseldorf +1

Transformer Interpretability Transformer Representation Probing

Aug 4, 2026cs.LG

Provably Learning Multi-Head Attention with Queries

We study the problem of learning multi-head softmax attention from black-box input-output access. The learner may query arbitrary real-valued token sequences and observe only the scalar output at the final token. Recent work gives an algorithm using

O(d^2)

value queries to recover the single-head parameters

(W,v)

. For multiple heads, the same work establishes identifiability under the assumption that the heads occupy pairwise orthogonal subspaces. Applying the single-head recovery algorithm separately to the heads additionally requires bases for these subspaces to be known. We recover a canonical representation by merging heads with the same

W_h

, summing their corresponding

v_h

, and discarding a merged head when this sum is zero, without these subspace assumptions. By varying the number of copies of a token, our algorithm obtains samples of a rational function whose interpolation separates the canonical heads. Additional queries formed by adding selected token vectors then match the same head across different queries. When the oracle outputs and all subsequent computations are exact, the learner chooses its query vectors at random and recovers the canonical pairs

\{(W_h,v_h):h\in[H]\}

up to permutation with probability one. When

H

is known, it uses exactly

4Hd^2-2H+1

value queries of maximum length

2H+1

. If only a known upper bound

H_0

is available, the algorithm uses

4H_0d^2-2H_0+1

value queries of maximum length

2H_0+1

. For approximate oracle outputs, we give conditions under which the parameter error is at most a model- and query-dependent constant multiple of the output error. Finally, we extend our result to a one-layer Transformer with multi-head attention followed by a bias-free ReLU feed-forward network. Under additional conditions, we recover a functionally equivalent Transformer without relying on a separate algorithm for learning the feed-forward network.

Sunyeop Kim, Insung Kim, Jian Guo

Korea University, Republic of Korea · Nanyang Technological University, Singapore

Softmax Attention Transformer Transformer Attention Multi-Head Attention

Aug 3, 2026cs.LG

Scaling an Autoregressive Transformer for Single-Cell Generation

We study a self-supervised generation task for single-cell gene expression vectors: given a set of vectors from a cell type, we aim to generate additional gene expression vectors of that cell type. For this task we characterize both the biological fidelity of the generated gene expression vectors and the scaling behavior of the pretraining loss. The model is a causal transformer paired with a learned quantized VAE tokenizer, trained with a cross-entropy loss. To evaluate the model, we condition it on held-out gene expression vectors of a cell type and generate vectors of gene expression, comparing the resulting distribution over gene expression vectors to the ground truth distribution of that cell type. We study the scaling properties of the proposed architecture by varying the number of trained parameters and the amount of training data. To our knowledge, we find the first jointly-fit two-exponent scaling law and compute-optimal frontier for a single-cell foundation model. Finally, we discuss how this pretrained model could be finetuned for perturbation response prediction.

Aleksandr Sharipov, Yusif Mukhtarov, Igor Molybog

HawAII, University of Hawai’i at Manoa

Transformer Autoregressive Generation Single-Cell Transcriptomics AI Scaling Laws

Aug 3, 2026cs.LG

Feed-Forward Steering in Transformer Residual Dynamics

Attention-only dynamical theories model Transformer residual directions as particles aggregating on a sphere. We extend this framework by incorporating the feed-forward network (FFN) term as a local steering field acting on each token state. The resulting theory predicts that the tangential component of the FFN field is necessary for motion in residual-direction space, that critical residual directions correspond to nonlinear projective equilibria, and that a commutator defect determines when a finite attention--FFN block can be accurately approximated by a parallel, additive flow. Across GPT-2, Pythia, Mistral, and Llama models, the extended theory improves one-step angular prediction relative to an attention-only baseline, with the contribution of the FFN increasing from GPT-2 to Llama-3-8B. Intervention experiments show that retaining only the tangential FFN component preserves most model quality, whereas retaining only the radial component causes performance to collapse. The tangential component also preserves output diversity under aggregation pressure. As a practical application, layers with small commutator defects can be approximately parallelized with only a modest increase in loss, whereas layers with large defects degrade rapidly. These findings support the interpretation of FFN layers as directional steering fields that shape Transformer residual geometry and govern the feasibility of block-level interventions.

Timur Mudarisov, Mikhail Burtsev, Radu State

University of Luxembourg · 2London Institute of Mathematical Sciences

Transformer Interpretability Transformer FFNs Transformer Transformer Attention

Aug 3, 2026cs.LG

Geometry-Guided Layerwise FFN Width Allocation in Transformers

Feed-forward networks (FFNs) account for a large fraction of Transformer parameters, yet their hidden width is usually constant across depth. We ask whether this capacity can instead be allocated from a forward-pass measurement of layer behavior. We view each FFN as transporting a cloud of token representations and quantify the induced geometric change using correspondence-preserving shift, Gromov-Wasserstein distortion, and degree-one persistent homology under raw and scale-normalized metrics. A layerwise approximation surrogate yields an exact fixed-budget optimizer. Across seven pretrained language models, raw Euclidean work largely tracks residual-norm growth, whereas normalized work is predominantly front-loaded. Gromov-Wasserstein work is more consistently associated with perturbation-based layer sensitivity than the finite-sample topological estimate. In paired 128M and 256M training runs, several normalized-work schedules reduce mean validation loss relative to both uniform width and a hand-designed cosine taper. With the amplified paired differences at 440M, the best geometry-based allocations improve over uniform substantially larger than the cosine taper, while the anti-topological raw control is worse than uniform.

Timur Mudarisov, Mikhail Burtsev, Radu State

University of Luxembourg · London Institute of Mathematical Sciences

Transformer FFNs Transformer

Aug 2, 2026cs.LG

Riemannian Attention Mechanisms for Transformers: A Theoretical Framework and Architecture Design

All Transformer-based large language models compute attention via the Euclidean inner product, an architectural choice that Dong et al. (2021) proved causes representational rank to decay doubly exponentially with depth in pure self-attention stacks. We develop a theoretical framework that targets this structural limitation at the mathematical level by replacing the flat Euclidean metric with learned per-token Riemannian metrics. Our contributions are threefold. (1) We prove that Riemannian attention scores with heterogeneous per-token metrics are non-Gram---they cannot be factorized as QK^T with factorization dimension O(d). We are explicit that this is a structural observation, not a proof of rank preservation. (2) We establish that low-rank metric factors render all geometric operations tractable: geodesic distance in O(dr) per token and metric inversion in O(dr^2) via the Woodbury identity---both far below the O(d^3) cost of a general matrix---making Riemannian attention feasible at billion-parameter scale with negligible overhead. (3) We present the Fiber Bundle Transformer, a complete architecture specification in which each token position carries its own Riemannian metric, attention is geodesic distance computation, feed-forward updates use metric-preconditioned steps, and the connection carries explicit curvature and torsion proxies. We derive formal predictions about correctly implemented geometric architectures and identify the central open problem: proving or disproving that heterogeneous Riemannian metrics prevent the rank collapse that row-stochastic attention matrices otherwise cause. This paper presents theoretical analysis and architectural design; empirical validation is the subject of future work.

Sen Song

Independent Researcher, Guangzhou, China

Transformer Self-Attention Attention Mechanisms Representation Geometry in Language Models

Jul 31, 2026cs.LG

Transcript-Managed Transformers: Monotone Multi-Agent Collapse and Universality with Two Pop-Enabled Transcripts

We study transcript management for fixed, finite-precision causal Transformers. A transcript is partitioned into channels of bounded blocks. Each transition consults a fixed visible suffix and may append one block, leaving the model, weights, and token protocol unchanged. The operation

P_c:=\PopContext(c)

deletes the newest block on channel

c

and exposes its predecessor. We model the layer by the Transcript-Managed Transducer

\TMTn{k}

: one finite controller,

k

channels, and per-round actions from stay, push, and pop under a caller-driven status map. Fixed visible windows encode as finite symbols. The pop-free Restricted Transcript-Managed Transducer

\RTMTn{k}

is the standard append-only layer and, for every fixed

k

, realizes exactly the deterministic finite-state transductions. The same holds for every fixed finite agent population under a monotone protocol that appends, routes, and copies visible blocks. Admitting

\{P_c\}_{c=1}^k

restores pop. Newest-first, a pop-enabled channel is a stack; compiling to the Hopcroft--Ullman presentation transfers the classical hierarchy:

\DCFL

for

k=1

and

\RE

for every

k\ge2

. Orchestrated one-channel agents match one controller with

k

channels, so two pop-enabled transcripts---in one agent or two---suffice for universality. Simulation costs and invariance to fixed block size and visible radius are stated. The bounds fix precision, alphabets, blocks, visibility, controller state, and population; growing exact context, hidden-block access, writable stores, and unbounded \textbf{Spawn} add further state.

Sergey Salishev

AI Foundry San Francisco, CA, USA

Transformer Expressivity Transformer Multi-Agent Systems

Jul 30, 2026hep-th

Learning to Trace Seiberg Dualities

Dualities play an important role in establishing both microscopic and emergent phenomena in a wide range of physical systems. In practice, though, it can often be computationally challenging to establish when two systems are dual, even when all of the "rules of the game" are well-known. Said differently, when confronted with two systems, how can one efficiently establish that they are in fact dual? In this paper we use machine learning methods to address this question for Seiberg dualities of supersymmetric quiver gauge theories. Mathematically, this involves establishing mutations of quivers, which is in turn a variation on the theme of "learning to unknot". On the one hand, this leads us to a practical tool for establishing the computational complexity of different dualities. On the other hand, it also allows us to study how different network architectures learn how to trace Seiberg dualities. We find that for quivers with a modest number of quiver nodes (of order

10

), different network architectures consisting of transformers and multi-layer perceptrons tend to outperform deterministic algorithms. Supplementing the network by well-established pathfinder algorithms (essentially "Google Maps for quivers") leads to an additional improvement in the efficiency and accuracy of the search strategy. We anticipate that this class of questions can serve as a useful benchmark for frontier AI models applied to theoretical physics.

Jonathan J. Heckman, Shani Meynet, Alessandro Mininno +1

Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA · Department of Physics, University of Wisconsin–Madison, 1150 University Avenue, Madison, WI 53706, USA

Transformer Scientific ML Learning-Augmented Algorithms

Jul 30, 2026cs.AI

MUL-T: Decoding Spatial Cellular Architecture in Multiplexed Tissue Images

Understanding tissue organisation in multiplexed imaging requires modelling both cellular phenotypes and their spatial context. Existing approaches typically rely on handcrafted features, such as marker intensity statistics or cell-type proportions, which often fail to scale or generalise across cohorts with heterogeneous marker panels. We introduce MUL-T, a lightweight transformer framework that reframes tissue architecture as a masked contextual prediction task over discrete cell tokens. By learning contextualised [CLS] embeddings without task-specific supervision, the model captures higher-order cellular interactions while remaining computationally efficient. We evaluate MUL-T on several clinically relevant downstream tasks, including core-level tumour pattern classification, patient-level grading, PD-L1 positivity prediction, and cross-dataset treatment response prediction. Across tasks, MUL-T consistently outperforms classical feature-based baselines and achieves performance comparable to a foundation ViT model, despite substantially fewer parameters and lower training cost.

Farzaneh Seyedshahi, Kai Rakovic, Adalberto Claudio Quiros +2

Cancer Research UK Scotland Institute, Glasgow, UK · University of Glasgow, Glasgow, UK

Transformer Generative Modeling Histopathology Image Classification Medical Image Representation Learning Microscopy Image Analysis

Jul 30, 2026cs.LG

Generalization Bounds on Optimal Control for Transformer Training and Wasserstein Distributional Robustness

We derive finite-sample generalization bounds for Transformers trained with dynamic programming recursions. Building on the doubly lifted, measure-valued formulation of Transformer dynamics, we view data sets as probability laws on pairs of empirical input-output measures, allowing us to interpret the training problem as a finite-horizon Markovian control problem. We then analyze a quantized model, derived by quantizing the state, action, and measure-state spaces, and derive explicit finite-sample generalization bounds using concentration inequalities for empirical laws on finite metric spaces together with a Lipschitz stability estimate for the value function. These bounds are transferred to the base model at the cost of an explicit approximation error. Finally, we show that the same machinery yields a distributionally robust control formulation of the training problem, connecting Transformer generalization to Wasserstein distributionally robust optimization.

Kağan Akman, Naci Saldi, Serdar Yüksel

Department of Mathematics, Bilkent University, 06800, Ankara, Turkey · Department of Mathematics and Statistics, Queen’s University, Kingston, K7L 3N8, Ontario, Canada

Transformer Wasserstein Distributionally Robust Optimization Optimal Control Generalization Bounds

Jul 29, 2026cs.FL

A Compositional Theory of Causally Masked Transformers

What types of decision problems can a causally masked, finite-precision transformer solve for inputs of arbitrary length? Existing answers often rely on idealized arithmetic, but under finite precision, rounding and evaluation order can change what information attention retains and therefore what the model can compute. We develop an algebraic formalization that derives expressivity directly from the model's implemented dynamics. Its central object is its memory; the finite internal state computed by attention that summarizes the information from the prefix available to all future queries. Each attention head updates its own state independently within a layer, while layers compose hierarchically, providing a uniform route from model assumptions to expressivity bounds. Applying this method to transformers without positional embeddings, we obtain an expressivity hierarchy governed by the attention type under specific numerical semantics. Width-one sliding-window attention supports bounded-suffix memory, while a modified form of soft attention supports irreversible, checklist-like state, and combining the two mechanisms provides an interplay of both. Ordinary left-to-right floating-point soft attention can realize more expressive memory operations than any of the above. Algebraically, the four cases correspond to definite, R-trivial, locally R-trivial, and aperiodic semigroups. Under an explicit free-wiring assumption, all four bounds are tight.

Franz Nowak, Ryan Cotterell, Reda Boumasmoud

1ETH Zürich

Transformer Expressivity Transformer Attention Mechanisms

Jul 29, 2026cs.LG

Placement Is Free, Composition Is Not: The Latin Square as a Provably-Balanced Construction for Heterogeneous Sequence-Mixer Stacks

Since GPT, most Transformers have repeated the same attention mechanism at every layer. Yet this design is largely a convention rather than a tested conclusion. When multiple sequence mixers are combined in one stack, improvements may arise from mechanism choice, placement, or both, making causal attribution difficult. We introduce Aether-7B-5Attn, a 6.59B-parameter mixture-of-experts model (

\approx

2.98B active) whose 49 layers contain seven sequence-mixing mechanisms arranged as a

7\times7

Latin square. Because each mechanism appears exactly once in every row and column, the design guarantees balanced exposure across depth while eliminating placement confounds. To evaluate this principle, we build a parameter-matched proxy with four mechanisms arranged as a

4\times4

Latin square over sixteen layers, matched to 700.9M parameters and trained with eight seeds per arm. The results reveal a clear dissociation. Rearranging a distributed heterogeneous stack into a balanced periodic cycle changes validation loss by only 0.16%, indicating that exact placement has little effect. In contrast, clustering the same mechanisms into contiguous depth bands incurs a 0.59% penalty, while replacing the heterogeneous stack with a homogeneous one incurs a 1.68% penalty. These results indicate that performance depends primarily on heterogeneous composition distributed across depth rather than on any particular permutation. We confirm this finding at 2.16

\times

larger scale (1.514B parameters), where the homogeneous-stack penalty increases to 2.63% and removing the SSM-family mechanism produces a 3.20% degradation. We further report per-mechanism cost profiles, English and Korean evaluations, and a causal-safety audit of all 49 layers. We release model weights, training recipes, training code, logs, and architecture source code.

Taebong Kim, Youngsik Hong, Minsik Kim +3

VIDRAFT AI Research · QuantumOS, Seoul, Republic of Korea

Jul 28, 2026cs.AI

Localized Adaptation Reveals Distinct Learning Signatures in Transformers

Transformer adaptation is typically distributed across model depth, even when the intended change is narrow. We investigate how adaptation site shapes what a model learns, how well that learning generalizes, and how selectively it is applied. We introduce a controlled benchmark spanning five objectives (lexical binding, factual association, behavioral policy learning, causal mapping, and procedural reasoning) and define each objective's "adaptation geometry" as its profile of acquisition, transfer, and boundedness under full-stack and early-, middle-, or late-layer LoRA. The objectives exhibit distinct geometries. Lexical binding favors early-layer adaptation for acquisition and boundedness but requires broader updates for transfer; factual association favors later layers among localized adapters; behavioral learning separates late-layer action acquisition from middle-layer policy gating; and causal and procedural transfer benefit most from middle- or full-stack adaptation. These patterns largely persist under parameter-matched controls, and most corresponding directional contrasts replicate across five model families. These findings establish adaptation site as a key design variable for controlling what models learn, generalize, and leave unchanged.

Rebecca Ramnauth, Brian Scassellati

Yale University

Fine-Tuning Transformer Low-Rank Adaptation

Jul 27, 2026cs.LG

Physics Transformer: Tailoring Transformer for General PDE Prediction

Transformer architectures have attracted increasing attention for solving partial differential equations (PDEs), owing to their flexibility in handling irregular discretizations and their ability to capture long-range physical dependencies. However, unlike discrete language tokens or fixed-resolution image patches, observed physical fields are finite samples of underlying infinite-dimensional functions. Consequently, effectively applying Transformers to PDEs requires a tokenizer that respects the functional nature of physical fields and constructs physically expressive tokens from arbitrary discretizations.To this end, we propose \methodname{Physics Transformer}, a function-projection-based Transformer architecture for physical field prediction. Physics Transformer treats a physical field as a continuous function and partitions its discretization into locality-preserving spatial patches. Within each patch, it dynamically learns a set of adaptive local basis functions and projects the sampled field onto these bases to obtain compact physics tokens. The resulting tokens capture diverse latent physical states while preserving fine-scale spatial structures, enabling efficient global interaction through factorized attention across space and physical states. The projected representation further supports efficient decoding at arbitrary query locations. Extensive experiments on diverse benchmarks, ranging from two-dimensional PDE dynamics to industrial-scale three-dimensional CFD simulations, demonstrate that Physics Transformer accurately captures fine-grained physical structures and achieves state-of-the-art predictive performance. These results establish function projection as a practical and effective foundation for designing Transformer architectures for PDE solving.

Guoze Sun, Rui Zhang, Jiankai Tang +4

Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China · School of Mechanics and Engineering Science, Peking University, Beijing, China

Transformer PDE Surrogate Modeling PDE Operator Learning

Jul 27, 2026cs.IR

SpecFormer: Mitigating Embedding and Attention Collapse via Spectral-Aware Transformer for Recommendation

Transformer architectures have achieved remarkable success across diverse domains; however, directly applying their standard self-attention mechanism to recommendation often yields suboptimal performance, sometimes even trailing behind well-designed simple recommendation models. In this paper, we reveal that this performance bottleneck stems from severe embedding and attention collapse unique to recommendation scenarios. The heterogeneity and long-tail nature of recommendation data lead to a severe spectral collapse dominated by a few principal singular values. We further theoretically demonstrate that this triggers a vicious cycle in recommendation model's forward and backward propagation, which accelerates embedding and attention collapse and limits the model's scaling capability with increased depth. To address these issues, we propose SpecFormer, a novel Spectral-Aware Transformer designed for mitigating embedding and attention collapse in recommendation. Specifically, SpecFormer introduces 1) a Learnable Spectral Softening module to dynamically smooth the singular values distribution of the input token embeddings; 2) a Spectrum-softened Attention mechanism to model feature interaction under a more uniform spectral distribution space; 3) a Spectral Residual Position Encoding via Taylor expansion of singular values, explicitly providing a spectral inductive bias for feature interactions. Extensive experiments on one industrial and two public datasets demonstrate that SpecFormer significantly outperforms state-of-the-art baselines. Notably, SpecFormer has been successfully deployed in a real-world commercial recommender system and exhibits exceptional scaling capabilities: stacking SpecFormer layers actively improves the attention effective rank and recommendation performance.

Yu Cui, Yi Xu, Jiahao Wang +6

Zhejiang University Hangzhou, China · Alibaba Group Beijing, China

Representation Collapse Transformer Recommender Systems Attention Mechanisms

Jul 26, 2026cs.LG

Multimodal Auto-regressive Transformer Surrogate for Modeling Variable Operations and Quantifying Uncertainty in Geological Carbon Storage

The use of variable well perforation and injection strategies can improve the efficiency of geological carbon storage operations. We develop a new multimodal auto-regressive transformer surrogate to model these operations under geological uncertainty. A modified SEAM CO2 geomodel, which involves a faulted system with three stacked aquifers, is considered. The two injection wells are perforated in stages, from bottom to top, with the stage durations and individual well injection rates treated as control variables. The surrogate model processes three input modalities - the 3D geomodel, scalar parameters characterizing relative permeability functions, and control variables - through separate encoders. These are fused via self-attention in a transformer encoder, and a temporal decoder generates predictions auto-regressively through encoder-decoder cross-attention. The surrogate is trained, using 4000 GEOS flow simulations, to predict saturation and pressure at monitoring locations, total injected and mobile CO2 mass, and saturation footprints. For a new test set, involving randomly sampled geomodels and control variables, the surrogate achieves a median saturation MAE of 0.028 and median relative errors of 0.2-5% for the other quantities of interest. Importantly, it captures the switch from rate to bottom-hole-pressure control. The surrogate model is used within a hierarchical Markov chain Monte Carlo data assimilation procedure for a synthetic true model under three operational strategies. Substantial uncertainty reduction is achieved for key metaparameters, particularly the fault permeabilities. Posterior predictions for saturation footprints and total injected and mobile CO2 mass are also shown to be generally consistent with true model results.

Yifu Han, Louis J. Durlofsky

Department of Energy Science and Engineering, Stanford University, Stanford, CA, 94305, USA

Neural Surrogate Modeling Uncertainty Quantification Transformer PDE Surrogate Modeling

Jul 25, 2026cs.CL

BERT-based Models vs. Large Language Models for Low-Resource Named Entity Recognition: A Comparative Study on Marathi

Named Entity Recognition (NER) for low-resource languages such as Marathi remains a challenging task due to limited annotated resources and linguistic complexity. Although recent Large Language Models (LLMs) have demonstrated strong performance across a wide range of natural language processing tasks, their effectiveness for language-specific NER in low-resource settings remains uncertain. In this study, we fine-tune MahaBERT-v2 on different variants of the MahaNER dataset and systematically compare the performance of these models with an existing MahaNER baseline and prominent general-purpose LLMs, including Gemini, LLaMA-3.3-70B, and Gemma models. All models are evaluated on a Marathi NER test dataset using standard metrics of precision, recall, and F1-score. The experimental results show that the fine-tuned MahaBERT-based models consistently outperform both the baseline and all evaluated LLMs, with the fine-tuned models achieving F1-scores ranging from 0.88 to 0.91, surpassing the existing MahaNER model (0.8843) and significantly exceeding the performance of LLM-based approaches, whose F1-scores range from 0.57 to 0.69. These findings demonstrate that task-specific, language-focused models trained on domain-relevant data remain more effective than general-purpose LLMs for Marathi NER, highlighting the continued importance of specialized architectures for low-resource language processing.

Hariom Ingle, Ronit Ghode, Ishwari Gondkar +2

Department of Information Technology, PICT, Pune, India · L3Cube Labs, Pune, India · Indian Institute of Technology Madras, Chennai, India

Named Entity Recognition LLM Evaluation Transformer LLM Fine-Tuning Low-Resource Language Processing

Jul 25, 2026cs.AI

CAPT: A Multi-task Continuous Autoregressive Transformer enabling Cross-dataset and Cross-species Transfer for Calcium Population Dynamics

Large-scale calcium imaging has created an opportunity to build foundation-style models for neural population dynamics, but a central question remains unresolved: \textbf{whether a model pretrained on one collection of recordings can generalize to new datasets, experimental paradigms, and even species.} Existing approaches are often designed for specific tasks and evaluated on a single dataset, making it unclear whether their learned representations are reusable for new calcium trace datasets. To tackle this gap, we present \textbf{CAPT}, a \textbf{C}ontinuous \textbf{A}utoregressive \textbf{P}opulation \textbf{T}ransformer for calcium population dynamics. CAPT models continuous calcium traces directly through a continuous patch tokenization strategy and is trained autoregressively, enabling end-to-end pretraining and adaptation to diverse downstream tasks. We first pretrain CAPT on a large-scale mouse calcium imaging dataset and evaluate its transferability across independent mouse, larval zebrafish, and \textit{C. elegans} datasets collected by different laboratories. In these transfer settings, the pretrained backbone is frozen and only adaptation modules are updated. Across neural population forecasting and behavior decoding tasks, CAPT consistently outperforms specialized and general-purpose baselines. Alongside predictive performance, multimodal analyses using NeuroPAL annotations in \textit{C. elegans} datasets show that CAPT embeddings form a shared functional space across datasets and capture anatomical cell-identity-related structure. These results suggest that the continuous autoregressive modeling opens up possibilities for a simple route towards general-purpose neural foundation models for calcium imaging, which can generalize across datasets, experimental paradigms, and species. Code is available at https://github.com/TSuXinH/CAPT.

Xinhong Xu, Yimeng Zhang, Yuanlong Zhang

School of Life Sciences Tsinghua University Beijing, China

Transformer Neural Decoding Transfer Learning Time-Series Foundation Models

Jul 25, 2026cs.AI

Structure over Depth: A Single-Block Spatio-Temporal Transformer for Multi-Entity Reasoning

Modeling multi-entity temporal data requires capturing dependencies across entities, time, and their interactions. Transformer-based approaches perform well but often rely on deep stacks of layers to learn these heterogeneous dependencies implicitly, increasing computational cost. We revisit this problem from a structural perspective and decompose multi-entity temporal dynamics into three interaction types: spatial interactions among entities, temporal interactions across time, and cross interactions coupling the two domains. We propose a structured spatio-temporal transformer block that explicitly models all three within a single stage. It uses parallel spatial and temporal self-attention, followed by bidirectional cross-attention, and combines the outputs through learnable gated fusion. By directly encoding these complementary views, the model reduces the need for deep stacking. We evaluate the approach on video-based group activity recognition, skeleton-based human interaction analysis, and wearable sensor-based activity recognition. Despite its simplicity, the single structured Transformer block matches or outperforms deeper architectures with only 1.76M parameters. The results suggest that depth in prior models partly compensates for implicit and entangled interaction modeling, whereas explicit factorization offers a more efficient and transparent alternative. More broadly, this work supports a structure-first design principle: expressive multi-entity temporal reasoning can emerge by exposing interaction structure rather than relying on depth.

Narthana Sivalingam, Santhirarajah Sivasthigan, Buddhi Wijenayake +3

Department of Electrical and Electronic Engineering University of Peradeniya Peradeniya, Sri Lanka

Spatiotemporal Reasoning Human Activity Recognition Transformer Temporal Attention

Jul 25, 2026cs.LG

Sensitivity Analysis of GRU, LSTM and Transformer Encoder in Classification of Automated Driving Systems

Automated driving systems (ADSs) are becoming ubiquitous. Future Software Defined Vehicles (SDVs) may be able to run multiple ADSs, both native and aftermarket such as Comma.ai's Openpilot. Monitoring systems to independently verify which automated driving system is active are important for safety monitoring, regulatory compliance, insurance assessment, and anomaly detection. In this paper, we first evaluate the effectiveness of three sequence-based classification models: Gated Recurrent Units (GRU), Long Short-Term Memory (LSTM) networks, and a Transformer encoder model for identifying Level 2 automated driving systems using vehicle telematics data alone: Comma Openpilot, Tesla Autopilot, and Cadillac Super Cruise, along with manual driving. All three models achieve strong clean-data performance with macro F1-scores of 0.92 (GRU), 0.90 (LSTM), and 0.93 (Transformer encoder model) when trained on clean data; threat-matched training yields 0.904-0.916 macro F1 with only a modest clean-data penalty. Second, we introduce a modular robustness evaluation framework that simulates realistic telematics degradation through five corruption families at five severity levels (L1-L5). Continuous channels are perturbed using additive white Gaussian noise with cumulative drift, correlated cross-channel noise, and temporal jitter. Binary event signals are subjected to burst loss, delayed transitions, spurious toggles and cross-feature inconsistencies inspired by communication errors. Robustness is measured using macro-F1, which gives equal weight to each class and is suitable for imbalanced multiclass evaluation. Our evaluation reveals a sharp failure-mode split: event-level corruptions reduce macro-F1 only slightly (greater than equal to 0.87 at L5), while temporal jitter collapses macro-F1 to 0.44-0.50 across GRU, LSTM, and Transformer encoder model.

Bidhya Shrestha, Christos Papadopoulos

University of Memphis

Transformer Time Series Classification Recurrent Neural Networks

Jul 24, 2026cs.LG

Hidden Boundary Motion in Transformer Optimization: Function-Space Orthogonalization of Affine Weight and Bias Updates

Weights and biases are normally optimized as separate parameter tensors, yet they do not represent separate functions when the input to an affine layer has nonzero mean. For an affine map

z=Wx+b

with input mean

μ

, a weight update contains a sample-independent displacement

ΔWμ

that is functionally indistinguishable from a bias update. We call this hidden contribution \emph{boundary motion} and decompose each update into a centered, sample-varying \emph{shape} component and a shared \emph{boundary} component. On a four-layer Transformer trained from scratch on IMDb, the bias-like term

g_bμ^\top

has a median norm equal to 0.664 of the raw weight-gradient norm across affine layers and training checkpoints. More strikingly, the median ratio

\norm{ΔWμ}/\norm{Δb}

is 134.7, while

\norm{ΔWμ}/\norm{Δb+ΔWμ}

is 0.994. Thus, under AdamW, the observed boundary motion is almost entirely realized through the weight matrix rather than the explicit bias. We implement a diagnostic optimizer, Shape--Boundary Orthogonal AdamW (SBO-AdamW), that optimizes

g_W-g_bμ^\top

and

g_b

with independent Adam states and compensates the weight-induced boundary displacement. In a single-seed experiment, SBO-AdamW raises validation accuracy from 81.68% to 85.81% and validation-selected test accuracy from 78.73% to 82.73%, with the best validation checkpoint occurring at step 800 instead of step 3000. However, the moving-batch-center compensation produces severe bias-coordinate drift and strongly reduces boundary energy. The present evidence therefore supports hidden boundary motion as an important optimization mechanism, but it does not yet establish a final general-purpose optimizer. A stable centered-affine parameterization is identified as the required next step.

Zhang Gongyue, Sheng Yixuan, Liu donghan +3

arXiv:2607.22927v1

Transformer Neural Network Optimization Adaptive Gradient Methods

Jul 24, 2026cs.LG

Interior interpretability with attention rollout: contraction and propagation profiles in Transformers

Feature-attribution methods assign scores relating input variables to a model's output, but do not by themselves characterize how explicitly defined interaction operators compose across its intermediate layers. We introduce \emph{interior interpretability}, a propagation-based perspective on internal model organization, and instantiate it for tabular Transformers using attention rollout. We interpret rollout as a row-stochastic operator encoding attention-mediated propagation between feature tokens. By applying classical Doeblin--Dobrushin contraction theory, we show that a rollout operator with a small Dobrushin coefficient is quantitatively close to a rank-one stochastic matrix whose common row is determined by its normalized column sums. This result gives a structural interpretation to the corresponding rollout propagation profile. In Transformers trained for metabolomic age prediction, the measured rollout contraction strengthens with depth. Trained and randomly initialized models also exhibit different propagation profiles, although the present experiments do not establish the predictive relevance of individual rollout-ranked variables. Exploratory comparisons with PCA and GradientExplainer approximations to SHAP reveal localized agreement among highly ranked variables but weak agreement across complete rankings. Attention rollout is therefore used here as a diagnostic of attention-mediated propagation, not as a causal explanation or faithful attribution of the complete Transformer.

Umberto Biccari, Qian Huang, Enrique Zuazua

Transformer Interpretability Transformer

Jul 24, 2026cs.LG

Multimodal Surface EMG Hand Gesture Recognition Using Query-Based Transformers for Prosthetic Control

Hand gesture recognition via surface electromyography (sEMG) is fundamental to prosthetic control. In this field, deep learning approaches have become the gold standard. However, current architectures struggle to scale; model performance typically decreases as the number of hand movements increases. Performance degradation is tied to the increased statistical complexity of decoding expanded gesture sets and compounded by the limitations of state-of-the-art methods, which primarily rely on low-latency unimodal convolutional architectures. Convolutions operate locally, limiting model's ability to capture long-range sequential patterns. Unimodal setups cannot leverage complementary information from coordinated signals characterizing movement execution, such as inertial and eye-tracking data. These limitations motivate architectures that integrate local and global features across multimodal physiological sequences. To bridge this gap, this study introduces EMG-CrossFormer, an end-to-end hybrid convolutional-transformer for seamless multimodal integration. EMG-CrossFormer combines representations from an arbitrary number of unimodal encoders through cascaded cross-attention fusion layers, and decodes the fused representations using learnable gesture queries. EMG-CrossFormer was evaluated on four NinaPro datasets (DB2, DB3, DB7, and DB10) and benchmarked against six state-of-the-art models using an increasing number of modalities. Using only sEMG, EMG-CrossFormer achieved mean accuracies of 72.33%, 52.48%, 79.16%, and 73.49% on DB2, DB3, DB7, and DB10, respectively. Incorporating inertial signals improved performance to 90.66%, 80.40%, 92.79%, and 92.06%. These results show that joint local-global feature modeling improves sEMG-only decoding and that multimodal fusion substantially amplifies this benefit, underscoring the value of both design principles for complex hand gesture recognition.

Federico Del Pup, Elisa Tentori, Manfredo Atzori

Department of Information Engineering, University of Padua, Padua, 35131, Italy · Padova Neuroscience Center, University of Padua, Padua, 35129, Italy · Department of Biomedical Sciences, University of Padua, Padua, 35131, Italy +2

EMG-Based Gesture Recognition Hybrid CNN-Transformer Architectures Transformer Assistive Robotics Multimodal Fusion

Jul 23, 2026cs.LG

Hierarchical Grading in Large Language Models

We introduce Graded Large Language Models (GLLMs), an algebraic framework that equips the representation space of a transformer with a grading and propagates the induced weighted scalar action through embeddings, self-attention, and the training objective. The construction extends the theory of graded neural networks and graded transformers to autoregressive language models while preserving expressive power, asymptotic computational complexity, and inference cost. The governing geometric picture is that of geometric invariant theory. The benefit of a grading is expressed by a Kempf--Ness functional on the grading torus; the grades that improve upon the uniform architecture form an open convex cone whose membership is decided by a Hilbert--Mumford-type criterion pairing a grade direction against two measurable profiles of the target and the data; the optimal grades are the coincidence point of two moment maps, given in closed form; and the ordinary transformer appears as a semistable isotropic point on the boundary of the cone: one member of a larger graded family rather than a distinguished optimum. Separately, for level-stratified targets we prove a minimax separation between the graded prior and its absence: over all estimators the risks of the graded and uniform target classes separate throughout an explicit window of sample sizes, by a factor that decays exponentially in the number of levels under geometric stratification. Both profiles are estimable offline, so the optimal grades solve a convex program certified before training begins. Because the grading is absorbed into the learned parameters after training, every GLLM compiles to a standard transformer of identical architecture and inference complexity.

T. Shaska

Transformer LLM Training

Jul 22, 2026cs.LG

Multi-modal transformer for signal classification in nanopore blockade experiments

Nanopore devices have emerged as powerful tools for single-molecule sensing, with potential for rapid, portable diagnostics. They detect changes in ionic current as analytes enter nanometer-scale pores, providing a means of identifying diverse biomarkers from their characteristic signal patterns. However, these signals are highly complex, and reliably assigning them to specific molecules remains a major challenge. Here, we address this by introducing a multi-modal deep learning architecture that jointly processes multiple signal representations, including raw time-series data, wavelet-based images, and static feature vectors. Our approach surpasses existing methods by more than 10 percentage points on a 42-peptide benchmark and transfers to a 20-amino-acid dataset with near-perfect accuracy. The model integrates complementary information from these representations, with attention analysis showing that the time-series and wavelet-image inputs emphasize different features of the same event. Together, these results demonstrate the potential of machine learning to enable robust, high-accuracy molecular identification with nanopore sensors.

Sandro Kuppel, Julian Hoßbach, Samuel Tovey +1

Institute for Computational Physics University of Stuttgart Allmandring 3, 70569 Stuttgart, Germany

Transformer Time Series Classification Multimodal Classification

Jul 22, 2026cs.AI

The Giant Hippocampus: From Structural Monoculture to a System of Systems

AI researchers describe state-of-the-art models as one thing repeated at scale: the Transformer, wired identically for text, pixels, or speech. Neuroscientists describe the cortex as a mosaic - dense Layer 4 in visual cortex for spatial encoding, thick Layers 5/6 in motion cortex for temporal integration - different jobs solved by different structures. This paper argues the gap is a structural error, not a stylistic one, and is measurable. A century of cytoarchitecture, from Brodmann to single-cell Patch-seq, shows distinct cognitive functions are implemented by qualitatively different structures, not by rescaling one template. The convolutional neural network is the field's own proof: local receptive fields and hierarchical depth encoded this prior directly, reaching strong image recognition on far less data than later architectures needed. The paper traces how this lesson was discarded: the "Hardware Lottery" made the Transformer the path of least resistance, not the principled choice, and Mixture-of-Experts, often cited as diversity, in fact partitions parameters among identical experts. A functionalist analysis shows the Transformer is best understood as a functional analog of the hippocampal formation, not a general-purpose cortex - the same mistake as treating cortex as one giant Broca's area, except the field has now standardized on a giant hippocampus, applied to tasks it was never built for: audition, executive gating, working memory. The paper closes with an alternative: a Heterogeneous Topological Network, a System of Systems in which distinct modules keep the inductive bias their computation demands and communicate through standardized interfaces. This is a design discipline for AI architects, not cognitive science: specify modularity before training, using structural evidence as a design input rather than reverse-engineering architecture from a trained model's behavior.

Jaeho Seol

Independent Researcher

Transformer Inductive Bias Modular Neural Networks

Jul 22, 2026cs.AI

Multi-Head Attention Residuals

Transformers propagate information across depth through a single additive residual stream: every sublayer reads only the most recent state. Attention residuals relax this by letting each sublayer attend, through a learned softmax. However, that read uses a single query shared across the entire width, so every feature subspace must read the depth history through one distribution. The cost of this forced compromise grows with how much the subspaces disagree about which layers to read, and disagreement grows with model width. We introduce Multi-Head Attention Residuals (MHAR): the routing query is reshaped into H per-subspace heads, each with its own softmax over the depth history. The read becomes block-diagonal, the reshape adds zero parameters and negligible compute, and H = 1 recovers attention residuals exactly. Trained from scratch on a deduplicated Nemotron-based anneal corpus that is quality-filtered and STEM- and code-heavy, MHAR improves validation loss over a standard Transformer at 100M, 350M, and 1B (-0.061, -0.149, and -0.140). It achieves the best result among four methods in every setting, with the gain increasing from 100M to the larger scales. The head count is a real design axis rather than a free knob: validation loss is U-shaped with respect to H, with a flat optimum at H = 4 or H = 8 across scales. We adopt H = 8 for large-scale models; over-splitting beyond this point (H = 16) consistently gives back part of the gain. A direct probe of the trained queries confirms that learned subspace disagreement is the underlying driver. Fused Triton routing kernels increase attention-residual training throughput from 0.2-0.5x to 0.55-0.88x of the baseline while maintaining near-baseline peak memory. An identity-preserving conversion using delta attention residuals supports 8B mid-training, yielding improvements of +3.2 on GSM8K and +3.1 on GPQA.

Cheng Luo, Zefan Cai, Junjie Hu

Independent Researcher · University of Wisconsin–Madison

Transformer Attention Residual Connections Language Modeling Multi-Head Attention

Jul 21, 2026cs.LG

Elicitation without Backpropagation: Steering Model Behavior by Optimizing the Latent Posterior

In the \emph{latent posterior model} of transformer behavior, the next-token distribution arises from a posterior over latent predictive models conditioned on the context, mixed to generate continuations. We exploit this model in settings where it is exact, namely Bayes-filtered transformers (BFTs) meta-learned on sequences from a hierarchical prior, to introduce \textbf{Posterior Prefix Tuning (PPT)}, a new method for \emph{eliciting} behavior from a transformer: given a utility function on continuations, find a prompt under which the transformer generates continuations of high expected utility. For a BFT, the elicitation objective factors through the latent posterior, and the gradient of this objective can be estimated from samples of the prior alone. PPT optimizes the parameters of a distribution over hard prompts: it draws prior samples once from the BFT via predictive Monte Carlo (PMC), then estimates the gradient by importance sampling against them. The optimization performs no transformer forward passes and no backpropagation through the transformer, and the prior samples are utility-independent, so a single set of samples drives elicitation against any number of utilities at negligible marginal cost. We validate PPT on Beta--Bernoulli and reinforced urn BFTs across three utility families (reverse cross-entropy, frequency matching, Dyck validity).

Garrett Baker, Vinayak Pathak, Daniel Murfet +1

Timaeus · CORAL · Monash University

Prompt Learning Transformer Prompt Optimization