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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

Jun 22, 2026cs.LG

The Energy Consumption of Transformer Fine-Tuning: A Roofline-Inspired Scaling Model

Transformer-based models underpin modern natural language processing but incur rapidly growing computational and energy costs. As training scales in both model size and parallelism, accurately predicting energy consumption has become critical for sustainable and cost-aware system design. We present a framework for modeling the energy consumption of Transformer training on multiple GPUs. Using controlled architectural sweeps of BERT models, we relate measured energy to lightweight proxies for compute, memory traffic, and hardware efficiency. Inspired by roofline models, our approach incorporates a speedup-based hardware-efficiency factor that captures the effects of tensor parallelism and fully sharded data parallelism. We derive a scaling law model that accurately predicts training energy across heterogeneous configurations.

Mansour Zoubeirou a Mayaki

Université Lumière Lyon 2, CNRS, Ecole Centrale de Lyon, INSA Lyon, Universite Claude Bernard Lyon 1, LIRIS, UMR5205, 69007 Lyon, France

Energy-Efficient ML Transformer Language Model Scaling Laws

Jun 22, 2026cond-mat.dis-nn

Scalable Physics-Inspired Transformers for Spin Glasses

Efficient sampling of the Boltzmann distribution in frustrated spin glasses is central to statistical mechanics and combinatorial optimization. Despite advances in machine-learning-based approaches, two issues persist: limited understanding of why variational models fail to benefit from increased scale, unlike the monotonic scaling law of large language models; and high computational cost on large systems that negates advantages over classical sampling methods. Here, we develop a physics-inspired transformer with interpretable sparse attention and spin-tailored positional embeddings to address these challenges. By further leveraging FlashAttention for parallel ancestral sampling, it achieves up to two orders of magnitude speedup over vanilla variational autoregressive networks, enabling neural-network simulations of spin-glass systems to unprecedented sizes on a single GPU. It can resolve full probability distributions, free energies, and overlap statistics across temperatures, for Sherrington-Kirkpatrick and 2D or 3D Edwards-Anderson models, where existing machine-learning methods encounter limitations at certain temperatures. This framework thus establishes a scalable paradigm for frustrated spin-glass systems.

Lu Zhong, Wenli Duan, Jing Liu +2

Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China · School of Physical Science and Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China · Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China +4

Jun 22, 2026cs.LG

BranchShine: Compact Raw-Audio-to-IPA Transcription with a RoPE E-Branchformer Encoder

Speech-to-IPA transcription is useful when the desired output is pronunciation rather than orthographic text, but competitive multilingual systems are often large and evaluation is sensitive to normalization choices. This paper presents BranchShine, a 33M-parameter raw-audio CTC recognizer with a lightweight convolutional front end and a 19-block RoPE E-Branchformer encoder. We find that BranchShine provides a compact and competitive operating point for IPA transcription under matched normalization and scoring. On a 16,660-utterance multilingual test set covering 41 language labels, BranchShine obtains 9.19% whitespace-insensitive IPA character error rate, compared with 9.78% for the 575.00M-parameter PhoneticXEUS baseline. A secondary child speech reading analysis shows a complementary operating profile: BranchShine is more conservative on incorrect readings, while Whisper-Medium is stronger on exact acceptance of correct readings. Overall, the results indicate that a compact raw-audio-to-IPA model can approach much larger baselines on character-level IPA transcription.

Nikhil Navas, Sergio Chevtchenko, Talisson Damiao +1

1International Centre for Neuromorphic Systems, Western Sydney University · 2Neurabuild

Transformer Multilingual ASR

Jun 19, 2026cs.LG

SOHET: Sequence Of Heterogeneous Events Transformer with Self-Supervised Pre-Training

Many machine learning applications rely on heterogeneous event streams to make predictions, either causally as events arrive or bidirectionally over complete sequences. We propose SOHET (Sequence Of Heterogeneous Events Transformer), a hierarchical architecture combining event-type-specific tabular encoders with temporal and type embeddings, processed by a causal or bidirectional transformer. We introduce three self-supervised pre-training objectives for the causal setting. On a proprietary large-scale real-world Booking.com fraud detection task with 17 event types, SOHET outperforms FlexTPP, NAPPT, and CIPPT by 5.8%. Pre-training yields an additional 2.6% gain and 2.4% faster convergence. On the EBES benchmark, bidirectional SOHET matches or exceeds the published best on 6 out of 8 tasks.

Kees Jan de Vries, Mustafa Radha, Mathijs de Jong

Booking.com, Amsterdam, The Netherlands

Transformer Self-Supervised Pre-Training Sequence Modeling

Jun 19, 2026cs.CL

Scalable Hierarchical Attention Transformers for Multi-Turn Jailbreak Detection in Long Conversations

Multi-turn jailbreaks can evade turn-level moderation by spreading unsafe intent across a dialogue through gradual escalation, reframing, and role manipulation. We address multi-turn jailbreak detection as a conversation-level classification problem and introduce an efficient hierarchical detector that avoids expensive long-context concatenation while retaining cross-turn reasoning. The model encodes individual turns to form compact turn representations and applies a lightweight conversation module that captures dialogue dynamics and selectively attends to fine-grained evidence when needed. On a challenging evaluation benchmark of 14,038 conversations, our approach achieves an F1 of 0.9394, outperforming Claude Opus 4.7, the strongest competing baseline, by 0.07 while halving its false-positive rate. Ablation studies confirm that each architectural component contributes meaningfully, with combining cross-attention and self-attention in the conversation module yielding a 2.26 percentage point reduction in false-positive rate over the self-attention-only variant.

Chenhui Hu, Muhammed Salih, Sudipto Guha +1

Zscaler, Inc.

Transformer Multi-Turn Jailbreak Attacks Jailbreak Detection Jailbreak Defense

Jun 19, 2026cs.CL

FiLM-Coordinated Dual-Branch Transformer for Global-Local Dependency Modeling in Language Modeling

Standard Transformers use a single self-attention pathway to model both global dependencies and local patterns, creating tension between long-range structural reasoning and fine-grained local representation learning. We propose a FiLM-coordinated dual-branch Transformer for language modeling, where each layer explicitly contains a global branch and a local branch, and feature-wise linear modulation (FiLM) is used for dynamic cross-branch coordination instead of simple concatenation or static addition. The key idea is that the two branches represent different dependency views of the same input, making channel-wise calibration more suitable than heavy token-level interaction. We therefore design a bidirectional FiLM module in which each branch generates per-channel scaling and shifting parameters to condition the other. Experiments on multiple small-scale language modeling settings show that the proposed structure consistently outperforms same-width single-branch baselines and weakened dual-branch variants under a fixed lightweight configuration. On TinyShakespeare and a 1M-character subset of WikiText-2, the full dual-branch FiLM model achieves the best results among same-width structural baselines. Multi-seed results support the stability of the gains, while mechanistic analyses show that FiLM learns input-dependent, layer-dependent, and channel-selective modulation patterns rather than static scaling. Parameter-matched widened single-branch baselines also indicate that the current design still leaves room for improvement in parameter efficiency.

Zhiqiang Zhou, Xu Ling, Junliang Dai

Transformer Language Modeling Sequence Modeling

Jun 18, 2026cs.LG

Learning through Internalization

We study internalization processes, by which neural-network-based systems absorb an explicit computational procedure into their own weights, and how they facilitate learning. We investigate how transformers internalize the simulation of semiautomata by internalizing chain-of-thought (CoT) tokens, which classes of semiautomata are harder to internalize, and expose the flip side of internalization, that is, a progressive degradation of out-of-distribution performance. We then provide the first provable analysis of successful internalization: for the task of learning parities, we show that a simplified one-layer transformer provably first learns the target with explicit CoT supervision and then internalizes the autoregressive generation as CoT tokens are progressively removed, learning to directly compute the parity. This task is computationally hard to learn from data without CoT supervision. Finally, we discuss how learning through internalization relates to the \textit{Positive Distribution Shift} phenomenon recently introduced by~\citet{Med+26}.

Nikolaos Tsilivis, Nirmit Joshi, Marko Medvedev +2

New York University · Toyota Technological Institute at Chicago · University of Chicago

Transformer OOD Generalization

Jun 18, 2026cs.CL

Comparing Transformers and Hybrid Models at the Token Level

Hybrid language models that mix attention and recurrent layers have shown promise: theoretically, recurrent layers ameliorate the limitations of pure transformers on state tracking, and empirically, hybrids can outperform pure transformers in loss and downstream evaluations \citep{waleffe2024empirical,merrill2026olmohybrid}. Yet it remains unclear which data or capabilities drive these gains, and to what degree they reflect the theoretical advantages motivating hybrid models. We address this question using the open weights from Olmo 3 \citep{olmo2025olmo3} and Olmo Hybrid \citep{merrill2026olmohybrid}: we compare the loss of a matched transformer and hybrid at the same target tokens under the same prefixes, stratifying the results by natural token tags, copy features, delimiter structure, and controlled synthetic probes. The hybrid has lower loss on most tag families, but the gains are not uniform: they are largest for open-class content words and smaller for many closed-class function words. Across prose, code, and markup, the hybrid's loss advantage is larger on opening delimiters than on the corresponding closing delimiters, and nearly vanishes on repeated

n

-grams. Synthetic probes show the same split: the hybrid is favored on pronoun-memory and entity-tracking tasks, whereas the transformer is favored on bracket-matching tasks that require choosing closing delimiters. These patterns suggest that the recurrent layers in hybrids improve predictions that leverage the semantic state of a document, whereas attention helps on tokens predictable by

n

-gram copying or syntactic bracket matching. We conclude with proof-of-concept filtered evaluations showing how token-level decompositions can sharpen pretraining diagnostics for hybrid architectures.

Yanhong Li, William Merrill

Allen Institute for AI

LLM Evaluation Transformer

Jun 18, 2026hep-ex

HEPTv2: End-to-End Efficient Point Transformer for Charged Particle Reconstruction

Charged-particle tracking -- reconstructing trajectories from sparse detector measurements -- is a fundamental high-energy-physics inference problem and a canonical example of learning under extreme combinatorial ambiguity. At the High-Luminosity Large Hadron Collider (HL-LHC), tracking must remain accurate and efficient despite unprecedented collision densities. Graph neural networks perform strongly, but incur substantial costs from graph construction and processing, while transformer-based approaches rely on auxiliary stages that prevent end-to-end optimization. To address this, we present HEPTv2, an end-to-end point-transformer architecture that reconstructs tracks from detector hits in one trainable pipeline. HEPTv2 combines a locality-aware point encoder with a track decoder that predicts complete trajectories without graph-building, clustering, or filtering. The encoder uses locality-sensitive hashing in detector coordinate space to preserve tracking-relevant geometry while enabling efficient local attention. The decoder resolves ambiguities through sectorized decoding and direct hit-to-track prediction under joint encoder-decoder supervision, allowing the full pipeline to be optimized end-to-end. On TrackML, HEPTv2 achieves 98.6% double-majority tracking efficiency at a 0.8% fake rate, while requiring only

\sim

15~~ms inference time and 0.4~~GB peak memory per event on a NVIDIA A100 GPU. Latency and memory scale approximately linearly for events with up to

5\times10^5

hits. HEPTv2 establishes a new state of the art in the accuracy-latency trade-off, improving efficiency by 4.5% over the strongest prior transformer and by 1.1--2.2% over optimized graph-based pipelines, while reducing latency by factors of 7 and 38--52, respectively. These results show end-to-end transformers can deliver the accuracy and efficiency required for real-time particle reconstruction at the HL-LHC.

Siqi Miao, Shitij Govil, Jack P. Rodgers +5

School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, USA. · Department of Physics and Astronomy, Purdue University, West Lafayette, IN, USA. · Department of Physics, University of California San Diego, La Jolla, CA, USA. +1

Efficient Transformer Inference Transformer High-Energy Physics

Jun 18, 2026cs.LG

OnDeFog: Online Decision Transformer under Frame Dropping

In challenging real-world reinforcement learning applications, communication delays or sensor failures often cause frame dropping, in which the agent cannot receive the dropped states and associated rewards. To address the performance degradation caused by frame dropping, the Decision Transformer under Random Frame Dropping (DeFog) was developed by incorporating additional mechanisms into the decision transformer to tackle frame dropping. Although DeFog can mitigate performance degradation in frame-dropping environments, since DeFog is an offline learning method, it struggles to effectively generalize to novel states not adequately represented in the training dataset. In this study, we propose OnDeFog, which integrates the mechanisms in DeFog with the online decision transformer (ODT), an online reinforcement learning method that learns policies through direct environmental interaction. Comprehensive experimental evaluation demonstrates that our proposed OnDeFog achieves superior performance compared to ODT in environments characterized by high dropping frame rate and outperforms DeFog on datasets containing a large amount of low-reward data.

Daiki Yotsufuji, Kenta Nishihara, Shoma Shimizu +2

Yokohama National University, Kanagawa, Japan

Reinforcement Learning Transformer Decision Transformer

Jun 18, 2026cs.LG

Efficiently Representing Algorithms With Chain-of-Thought Transformers

The increasing popularity of \emph{reasoning} models -- language models that output a series of reasoning or thought tokens before producing an answer -- is justified, in part, by theoretical results showing that chain-of-thought (CoT) transformers can simulate Turing machines, and thus perform arbitrary computation. However, the Turing machine, while suitable for complexity-theoretic analysis, is not convenient, intuitive, or efficient for discussing algorithms. Algorithms are typically designed and analyzed at a higher level of abstraction, captured by the \emph{Word RAM} model with random-access memory and unit-cost operations on

\bigO(\log n)

-bit words. As a result, Word RAM algorithms can be substantially more efficient than their Turing machine counterparts, raising the question: \emph{Can CoT transformers efficiently simulate Word RAM algorithms?} For instance, can they sort

n

items in

\bigO(n \log n)

steps or run Dijkstra's algorithm in

\bigO(E + V \log V)

steps? We answer affirmatively, up to poly-logarithmic overhead. We first establish this for finite-precision transformers with poly-logarithmic width and rightmost unique hard attention, then strengthen the result to two more practical settings with finite width and log-precision: \emph{continuous} CoT, where reasoning takes the form of vectors rather than tokens, and a \emph{hybrid} architecture in which transformer layers sit atop a recurrent (linear RNN) layer. In all three cases, we find that CoT \emph{can} efficiently simulate any Word RAM algorithm with only a poly-logarithmic overhead in

n

. This overhead reduces to log-square when the Word RAM has a ``flat'' instruction set, and only logarithmic for multiplication-free flat instructions -- in stark contrast to known CoT simulations of Turing machines, which require quadratic overhead over Word RAM.

Yanhong Li, Anej Svete, Ashish Sabharwal +1

Allen Institute for AI · ETH Zürich

Transformer CoT Reasoning Neural Algorithmic Reasoning Efficient Language Model Reasoning Algorithmic Reasoning

Jun 17, 2026cs.LG

Massive Activations Are Architecturally Robust: A Controlled Scratch/Commitment Residual Stream Test

Trained transformers reliably develop massive activations, a small number of hidden dimensions whose magnitude is far above the median and which concentrate on the sequence-start token. Whether these outliers are a removable artifact of the residual stream's overloaded read and write role, or instead a functional necessity, is actively debated. We test the artifact hypothesis directly, with an architectural intervention. Our architecture, Ledger Residuals, splits the residual stream into a mutable scratch stream (Deliberation) that intermediate computation may freely overwrite and a protected, decode-only accumulator (Commitment) that holds the representation the model reads out. If massive activations exist only because one stream is forced to be both scratchpad and answer, then a dedicated answer channel should remove the need for them. We find that it does not. In matched-loss language models at the 160M and 290M scales, the model rebuilds the canonical fixed-dimension, start-token outlier inside the protected channel. The rebuilt feature is smaller in magnitude than in a standard transformer but more sharply concentrated on the start token, and a stronger sparsity penalty makes it more persistent and more concentrated still, rather than removing it. Massive activations therefore look architecturally robust: they re-emerge in whichever representation the model decodes from, which is what we would expect if they are functional rather than incidental. We release our architecture and measurement code.

Maruthi Vemula

University of North Carolina at Chapel Hill

Jun 17, 2026cs.LG

Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale

Pretrained transformers sit near singular minima of the loss, where the Fisher information metric degenerates along dead directions: directions in parameter space along which the directional Fisher vanishes. Locating such a direction normally needs a forward pass and an eigendecomposition of activations, or a sampling-based complexity estimate; none returns a direction computable from the network's parameters alone. We give one, for LayerNorm transformers. The inverse-scale direction

γ^{-1}/\|γ^{-1}\|

of the LayerNorm affine is an exact algebraic kernel of the post-final-norm centred activation covariance, for any input distribution, and induces a corresponding dead direction in parameter space. It is read from the LN scale parameter alone, with no forward or backward pass and no eigensolve: the cheapest dead-direction read, specific to LayerNorm. We test it on

14

pretrained transformers (

9

LayerNorm,

5

RMSNorm;

160

M-

35

B; language and vision objectives). At random initialisation the predicted direction matches the measured bottom singular direction (one forward pass, direct SVD) to four decimal places on

9/9

LayerNorm models, and is correctly absent on

5/5

RMSNorm models, which lack the mean-subtraction projector that creates it. On the trained checkpoint the covariance eigenvalue along this direction deepens by

{\sim}10^3\times

and further dead directions open; the random-init-to-trained gap is a one-forward-pass, per-checkpoint readout of singular structure along the predicted coordinate. Two consequences follow in closed form: the residual stream's smallest singular value is preserved block-to-block on

13/14

transformers measured on their own input distribution, the one exception (Gemma

4

-

31

B) a genuine dead direction the same read pinpoints; and the kernel direction's presence classifies a transformer's normalisation from the parameters alone.

Tejas Pradeep Shirodkar, P. J. Narayanan

IIIT, Hyderabad

Information Geometry Transformer Neural Network Optimization Layer Normalization

Jun 17, 2026cs.SD

QC-GAN: A Parameter-Efficient Quaternion Conformer GAN for High-Fidelity Speech Enhancement

We propose a parameter-efficient speech enhancement framework, Quaternion Conformer GAN (QC-GAN), which combines a Quaternion Conformer generator with MetricGAN-based training. The Hamilton product encodes the magnitude and phase via structured weight sharing, reducing the number of layer parameters while preserving their interdependencies. A metric-learning discriminator was employed to maximize perceptual quality by optimizing the approximate perceptual evaluation scores. On the VoiceBank+DEMAND dataset, QC-GAN achieved a Perceptual Evaluation of Speech Quality (PESQ) score of 3.48 with only 0.89M parameters, delivering a performance comparable to state-of-the-art models at less than half their size. A 35K-parameter variant achieved a PESQ score of 3.23, surpassing conventional methods with significantly fewer parameters. Evaluation on the DNS-Challenge 3 dataset further confirmed generalization to real-world conditions.

Shogo Yamauchi, Hideaki Tamori, Makoto Sakai +2

The Asahi Shimbun Company, Japan · Tokyo Woman’s Christian University, Japan

Transformer Complex-Valued Neural Networks Speech Enhancement Generative Adversarial Networks

Jun 16, 2026cs.CL

Variable-Width Transformers

Scaling model size, specifically depth and width, has driven significant progress in transformer-based language models. However, most architectures maintain a constant width across all layers, allocating a fixed parameter and computation budget evenly despite different layers potentially playing distinct computational roles. In this work, we empirically investigate nonuniform capacity allocation across network depth by proposing a

\times

-shaped > <former architecture. This design maintains wider early and late layers while narrowing the middle layers, utilizing a parameter-free residual resizing mechanism. Across decoder-only language models ranging from 200M to 2B parameters (dense) and 3B parameters (MoE), our > <former consistently outperforms parameter-matched uniform baselines on language modeling loss. By reducing the average layer width, this architecture also requires fewer overall FLOPs (22% reduction under fitted loss-matched scaling curves) and smaller KV cache memory and I/O cost (15% reduction). In analysis, we show that this bottleneck structure results in qualitatively different representations in residual streams. Overall, our results demonstrate that nonuniform width allocation can result in more resource-optimal scaling of language models.

Zhaofeng Wu, Oliver Sieberling, Shawn Tan +3

ãMIT · èMIT-IBM Watson AI Lab

Transformer Decoder-Only Language Models Language Model Scaling

Jun 16, 2026cs.CV

HLS-GPT: A Generative Pretrained Transformer (GPT) for Continental-Scale NASA Harmonized Landsat and Sentinel-2 (HLS) Reflectance Reconstruction Across All Bands on Arbitrary Dates

Recent deep learning methods for Landsat and Sentinel-2 reflectance time series reconstruction remain limited by restricted spectral coverage, limited geographic scalability, or patch-based designs with short temporal contexts. We present HLS-GPT, a large-scale generative pretrained Transformer model for reconstructing NASA Harmonized Landsat Sentinel-2 30 m surface reflectance for all bands, any date, and any pixel location. HLS-GPT uses a hierarchical Transformer architecture to handle the different spectral band configurations of Landsat and Sentinel-2 and operates on single-pixel 12-month time series. To capture geographic and seasonal variability, the model was trained with nine years of HLS time series from more than 0.25 million training pixels across the conterminous United States. A random cropping and masking strategy extracts 12-month periods with varying start dates across epochs, masks 50% of valid observations, and trains the model to reconstruct the masked reflectance values from the remaining observations. Evaluation using more than 62,000 independent test pixels shows robust reconstruction under diverse land surface conditions, including complex crop phenology and sparse, irregular observations. Leave-one-observation-out evaluation achieved reconstruction RMSE below 0.026 for all HLS spectral bands, with relative RMSE below 35% for visible bands and below 13% for other bands. Red-edge band errors were comparable to red and near-infrared errors despite the absence of red-edge bands on Landsat. Sensitivity analyses that randomly masked 10% to 90% of test observations showed only modest degradation when 10% to 50% of observations were masked, with all-band RMSE below 0.028. Image reconstruction over nine independent 109 by 109 km CONUS HLS tiles further demonstrates that HLS-GPT outperforms two conventional methods and the NASA-IBM Prithvi model.

Junjie Li, Hankui K. Zhang, David P. Roy

Geospatial Sciences Center of Excellence, Department of Geography and Geospatial Sciences, South Dakota State University, Brookings, SD 57007, USA · Department of Geography, Environment, and Spatial Sciences, & Center for Global Change and Earth Observations, Michigan State University, MI 48824, USA

Transformer Remote Sensing

Jun 16, 2026cs.LG

Functional Equivalence in Attention: A Comprehensive Study with Applications to Linear Mode Connectivity

Neural network parameter spaces are inherently non-injective, as distinct parameter configurations can realize identical functions through functional equivalence. While this symmetry is well understood in classical fully connected and convolutional models, it becomes substantially more intricate in modern attention-based architectures. Existing analyses of multihead attention have largely focused on the vanilla formulation, overlooking positional encodings that fundamentally reshape architectural symmetries. In this work, we provide a formal study of functional equivalence in Transformers with positional encodings. Focusing on the two most widely used variants--sinusoidal and rotary positional encodings (RoPE)--we show that sinusoidal encodings preserve the equivalence structure of vanilla attention, whereas rotary encodings significantly reduce the symmetry group, thereby enhancing expressivity. This offers a principled explanation for the growing prominence of RoPE in practice. We further examine how positional encodings affect linear mode connectivity, and through an alignment algorithm, empirically demonstrate that the presence and variability of connectivity across Transformer settings crucially depend on the positional encoding.

Viet-Hoang Tran, Vinh Khanh Bui, Van-Hoan Trinh +2

National University of Singapore · Center for AI Research, VinUniversity · Technical University of Munich +1

Rotary Positional Embeddings Transformer Positional Encoding Multi-Head Attention

Jun 16, 2026cs.CR

TIGER: Inverting Transformer Gradients via Embedding-Subspace Distance Optimization

Federated learning allows multiple clients to jointly train a shared model by sending gradient updates to a central server while keeping raw inputs local. However, prior gradient inversion attacks show that these updates can reveal enough information to reconstruct client inputs. Existing attacks on transformers either optimize dummy inputs to match the true client updates, which is costly and unstable for modern models, or exploit the low rank of attention gradients to identify a subspace containing the true layer embeddings, followed by a discrete membership test for candidate tokens. However, this token test is brittle under numerical noise, i.e., from quantization or Differential Privacy (DP), and scales poorly for encoder models with non-causal attention. We introduce TIGER, a continuous gradient inversion attack that turns this subspace signal into a differentiable objective. Instead of searching over tokens or matching full gradients, TIGER directly optimizes token embeddings to minimize their distance to the subspace. Our experiments demonstrate that on encoder-only models, TIGER substantially improves both reconstruction quality and runtime over existing attacks, while on decoder models, TIGER is more robust than prior subspace-based attacks, enabling the first successful reconstructions in DP-defended federated learning settings.

William Kalikman, Ivo Petrov, Dimitar I. Dimitrov +1

ETH Zürich · INSAIT, Sofia University "St. Kliment Ohridski"

Gradient Inversion Attacks Transformer Adversarial Attacks Model Inversion Attacks Federated Learning

Jun 15, 2026cs.LG

Taming Curvature: Architecture Warm-Up for Stable Transformer Training

Training billion-parameter Transformers is often brittle, with transient loss spikes and divergence that waste compute. Even though the recently developed Edge of Stability (EoS) theory provides a powerful tool to understand and control the stability of optimization methods via the (preconditioned) curvature, these curvature-controlling methods are not popular in large-scale Transformer training due to the complexity of curvature estimation. To this end, we first introduce a fast online estimator of the largest (preconditioned) Hessian eigenvalue (i.e., curvature) based on a warm-started variant for power iteration with Hessian-vector products. We show theoretically, and verify empirically, that the proposed method makes per-iteration curvature tracking feasible at billion parameter scale while being more accurate. Using this tool, we find that training instabilities coincide with surges in preconditioned curvature and that curvature grows with depth. Motivated by these observations, we propose architecture warm-up: progressively growing network depth to carefully control the preconditioned Hessian and stabilize training. Experiments on large Transformers validate that our approach enables efficient curvature tracking and reduces instabilities compared to existing state-of-the-art stabilization techniques without slowing down convergence.

Sameera Ramasinghe, Ajanthan Thalaiyasingam, Hadi Mohaghegh Dolatabadi +6

Pluralis Research

Edge of Stability Transformer Second-Order Optimization Neural Network Training Dynamics

Jun 15, 2026stat.ML

Attention is Just Another Name for Coupling? A Fast-Slow ODE Perspective on Hierarchical Pretraining

We re-interpret Transformer pretraining as a fast-slow, singularly perturbed flow along depth, with untied weights as its non-autonomous feature. The linearised dynamics is a depth-ordered product of layer maps. Along a token-homogeneous reference trajectory, the linearised layer factorises along the eigenbasis of a frozen attention kernel. Past a computable saturation depth, the flow factors through the block coarse-graining -- in other words, running the layers is running the coarse variable, dually. Weight perturbations supported on the decaying bundle move neither the persistent component of the distinguished trajectory nor the frozen kernel to first order, so the framework partitions parameter space into visible and invisible directions, with the cross-block coupling of the slow path sitting entirely on the visible side. How large a gate the slow path can carry is bounded by a stability margin. On the data side: if block emissions follow an exponential family, block-mean pooling captures all the information the slow path can use; but if neighbouring blocks carry no shared structure, no cross-block channel can help the prediction, and the gate amplitude is invisible in the prediction risk. Stability delimits what the architecture may do; the data decides what it will.

Zhengyuan Gao

Independent scholar

Dynamical Systems Transformer

Jun 15, 2026eess.AS

CraBERT: Efficient Phoneme Encoder Pre-Training via Cascade Fusion of Subword Representations for Text-to-Speech

This paper introduces CraBERT, a pre-trained phoneme encoder (PPEnc) designed for efficient pre-training in text-to-speech (TTS). CraBERT employs a cascade-fusion architecture and a subword-phoneme alignment algorithm to integrate representations from a pre-trained subword-level BERT into a phoneme-level BERT. This design provides prior word- and sentence-level information, reducing the amount of pre-training required by the phoneme encoder. Subjective listening evaluations show that CraBERT achieves MOS values comparable to existing PPEncs after approximately one epoch of pre-training, whereas the baselines in our comparison are pre-trained for approximately ten epochs. These results demonstrate that CraBERT can efficiently learn representations suitable for improving the perceived naturalness and prosody of synthesized speech.

Dong Yang, Yuki Saito, Wataru Nakata +1

The University of Tokyo, Japan

Language Model Pretraining Representation Learning TTS Synthesis Transformer Representation Alignment

Jun 15, 2026cs.AR

NeuronFabric: A Software Reference Architecture for On-Chip Transformer Training with Local Adam

Publicly documented accelerator architectures generally separate training computation from optimizer-state updates or rely on external memory and host orchestration. This paper presents NeuronFabric, a software reference architecture intended for future FPGA and ASIC implementations of transformer training with local Adam updates. A complete C# prototype implements forward pass, backpropagation, and Adam optimization without external machine-learning frameworks. The goal is to validate numerical correctness and memory requirements before hardware implementation. The evaluated model is a 334K-parameter autoregressive transformer (d=88, H=4, f=264, L=4, vocab=256) trained on the Shakespeare corpus. The BF16W configuration achieves evaluation loss 1.5426 after 80K samples, compared with 1.5224 for an FP32 GPU reference, while producing coherent character-level text. The paper introduces BF16W, which stores weights in BF16 while retaining Adam optimizer moments in FP32. This reduces memory requirements for on-chip training. A 334K-parameter FP32 model with Adam moments requires approximately 4.0 MB, matching the BRAM capacity of a Xilinx ZCU102 device. The BF16W variant requires approximately 3.34 MB, leaving memory available for activation storage. We describe the vocabulary-budget constraint observed during earlier experiments, quantify BF16W memory savings, and outline FPGA training as the next stage of development. No FPGA measurements are included in this paper. This publication serves as a public architectural disclosure and software reference implementation for future FPGA and ASIC exploration of the NeuronFabric architecture.

Evgeny Ukladchikov

Independent Researcher

Deep Learning Optimization Transformer FPGA-Based Neural Network Acceleration

Jun 15, 2026cs.LG

Scaling Adaptive Depth with Norm-Agnostic Residual Networks

Residual architectures are ubiquitous in deep learning, but they suffer from a subtle structural limitation: the norm of the residual stream can grow rapidly with depth. As a result, updates from later layers become small relative to the accumulated residual state. This reduces their impact on the representation and limits the benefits of scaling models in depth. To address this, we introduce NAG, a norm-agnostic residual architecture that separates magnitude from directional information in the residual stream, preserving meaningful layer contributions throughout depth and preventing later updates from being systematically suppressed by residual-norm growth. Importantly, NAG introduces only a negligible number of additional parameters and relies on simple operations that are easily kernel-fusible, preserving training efficiency in practice. We show that this architecture outperforms baseline Transformers, with gains that increase substantially as depth grows, enabling effective training of much deeper models. The norm-agnostic formulation also leads to an interpretable Mixture-of-Depths (MoD) mechanism that adaptively skips both attention and MLP layers. Beyond serving as a post-training accuracy-compute tradeoff, this mechanism can be used as a pretraining-time scaling strategy: under iso-FLOP training, compute saved by reducing per-token forward-pass cost can be reinvested into training on more tokens while keeping the total parameter count and KV-cache budget fixed. In our experiments, moderate Mixture-of-Depths rates of approximately 20%-25% match full-depth baseline performance under equal training compute while substantially reducing the number of executed layer parameters and forward-pass FLOPs. These results identify sparsity in depth as a new scaling axis for fixed-compute training, enabling very deep yet FLOP-efficient models.

Tomás Figliolia, Beren Millidge

Zyphra San Francisco, CA

Efficient Neural Network Inference Dynamic Neural Networks Transformer Residual Learning

Jun 14, 2026cs.LG

David vs. Goliath in Next Activity Prediction: Argmax vs. LSTM, Transformer, and LLM

Next activity prediction (NAP) is a cornerstone of predictive process monitoring (PPM), enabling organizations to move from retrospective analysis to proactive process steering. The PPM field has progressed from classical machine learning through deep learning architectures such as LSTMs and Transformers to large language models (LLMs). Despite growing model complexity, no benchmark jointly compares LLMs, Transformers, LSTMs, and simple baselines in a direct sequence modeling setting for NAP. In this paper, we fill this gap with a systematic benchmark. We compare vocabulary-adapted LLMs, Transformers trained from scratch, LLM-distilled Transformers, and LSTMs against a simple counting-based argmax baseline across seven real-life event logs. Our results tell a David vs. Goliath story: pretraining confers no consistent improvement over training from scratch, model size shows little effect on performance, and on most datasets the argmax baseline matches or approaches the performance of billion-parameter LLMs.

Hans Weytjens, Ingo Weber

Technical University of Munich, School of CIT, Germany · Fraunhofer Gesellschaft, Munich, Germany

LLM Evaluation Predictive Process Monitoring Transformer Next-Action Prediction Long Short-Term Memory Networks

Jun 13, 2026cs.LG

Transformers Learn the Mestre-Nagao Heuristic

We train a two-layer transformer encoder to classify rational elliptic curves

E/\mathbb{Q}

of conductor

\leq 10000

as either rank 0 or rank 1 from the first 128 normalized Frobenius traces. We achieve >99% accuracy on both classes, and accuracy is essentially unchanged on test curves with no isogeny or quadratic-twist relative in the training set. We then apply techniques from mechanistic interpretability such as attention analysis, linear probing, activation patching, logit attribution, and neuron-level circuit analysis to reverse-engineer the algorithm the (centroid in function space) model learned. We find that a sparse circuit of 20 out of 512 layer-1 MLP neurons is sufficient for rank prediction under a linear probe with an AUROC of 0.992 at plateau, implementing a push-pull detector architecture of rank-0 and rank-1 detectors with a one-sided readout. However, we notice that the model has sub-optimal readout problems indicating a mismatch in rank-order between the readout pathway and the discriminative circuit. Critically, the learned input weights of the top discriminating neuron match the Mestre-Nagao sum heuristic weights

\log(p)/(p\cdot \log{B})

with a Spearman coefficient

r = 0.997

and Pearson coefficient

r = 0.952

: the model has learnt a result from analytic number theory from the Frobenius trace data alone. We additionally find that all 50 independently trained models concentrate CLS attention on prime positions at 2-50

\times

the rate of composite positions. The CLS embedding encodes

\log{L(E,1)}

with

R^2 = 0.962\pm 0.011

across the 50 models (after controlling for the conductor). Activation patching analysis reveals that attention weights are dissociated from causal information flow. Additionally, the 50 solutions from training are near-identical in function space (with pairwise agreement

>

98.8%) despite large weight space barriers.

Pranav Venkata Konda

Transformer Interpretability Transformer Classification

Jun 12, 2026cs.CL

Simplifying the Modeling of Arbitrary Conditionals in Natural Language

Causal Transformers model sequences through an autoregressive factorization of the joint distribution, which enables efficient left-to-right decoding and conditional likelihood computation. However, they cannot tractably sample from or evaluate arbitrary conditionals -- e.g., a block of text conditioned on past and future tokens. Recent work aims to solve this problem through novel architectures, but they often lead to sub-optimal modeling of such conditionals and degraded generations. We propose Arbitrary Conditionals GPT (AC-GPT) which introduces a simple modification to standard causal Transformers to enable evaluating and sampling from arbitrary conditionals -- including past, future, and mixed contexts -- within a single forward pass. Unlike prior approaches, our method preserves the standard left-to-right ordering and next-token prediction objective essential for both strong performance and efficient training on natural language. Crucially, this compatibility allows existing LLMs to be fine-tuned for arbitrary conditioning. Our empirical results indicate that our method outperforms baselines on modeling arbitrary conditionals, without degrading standard left-to-right performance.

Yinhan Lu, Eric Elmoznino, Léo Gagnon +3

Mila — Quebec AI Institute · McGill University · Université de Montréal

Transformer Autoregressive Language Modeling Language Modeling Conditional Generative Modeling

Jun 12, 2026cs.LG

How Linear Is a Transformer Feed-Forward Block? Per-Block Linear Recoverability Is Learned, Not Architectural

Transformer feed-forward networks (FFNs) are often treated as nonlinear stores of computation, yet how nonlinear a trained FFN block actually is has rarely been measured. We treat each FFN as a position-wise input-to-output map and split it into the exact least-squares linear approximation plus a residual. The held-out variance the closed-form linear map explains defines a block's linear recoverability (R^2_lin), an optimiser-free measure of its linearity. Across all twelve blocks of GPT-2, Pythia-160m, and llama-160m, R^2_lin is highly heterogeneous and non-monotone with depth, ranging from near-linear (>0.99) to strongly nonlinear (<0.3) between adjacent blocks, and is not set by the activation function: same-width GELU models GPT-2 and Pythia-160m have sharply different profiles, so recoverability is a learned property of individual trained blocks, not an architectural one. A low-rank bilinear probe of the residual recovers only a few points of R^2, with gain uncorrelated with residual nonlinearity: the unrecovered computation is not a single position-wise product but higher-order or distributed structure. The measurement also serves as a targeted compression signal: recoverable blocks admit large single-layer replacements (GPT-2's early FFN at 8x fewer parameters for +0.77 perplexity), while low-recoverability blocks flag where this is unsafe. It further exposes a methodological pitfall: trained linear baselines can badly under-converge on ill-conditioned transformer activations, so we report the exact closed-form least-squares ceiling throughout.

Stuart Whipp

Independent Research

Transformer FFNs Transformer Expressivity Transformer Feedforward Neural Networks

Jun 12, 2026cs.CV

HiST: A Hierarchical Sparse Transformer for Cross-Modal Spatial Transcriptomics Modeling

Spatial transcriptomics (ST) links gene expression with tissue morphology but remains expensive and low-throughput, motivating surrogates that infer expression from routine histology. Whole-slide H&E-to-ST inference pairs a gigapixel image with gene measurements at a sparse, irregular set of locations, making multiscale modeling challenging without incurring dense-grid overhead or quadratic token mixing. We propose HiST, a hierarchical sparse transformer that treats measured locations as a lattice-indexed sparse field and builds a dyadic encoder--decoder directly on the active tissue footprint. HiST combines sparse window attention for local geometric correspondence with resolution-changing operators for rapid multiscale context integration. For a fixed window size, the dominant runtime and memory scale with the number of observed locations rather than the dense slide area. To mitigate slide-specific acquisition variation, HiST adds a bottlenecked global conditioning pathway via a \emph{slide calibration token} that summarizes slide-level context and conditions local representations. On a multi-organ benchmark spanning diverse tissues and acquisition sources, HiST improves predictive performance over recent baselines while reducing runtime and peak memory.

Weiyi Wu, Xinwen Xu, Xingjian Diao +4

Dartmouth College · Mass General Hospital · New Jersey Institute of Technology +1

Computational Pathology Spatial Transcriptomics Cross-Modal Representation Learning Transformer Hierarchical Representation Learning Spatial Gene Expression Prediction+1

Jun 10, 2026cs.CV

Illumination-Robust Camera-Based Heart-Rate Estimation for Physiological Sensing in Robots

Physiological awareness is important for service, social, and assistive robots that interact with humans in everyday environments. Remote photoplethysmography (rPPG) enables non-contact heart-rate (HR) estimation from an RGB camera, making it a promising sensing modality for robot-mounted vision systems. However, illumination variation remains a major barrier to robust deployment. This paper presents an end-to-end spatial-temporal transformer framework for remote HR estimation on a new dataset with varied illumination. Our estimator integrates PRNet-based 3D face alignment, clip-level illumination augmentation, the Residual Temporal Standardization Module, and controlled hybrid temporal-frequency supervision. The training objective combines a Soft-Shifted Pearson waveform loss with a spectral Kullback-Leibler divergence loss, where a tuned weight (

\mathbfβ

) controls the contribution of frequency-domain heart-rate guidance. Experiments on a static all-level mix protocol covering three illumination levels show that

\mathbfβ=5

provides the strongest result among the tested beta settings, achieving a best-run HR mean absolute error (MAE) of 0.79 bpm and an HR correlation of 0.982. Compared with the PhysFormer baseline evaluated on our dataset, our estimator reduces HR MAE by 93.6 %, while increasing HR correlation from 0.088 to 0.982, making it usable when illumination varies.

Zhi Wei Xu, Torbjörn E. M. Nordling

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan.

Remote Photoplethysmography Distribution Shift Robustness Transformer Heart Rate Estimation Photoplethysmography Robotic Perception

Jun 10, 2026cs.CV

Vision Transformers for Face Recognition Need More Registers

Recent advances in Vision Transformers (ViTs) for face recognition (FR) have moved beyond the standard CLS-token paradigm. In this paradigm, a special classification token (CLS) is prepended to the patch embeddings and used as a representation of the input for downstream tasks. An alternative approach, Concatenated Patch Embeddings (CPE), instead leverages all patch tokens by concatenating them into a single vector, which is then projected into a compact face representation. CPE has been shown to improve recognition performance in comparison to CLS-based ones, but our qualitative analysis of attention maps showed the presence of artifacts that limit their interpretability. To address this issue, we incorporate register tokens, learnable tokens concatenated to the initial patch embeddings, and processed jointly through the ViT encoder blocks. This mechanism has been shown to produce more structured and interpretable attention maps compared to baseline ViT. We empirically demonstrate that these artifacts consistently appear across various ViT backbones, including small and large models, and that introducing register tokens effectively mitigates them. Adding four or eight registers significantly enhances interpretability, with eight registers providing the highest verification accuracies and smoothest attention structures. Our resulting model, ViT-8R, corresponds to a CPE-based ViT-B architecture augmented with eight register tokens achieves state-of-the-art performance among ViT-based FR models on large-scale IJB-B and IJB-C benchmarks. Also, ViT-8R produces substantially clearer attention maps compared with the baseline model, which offer deeper insight into the model's attention behavior (https://github.com/TaharChettaoui/ViT-FR-Registers)

Tahar Chettaoui, Guray Ozgur, Eduarda Caldeira +2

Fraunhofer Institute for Computer Graphics Research IGD, Germany · Department of Computer Science, TU Darmstadt, Germany

Transformer Interpretability Transformer Vision Transformer Face Recognition