Transformer

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Overview

Transformers represent inputs as tokens and use self-attention to let each token draw on information from other positions, with feed-forward layers refining the resulting representations. Encoder-only models such as BERT, autoregressive decoder-only language models, and encoder-decoder systems are adapted for tasks ranging from text generation and image recognition to forecasting and scientific simulation. Current approaches improve efficiency and capability through local or sparse attention, retrieval and memory, hierarchical processing, and hybrids with convolutional or state-space layers; evaluation spans language-modeling, long-context, vision, and domain-specific benchmarks. A central tension is whether architectural changes and larger models deliver reliable gains in generalization and reasoning while controlling training and inference cost, and theory and interpretability work continues to probe how Transformers learn and compute.

Latest papers

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544 papers70 papers in the last four weeks, up 71% on the four weeks before. 0.4% of all new papers.

Mar 18, 2026

Beyond Muon: MUD (MomentUm Decorrelation) for Faster Transformer Training

Orthogonalized-momentum optimizers such as Muon improve transformer training by approximately whitening/orthogonalizing matrix-valued momentum updates via a short polar-decomposition iteration. However, polar-factor approximations typically require multiple large matrix multiplications, and the resulting overhead can be substantial and hardware-dependent. We introduce MUD (MomentUm Decorrelation), a complementary whitening approach that replaces Muon's polar update with a triangular (Cholesky-like) whitening surrogate inspired by classical Gram--Schmidt and Gauss-Seidel ideas. We show that row-orthonormal matrices are fixed points of the MUD map, relate the inner step to symmetric Gauss-Seidel preconditioning of the Gram matrix, and prove quadratic local convergence near the fixed point. In terms of time-to-perplexity, MUD yields consistent 10-50% wall-clock improvements over tuned AdamW and Muon in time-to-perplexity, typically converging slightly slower per step than Muon but with substantially lower optimizer overhead -- relative to Muon, MUD improves peak tokens/s by roughly 1.3−2.6×1.3-2.6\times across most settings and up to nearly 3×3\times on GPT-2 large on an A100. We also demonstrate training a ESM-2 150M protein language model, where MUD matches Muon-level validation perplexity in significantly less wall-clock time.

Ben S. Southworth, Stephen Thomas

Theoretical Division, Los Alamos National Laboratory, USA. · Lehigh University, Computer Science

Deep Learning OptimizationMuon OptimizerTransformer
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Mar 18, 2026

The Phasor Transformer: Resolving Attention Bottlenecks on the Unit Circle

Transformer models have redefined sequence learning, yet dot-product self-attention introduces a quadratic token-mixing bottleneck for long-context time-series. We introduce the Phasor Transformer block, a phase-native alternative representing sequence states on the unit-circle manifold S1S^1. Each block combines lightweight trainable phase-shifts with parameter-free Discrete Fourier Transform (DFT) token coupling, achieving global O(Nlog⁡N)\mathcal{O}(N\log N) mixing without explicit attention maps. Stacking these blocks defines the Large Phasor Model (LPM). We validate LPM on autoregressive time-series prediction over synthetic multi-frequency benchmarks against honest baselines: it beats a zero-parameter persistence baseline and, with the corrected gradient path, improves monotonically with depth before saturating, while remaining competitive-but-not-superior to self-attention at a fraction of the parameter count. Our results establish an explicit efficiency--accuracy frontier, showing that scalable temporal modeling in oscillatory domains can emerge from geometry-constrained phase computation with deterministic global coupling.

Dibakar Sigdel

Mindverse Computing LLC, WA 98087

TransformerTime Series ForecastingTime Series Transformers
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Mar 17, 2026

Transformers are Bayesian Networks

Transformers are the dominant architecture in AI, yet why they work remains poorly understood. This paper offers a precise answer: a transformer is a Bayesian network. We establish this in five ways. First, we prove that every sigmoid transformer with any weights implements weighted loopy belief propagation on its implicit factor graph. One layer is one round of BP. This holds for any weights -- trained, random, or constructed. Formally verified against standard mathematical axioms. Second, we give a constructive proof that a transformer can implement exact belief propagation on any declared knowledge base. On knowledge bases without circular dependencies this yields provably correct probability estimates at every node. Formally verified against standard mathematical axioms. Third, we prove uniqueness: a sigmoid transformer that produces exact posteriors necessarily has BP weights. There is no other path through the sigmoid architecture to exact posteriors. Formally verified against standard mathematical axioms. Fourth, we delineate the AND/OR boolean structure of the transformer layer: attention is AND, the FFN is OR, and their strict alternation is Pearl's gather/update algorithm exactly. Fifth, we confirm all formal results experimentally, corroborating the Bayesian network characterization in practice. We also establish the practical viability of loopy belief propagation despite the current lack of a theoretical convergence guarantee. We further prove that verifiable inference requires a finite concept space. Any finite verification procedure can distinguish at most finitely many concepts. Without grounding, correctness is not defined. Hallucination is not a bug that scaling can fix. It is the structural consequence of operating without concepts. Formally verified against standard mathematical axioms.

Gregory Coppola

Belief PropagationTransformerBayesian NetworksTransformer Interpretability
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Mar 17, 2026

Transformers Can Learn Rules They've Never Seen: Proof of Computation Beyond Interpolation

A central question in the debate over large language models is whether transformers can learn rules they have never seen, or whether they can only interpolate: predict new cases from their similarity to training examples. We test this in a controlled setting where interpolation provably fails, so success can only come from computation beyond interpolation. We train small transformers to predict the rollout of a cellular automaton whose update rule is pure XOR, and remove one entry of the rule's truth table from all direct supervision. The missing entry's output is never shown to the model; its only trace is indirect, as wrong values corrupt visible predictions at later timesteps. Because XOR parity flips whenever one input bit is changed, every one-bit neighbour of the missing entry carries the opposite label, and we prove that similarity-based predictors, including nearest-neighbour, kernel, and Gaussian-process methods, are forced to the wrong answer. A two-layer transformer can nevertheless recover the missing entry, and circuit extraction confirms it computes XOR exactly. Ablations show the recovery depends on gradient signal propagating through multi-step prediction, and a second, structurally unrelated benchmark on symbolic operator chains exhibits the same capacity under ordinary autoregressive training. Together with a constructive proof that a standard transformer block can implement exact local Boolean rules, these results provide an existence proof that transformers can learn rule structure not directly observed in training and express it explicitly. This rules out the strongest architectural form of the interpolation-only account, the claim that transformers cannot in principle discover and communicate unseen rules, while leaving open when such behaviour arises in large-scale language training.

Andy Gray

Kortical

TransformerNeural Network GeneralizationTransformer Expressivity
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Mar 17, 2026

Long-Horizon Traffic Forecasting via Incident-Aware Conformal Spatio-Temporal Transformers

Reliable multi-horizon traffic forecasting is challenging because network conditions are stochastic, incident disruptions are intermittent, and effective spatial dependencies vary across time-of-day patterns. This study is conducted on the Ohio Department of Transportation (ODOT) traffic count data and corresponding ODOT crash records. This work utilizes a Spatio-Temporal Transformer (STT) model with Adaptive Conformal Prediction (ACP) to produce multi-horizon forecasts with calibrated uncertainty. We propose a piecewise Coefficient of Variation (CV) strategy that models hour-to-hour traveltime variability using a log-normal distribution, enabling the construction of a per-hour dynamic adjacency matrix. We further perturb edge weights using incident-related severity signals derived from the ODOT crash dataset that comprises incident clearance time, weather conditions, speed violations, work zones, and roadway functional class, to capture localized disruptions and peak/off-peak transitions. This dynamic graph construction replaces a fixed-CV assumption and better represents changing traffic conditions within the forecast window. For validation, we generate extended trips via multi-hour loop runs on the Columbus, Ohio, network in SUMO simulations and apply a Monte Carlo simulation to obtain travel-time distributions for a Vehicle Under Test (VUT). Experiments demonstrate improved long-horizon accuracy and well-calibrated prediction intervals compared to other baseline methods.

Mayur Patil, Qadeer Ahmed, Shawn Midlam-Mohler +4

Department of Mechanical and Aerospace Engineering and the Center for Automotive Research, The Ohio State University · Ohio Department of Transportation · Honda Research Institute USA, Inc.

Spatiotemporal TransformersTraffic ForecastingTransformer
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Mar 17, 2026

Diverging Transformer Predictions for Human Sentence Processing: A Comprehensive Analysis of Agreement Attraction Effects

Transformers underlie almost all state-of-the-art language models in computational linguistics, yet their cognitive adequacy as models of human sentence processing remains disputed. In this work, we use a surprisal-based linking mechanism to systematically evaluate eleven autoregressive transformers of varying sizes and architectures on a more comprehensive set of English agreement attraction configurations than prior work. Our experiments yield mixed results: While transformer predictions generally align with human reading time data for prepositional phrase configurations, performance degrades significantly on object-extracted relative clause configurations. In the latter case, predictions also diverge markedly across models, and no model successfully replicates the asymmetric interference patterns observed in humans. We conclude that current transformer models do not explain human morphosyntactic processing, and that evaluations of transformers as cognitive models must adopt rigorous, comprehensive experimental designs to avoid spurious generalizations from isolated syntactic configurations or individual models.

Titus von der Malsburg, Sebastian Padó

University of Stuttgart, Germany

TransformerCognitive Modeling
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Mar 17, 2026

ASCENT: Transformer-Based Aircraft Trajectory Prediction in Non-Towered Terminal Airspace

Accurate trajectory prediction can improve General Aviation safety in non-towered terminal airspace, where high traffic density increases accident risk. We present ASCENT, a lightweight transformer-based model for multi-modal 3D aircraft trajectory forecasting, which integrates domain-aware 3D coordinate normalization and parameterized predictions. ASCENT employs a transformer-based motion encoder and a query-based decoder, enabling the generation of diverse maneuver hypotheses with low latency. Experiments on the TrajAir and TartanAviation datasets demonstrate that our model outperforms prior baselines, as the encoder effectively captures motion dynamics and the decoder aligns with structured aircraft traffic patterns. Furthermore, ablation studies confirm the contributions of the decoder design, coordinate-frame modeling, and parameterized outputs. These results establish ASCENT as an effective approach for real-time aircraft trajectory prediction in non-towered terminal airspace.

Alexander Prutsch, David Schinagl, Horst Possegger

Institute of Visual Computing, Graz University of Technology, Austria

Trajectory PredictionMultimodal Trajectory PredictionAir Traffic ManagementTransformer
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Mar 17, 2026

SignNav: Leveraging Signage for Semantic Visual Navigation in Large-Scale Indoor Environments

Humans routinely leverage semantic hints provided by signage to navigate to destinations within novel Large-Scale Indoor (LSI) environments, such as hospitals and airport terminals. However, this capability remains underexplored within the field of embodied navigation. This paper introduces a novel embodied navigation task, SignNav, which requires the agent to interpret semantic hint from signage and reason about the subsequent action based on current observation. To facilitate research in this domain, we construct the LSI-Dataset for the training and evaluation of various SignNav agents. Dynamically changing semantic hints and sparse placement of signage in LSI environments present significant challenges to the SignNav task. To address these challenges, we propose the Spatial-Temporal Aware Transformer (START) model for end-to-end decision-making. The spatial-aware module grounds the semantic hint of signage into physical world, while the temporal-aware module captures long-range dependencies between historical states and current observation. Leveraging a two-stage training strategy with Dataset Aggregation (DAgger), our approach achieves state-of-the-art performance, recording an 80% Success Rate (SR) and 0.74 NDTW on val-unseen split. Real-world deployment further demonstrates the practicality of our method in physical environment without pre-built map.

Jian Sun, Yuming Huang, He Li +6

Faculty of Science and Technology, University of Macau · Department of Robotics, University of Michigan

Spatiotemporal TransformersVisual NavigationEmbodied NavigationTransformer
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Mar 17, 2026

Residual Stream Duality in Modern Transformer Architectures

Recent work has made clear that the residual pathway is not mere optimization plumbing; it is part of the model's representational machinery. We agree, but argue that the cleanest way to organize this design space is through a two-axis view of the Transformer. A decoder evolves information along two ordered dimensions: sequence position and layer depth. Self-attention already provides adaptive mixing along the sequence axis, whereas the residual stream usually performs fixed addition along the depth axis. If we fix a token position and treat layer index as the ordered variable, then a causal depth-wise residual attention read is exactly the same local operator as causal short sliding-window attention (ShortSWA), except written over depth rather than over sequence. This is the core residual stream duality behind Transformer2^2. This perspective also clarifies the recent literature. ELC-BERT and DenseFormer already show that learned aggregation over depth can outperform uniform residual accumulation, while Vertical Attention, DeepCrossAttention (DCA), MUDDFormer, and Attention Residuals move further toward explicit attention-based routing over earlier layers. The key point, however, is that operator-level duality does not imply systems-level symmetry. For large-scale autoregressive models, sequence-axis ShortSWA is usually the more hardware-friendly placement because it reuses token-side sliding-window kernels, KV-cache layouts, and chunked execution. If the goal is instead to change the shortcut itself, Deep Delta Learning (DDL) is the cleaner intervention because it modifies the residual operator directly rather than adding a separate cross-layer retrieval path. Our recommendation is therefore simple: use DDL when the shortcut is the object of interest, and use sequence-axis ShortSWA when the goal is local adaptive mixing.

Yifan Zhang

TransformerAttention MechanismsAttention Residual Connections
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Mar 16, 2026

A Family of LLMs Liberated from Static Vocabularies

Tokenization is a central component of natural language processing in current large language models (LLMs), enabling models to convert raw text into processable units. Although learned tokenizers are widely adopted, they exhibit notable limitations, including their large, fixed vocabulary sizes and poor adaptability to new domains or languages. We present a family of models with up to 70 billion parameters based on the hierarchical autoregressive transformer (HAT) architecture. In HAT, an encoder transformer aggregates bytes into word embeddings and then feeds them to the backbone, a classical autoregressive transformer. The outputs of the backbone are then cross-attended by the decoder and converted back into bytes. We show that we can reuse available pre-trained models by converting the Llama 3.1 8B and 70B models into the HAT architecture: Llama-3.1-8B-TFree-HAT and Llama-3.1-70B-TFree-HAT are byte-level models whose encoder and decoder are trained from scratch, but where we adapt the pre-trained Llama backbone, i.e., the transformer blocks with the embedding matrix and head removed, to handle word embeddings instead of the original tokens. We also provide a 7B HAT model, Llama-TFree-HAT-Pretrained, trained entirely from scratch on nearly 4 trillion words. The HAT architecture improves text compression by reducing the number of required sequence positions and enhances robustness to intra-word variations, e.g., spelling differences. Through pre-training, as well as subsequent supervised fine-tuning and direct preference optimization in English and German, we show strong proficiency in both languages, improving on the original Llama 3.1 in most benchmarks. We release our models (including 200 pre-training checkpoints) on Hugging Face.

Aleph Alpha, :, Adnen Abdessaied +35

Aleph Alpha Research

Language ModelingByte-Level Language ModelTokenization in Language ModelsAutoregressive Language ModelingTransformerLanguage Model Pretraining
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Mar 16, 2026

Learning to Recall with Transformers Beyond Orthogonal Embeddings

Modern large language models (LLMs) excel at tasks that require storing and retrieving knowledge, such as factual recall and question answering. Transformers are central to this capability because they can encode information during training and retrieve it at inference. Existing theoretical analyses typically study transformers under idealized assumptions such as infinite data or orthogonal embeddings. In realistic settings, however, models are trained on finite datasets with non-orthogonal (random) embeddings. We address this gap by analyzing a single-layer transformer with random embeddings trained with (empirical) gradient descent on a simple token-retrieval task, where the model must identify an informative token within a length-LL sequence and learn a one-to-one mapping from tokens to labels. Our analysis tracks the ``early phase'' of gradient descent and yields explicit formulas for the model's storage capacity -- revealing a multiplicative dependence between sample size NN, embedding dimension dd, and sequence length LL. We validate these scalings numerically and further complement them with a lower bound for the underlying statistical problem, demonstrating that this multiplicative scaling is intrinsic under non-orthogonal embeddings.

Nuri Mert Vural, Alberto Bietti, Mahdi Soltanolkotabi +1

University of Toronto and Vector Institute · Flatiron Institute · University of Southern California +1

TransformerMemorization in Language ModelsRepresentation Geometry in Language Models
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Mar 16, 2026

Towards Foundation Models for Consensus Rank Aggregation

Aggregating a consensus ranking from multiple input rankings is a fundamental problem with applications in recommendation systems, search engines, job recruitment, and elections. Despite decades of research in consensus ranking aggregation, minimizing the Kemeny distance remains computationally intractable. Specifically, determining an optimal aggregation of rankings with respect to the Kemeny distance is an NP-hard problem, limiting its practical application to relatively small-scale instances. We propose the Kemeny Transformer, a novel Transformer-based algorithm trained via reinforcement learning to efficiently approximate the Kemeny optimal ranking. Experimental results demonstrate that our model outperforms classical majority-heuristic and Markov-chain approaches, achieving substantially faster inference than integer linear programming solvers. Our approach thus offers a practical, scalable alternative for real-world ranking-aggregation tasks.

Yijun Jin, Simon Klüttermann, Chiara Balestra +1

TU Dortmund University, Dortmund, Germany · Research Center Trustworthy Data Science and Security, University Alliance Ruhr, Dortmund, Germany

Rank AggregationTransformer
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Mar 16, 2026

Directional Routing in Transformers

We introduce directional routing, a lightweight mechanism that gives each transformer attention head learned suppression directions controlled by a shared router, at 3.9% parameter cost. We train a 433M-parameter model alongside an identical baseline in a single run, then trace the resulting circuits through mechanistic interpretability. Routing becomes the model's dominant computational pathway. Disabling it collapses factual recall to near-zero probability across all 8 test prompts and drops induction accuracy from 93.4% to 0.0%. Knocking out individual attention heads has negligible effect: the primary mover head's removal actually increases target probability, and induction heads retain 98.6% accuracy without their strongest member. The coordination mechanism is irreplaceable; the components it coordinates are not. The model also self-organizes, without explicit pressure, into two regimes: domain-adaptive routing in early layers and fixed syntactic pruning in late layers, where the least-varying layer is the most critical (+42.6 PPL when disabled). Routing reduces perplexity 31-56% relative to the baseline, though downstream multiple-choice benchmarks do not yet reflect these gains.

Kevin Taylor

Attention RoutingTransformerLLM RoutingTransformer Attention
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Mar 16, 2026

Ablate and Rescue: A Causal Analysis of Residual Stream Hyper-Connections

Multi-stream transformer architectures have recently been proposed as a promising direction for managing representation collapse and the vanishing gradient problem for residual connections, yet their internal mechanisms remain unexplored. In particular, the recently introduced Manifold-Constrained Hyper-Connections (mHC) architecture posits multiple residual streams with constrained interaction, but lacks in-depth mechanistic analysis. We present the first open-source mHC language model (https://huggingface.co/wgpeng/mhc-780m) and analyze the multiple-stream architecture with a suite of representation-level metrics and causal interventions to probe how parallel streams encode and utilize information. Specifically, we introduce a systematic stream ablation-and-rescue framework that enables direct causal comparison of residual streams during inference. Through targeted pairwise interventions and controlled recovery experiments, we distinguish functional redundancy from asymmetric utilization and reveal how information is distributed across streams beyond what is observable from representational similarity alone.

William Peng, Josheev Rai, Kevin Tseng +2

Stanford University · Georgia Institute of Technology · University of California, Berkeley +2

TransformerHyper-ConnectionsResidual LearningTransformer InterpretabilityCausal Interventions in Language Models
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Mar 15, 2026

End-to-End Spatial-Temporal Transformer for Real-time 4D HOI Reconstruction

Monocular 4D human-object interaction (HOI) reconstruction - recovering a moving human and a manipulated object from a single RGB video - remains challenging due to depth ambiguity and frequent occlusions. Existing methods often rely on multi-stage pipelines or iterative optimization, leading to high inference latency, failing to meet real-time requirements, and susceptibility to error accumulation. To address these limitations, we propose THO, an end-to-end Spatial-Temporal Transformer that predicts human motion and coordinated object motion in a forward fashion from the given video and 3D template. THO achieves this by leveraging spatial-temporal HOI tuple priors. Spatial priors exploit contact-region proximity to infer occluded object features from human cues, while temporal priors capture cross-frame kinematic correlations to refine object representations and enforce physical coherence. Extensive experiments demonstrate that THO operates at an inference speed of 31.5 FPS on a single RTX 4090 GPU, achieving a >600x speedup over prior optimization-based methods while simultaneously improving reconstruction accuracy and temporal consistency. The project page is available at: https://nianheng.github.io/THO-project/

Haoyu Zhang, Wei Zhai, Yuhang Yang +2

University of Science and Technology of China

Spatiotemporal Transformers4D Reconstruction3D Human ReconstructionTransformer
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Mar 14, 2026

Enhancing Mental Health Classification with Layer-Attentive Residuals and Contrastive Feature Learning

The classification of mental health is challenging for a variety of reasons. For one, there is overlap between the mental health issues. In addition, the signs of mental health issues depend on the context of the situation, making classification difficult. Although fine-tuning transformers has improved the performance for mental health classification, standard cross-entropy training tends to create entangled feature spaces and fails to utilize all the information the transformers contain. We present a new framework that focuses on representations to improve mental health classification. This is done using two methods. First, layer-attentive residual aggregation which works on residual connections to to weigh and fuse representations from all transformer layers while maintaining high-level semantics. Second, supervised contrastive feature learning uses temperature-scaled supervised contrastive learning with progressive weighting to increase the geometric margin between confusable mental health problems and decrease class overlap by restructuring the feature space. With a score of 74.36%, the proposed method is the best performing on the SWMH benchmark and outperforms models that are domain-specialized, such as MentalBERT and MentalRoBERTa by margins of (3.25% - 2.2%) and 2.41 recall points over the highest achieving model. These findings show that domain-adaptive pretraining for mental health text classification can be surpassed by carefully designed representation geometry and layer-aware residual integration, which also provide enhanced interpretability through learnt layer importance.

Menna Elgabry, Ali Hamdi, Khaled Shaban

Department of Computer Science, Modern Sciences and Arts University, Cairo, Egypt. · Computer Science and Engineering Department, College of Engineering, Qatar University, Doha, Qatar.

Mental HealthTransformerSupervised Contrastive Learning
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Mar 14, 2026

MeTok: An Efficient Meteorological Tokenization with Hyper-Aligned Group Learning for Precipitation Nowcasting

Recently, Transformer-based architectures have advanced meteorological prediction. However, this position-centric tokenizer conflicts with the core principle of meteorological systems, where the weather phenomena undoubtedly involve synergistic interactions among multiple elements while positional information constitutes merely a component of the boundary conditions. This paper focuses primarily on the task of precipitation nowcasting and develops an efficient distribution-centric Meteorological Tokenization (MeTok) scheme, which spatially sequences to group similar meteorological features. Based on the rearrangement, realigned group learning enhances robustness across precipitation patterns, especially extreme ones. Specifically, we introduce the Hyper-Aligned Grouping Transformer (HyAGTransformer) with two key improvements: 1) The Grouping Attention (GA) mechanism uses MeTok to enable self-aligned learning of features from different precipitation patterns; 2) The Neighborhood Feed-Forward Network (N-FFN) integrates adjacent group features, aggregating contextual information to boost patch embedding discriminability. Experiments on the ERA5 dataset for 6-hour forecasts show our method improves the IoU metric by at least 8.2% in extreme precipitation prediction compared to other methods. Additionally, it gains performance with more training data and increased parameters, demonstrating scalability, stability, and superiority over traditional methods.

Qizhao Jin, Xianhuang Xu, Yong Cao +2

School of Artificial Intelligence, University of Chinese Academy of Sciences · China Meteorological Administration, National Meteorological Centre · State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation

Precipitation NowcastingTransformer
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Mar 13, 2026

GeoChemAD: Benchmarking Unsupervised Geochemical Anomaly Detection for Mineral Exploration

Geochemical anomaly detection plays a critical role in mineral exploration as deviations from regional geochemical baselines may indicate mineralization. Existing studies suffer from two key limitations: (1) single region scenarios which limit model generalizability; (2) proprietary datasets, which makes result reproduction unattainable. In this work, we introduce GeoChemAD, an open-source benchmark dataset compiled from government-led geological surveys, covering multiple regions, sampling sources, and target elements. The dataset comprises eight subsets representing diverse spatial scales and sampling conditions. To establish strong baselines, we reproduce and benchmark a range of unsupervised anomaly detection methods, including statistical models, generative and transformer-based approaches. Furthermore, we propose GeoChemFormer, a transformer-based framework that leverages self-supervised pretraining to learn target-element-aware geochemical representations for spatial samples. Extensive experiments demonstrate that GeoChemFormer consistently achieves superior and robust performance across all eight subsets, outperforming existing unsupervised methods in both anomaly detection accuracy and generalization capability. The proposed dataset and framework provide a foundation for reproducible research and future development in this direction.

Yihao Ding, Yiran Zhang, Chris Gonzalez +2

The University of Western Australia, Perth, WA, Australia

Unsupervised Anomaly DetectionAnomaly DetectionGeospatial Representation LearningTransformer
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Mar 11, 2026

On the Computational Hardness of Transformers

The transformer has revolutionized modern AI across language, vision, and beyond. It consists of LL layers, each running HH attention heads in parallel and feeding the combined output to the subsequent layer. In attention, the input consists of NN tokens, each a vector of dimension mm. The attention mechanism involves multiplying three N×mN \times m matrices, applying softmax to an intermediate product. Several recent works have advanced our understanding of the complexity of attention. Known algorithms for transformers compute each attention head independently. This raises a fundamental question that has recurred throughout TCS under the guise of ``direct sum'' problems: can multiple instances of the same problem be solved more efficiently than solving each instance separately? Many answers to this question, both positive and negative, have arisen in fields spanning communication complexity and algorithm design. Thus, we ask whether transformers can be computed more efficiently than LHLH independent evaluations of attention. In this paper, we resolve this question in the negative, and give the first non-trivial computational lower bounds for multi-head multi-layer transformers. In the small embedding regime (m=No(1)m = N^{o(1)}), computing LHLH attention heads separately takes LHN2+o(1)LHN^{2 + o(1)} time. We establish that this is essentially optimal under SETH. In the large embedding regime (m=Nm = N), one can compute LHLH attention heads separately using LHNω+o(1)LHN^{ω+ o(1)} arithmetic operations (plus exponents), where ωω is the matrix multiplication exponent. We establish that this is optimal, by showing that LHNω−o(1)LHN^{ω- o(1)} arithmetic operations are necessary when ω>2ω> 2. Our lower bound in the large embedding regime relies on a novel application of the Baur-Strassen theorem, a powerful algorithmic tool underpinning the famous backpropagation algorithm.

Barna Saha, Yinzhan Xu, Christopher Ye +1

University of California San Diego · Columbia University

TransformerAttention Mechanisms
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Mar 11, 2026

Algorithmic Task Capture, Computational Complexity, and Inductive Bias of Infinite Transformers

We formally define algorithmic capture of combinatorial tasks as the ability of a transformer to extrapolate to arbitrary task sizes with controllable error and logarithmic sample adaptation, providing a sharp scaling criterion for distinguishing logic internalization from statistical interpolation. Empirically, across scaling ranges spanning up to 2.5 orders of magnitude, we observe evidence of capture and non-capture. By analyzing infinite-width transformers in both the lazy and rich regimes, we derive upper bounds on the inference-time computational complexity of the combinatorial tasks these networks can capture. We show that, despite their universal expressivity, transformers possess an inductive bias that disfavors higher-complexity algorithmic procedures within the efficient polynomial-time heuristic scheme class, consistent with successful capture on simpler combinatorial tasks such as induction heads, sort, and string matching.

Orit Davidovich, Zohar Ringel

IBM Research, Haifa, Israel · Racah Institute of Physics, Hebrew University, Jerusalem, Israel

Algorithmic GeneralizationTransformerAlgorithmic ReasoningTransformer Expressivity
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Mar 11, 2026

Graph Tokenization for Bridging Graphs and Transformers

The success of large pretrained Transformers is closely tied to tokenizers, which convert raw input into discrete symbols. Extending these models to graph-structured data remains a significant challenge. In this work, we introduce a graph tokenization framework that generates sequential representations of graphs by combining reversible graph serialization, which preserves graph information, with Byte Pair Encoding (BPE), a widely adopted tokenizer in large language models (LLMs). To better capture structural information, the graph serialization process is guided by global statistics of graph substructures, ensuring that frequently occurring substructures appear more often in the sequence and can be merged by BPE into meaningful tokens. Empirical results demonstrate that the proposed tokenizer enables Transformers such as BERT to be directly applied to graph benchmarks without architectural modifications. The proposed approach achieves state-of-the-art results on 14 benchmark datasets and frequently outperforms both graph neural networks and specialized graph transformers. This work bridges the gap between graph-structured data and the ecosystem of sequence models. Our code is available at bluehere.

Zeyuan Guo, Enmao Diao, Cheng Yang +1

Beijing University of Posts and Telecom., Beijing 100876, China · DreamSoul

Graph Representation LearningTransformer
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Mar 11, 2026

Multimodal Self-Attention Network with Temporal Alignment for Audio-Visual Emotion Recognition

Audio-visual emotion recognition (AVER) methods typically fuse utterance-level features, and even frame-level attention models seldom address the frame-rate mismatch across modalities. In this paper, we propose a Transformer-based framework focusing on the temporal alignment of multimodal features. Our design employs a multimodal self-attention encoder that simultaneously captures intra- and inter-modal dependencies within a shared feature space. To address heterogeneous sampling rates, we incorporate Temporally-aligned Rotary Position Embeddings (TaRoPE), which implicitly synchronize audio and video tokens. Furthermore, we introduce a Cross-Temporal Matching (CTM) loss that enforces consistency among temporally proximate pairs, guiding the encoder toward better alignment. Experiments on CREMA-D and RAVDESS datasets demonstrate consistent improvements over recent baselines, suggesting that explicitly addressing frame-rate mismatch helps preserve temporal cues and enhances cross-modal fusion.

Inyong Koo, yeeun Seong, Minseok Son +2

School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea · Graduate School of Green Growth and Sustainability, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, South Korea

Multimodal Emotion RecognitionAudio-Visual AlignmentMultimodal FusionCross-Modal AttentionTransformer
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Mar 10, 2026

Lost in the Middle at Birth: An Exact Theory of Transformer Position Bias

The ``Lost in the Middle'' phenomenon -- a U-shaped performance curve where LLMs retrieve well from the beginning and end of a context but fail in the middle -- is widely attributed to learned Softmax artifacts or the distance-decay of positional encodings like RoPE. This paper makes a single, precise claim: the U-shape is already present at initialization, before any training or positional encoding takes effect. It is an inherent geometric property of the causal decoder with residual connections. We model multi-layer causal attention as iterated powers of the Cesàro matrix and derive the exact closed-form influence density in the continuous limit. Causal masking forces a logarithmic divergence of gradient influence at the start of the prompt (the Primacy Tail), while residual connections create an isolated O(1)\mathcal{O}(1) anchor at the final token (the Recency Delta). Between these extremes lies a factorial dead zone of order O(1/(H−1)!)\mathcal{O}(1/(H{-}1)!), where HH is the network depth, making middle-context retrieval and training structurally hostile. We validate empirically that untrained Qwen2 and GPT-2 architectures exhibit this U-shape at Step~0, and that it is identical with or without RoPE. Comparing initialized and pretrained networks, we show that standard training does not overcome the topological valley, confirming that the U-shape persists as an architectural baseline under standard pretraining objectives. We do not claim that this bias is insurmountable, nor that interventions such as RoPE modifications are useless. We establish what the baseline is and where it comes from, so that future efforts to overcome it can be precisely targeted.

Borun D Chowdhury

Meta, London, W1T 1FB, UK

Lost-in-the-Middle EffectTransformerTransformer AttentionDecoder-Only Language ModelsAttention Residual Connections
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Mar 10, 2026

Correction of Transformer-Based Models with Smoothing Pseudo-Projector

The pseudo-projector is a lightweight modification that can be integrated into existing language models and other neural networks without altering their core architecture. It can be viewed as a hidden-representation corrector that reduces sensitivity to noise by suppressing directions induced by label-irrelevant input content. The design is inspired by the multigrid (MG) paradigm, originally developed to accelerate the convergence of iterative solvers for partial differential equations and boundary value problems, and later extended to more general linear systems through algebraic multigrid methods. We refer to the method as a pseudo-projector because its linear prototype corresponds to a strictly idempotent orthogonal projector, whereas the practical formulation employs learnable restriction and prolongation operators and therefore does not, in general, satisfy the properties of an exact orthogonal projection. We evaluate the proposed approach on transformer-based text classification tasks, as well as controlled synthetic benchmarks, demonstrating its effectiveness in improving training dynamics and robustness. Experimental results, together with supporting theoretical heuristics, indicate consistent improvements in training behavior across a range of settings, with no adverse effects observed otherwise. Our next step will be to extend this approach to language models.

Vitaly Bulgakov

Profiteya LLC, Boston, MA, USA · Mass General Brigham, Boston, MA, USA

Noise RobustnessTransformer
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Mar 10, 2026

Routing without Forgetting

Continual learning in transformers is commonly addressed through parameter-efficient adaptation: prompts, adapters, or LoRA modules are specialized per task while the backbone remains frozen. Although effective in controlled multi-epoch settings, these approaches rely on gradual gradient-based specialization and struggle in Online Continual Learning (OCL), where data arrive as a non-stationary stream and each sample may be observed only once. We recast continual learning in transformers as a routing problem: under strict online constraints, the model must dynamically select the appropriate representational subspace for each input without explicit task identifiers or repeated optimization. We thus introduce Routing without Forgetting (RwF), a transformer architecture augmented with energy-based associative retrieval layers inspired by Modern Hopfield Networks. Instead of storing or merging task-specific prompts, RwF generates dynamic prompts through single-step associative retrieval over the transformer token embeddings at each layer. Retrieval corresponds to the closed-form minimization of a strictly convex free-energy functional, enabling input-conditioned routing within each forward pass, independently of iterative gradient refinement. Across challenging class-incremental benchmarks, RwF improves over existing prompt-based methods. On Split-ImageNet-R and Split-ImageNet-S, RwF outperforms prior prompt-based approaches by a large margin, even in few-shot learning regimes. These results indicate that embedding energy-based associative routing directly within the transformer backbone provides a principled and effective foundation for OCL.

Alessio Masano, Giovanni Bellitto, Dipam Goswani +2

University of Catania · Department of Computer Science, Universitat Autònoma de Barcelona Computer Vision Center, Barcelona

Online Continual LearningClass-Incremental LearningTransformer
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Mar 10, 2026

An Optimal Control Approach To Transformer Training

In this paper, we develop a rigorous optimal control-theoretic approach to Transformer training that respects key structural constraints such as (i) realized-input-independence during execution, (ii) the ensemble control nature of the problem, and (iii) positional dependence. We model the Transformer architecture as a discrete-time controlled particle system with shared actions, exhibiting noise-free controlled McKean--Vlasov dynamics, and we show that lifting the dynamics to probability measures produces a fully-observed Markov decision process (MDP). Positional encodings are incorporated into the state space to preserve the sequence order under lifting. Using the dynamic programming principle, we establish the existence of globally optimal policies under mild assumptions of compactness. We further prove that closed-loop policies in the lifted problem is equivalent to an initial-distribution dependent open-loop policy, which are realized-input-independent and compatible with standard Transformer training. To train a Transformer, we propose a triply quantized training procedure for the lifted MDP by quantizing the state space, the space of probability measures, and the action space, and show that any optimal policy for the triply quantized model is near-optimal for the original training problem. Finally, we establish stability and empirical consistency properties of the lifted model by showing that the value function is continuous with respect to the perturbations of the initial empirical measures and convergence of policies as the data size increases. This approach provides a globally optimal and robust theoretical alternative to gradient-based training without requiring smoothness or convexity.

Kağan Akman, Naci Saldi, Serdar Yüksel

Department of Mathematics, Bilkent University, Ankara, 06800, Turkey · Department of Mathematics and Statistics, Queen’s University, Kingston K7L 3N6, ON, Canada

TransformerTransformer Training DynamicsOptimal Control
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Mar 10, 2026

Decoding the decoder: Contextual sequence-to-sequence modeling for intracortical speech decoding

Speech brain--computer interfaces require decoders that translate intracortical activity into linguistic output while remaining robust to limited data and day-to-day variability. While prior high-performing systems have largely relied on framewise phoneme decoding combined with downstream language models, it remains unclear what contextual sequence-to-sequence decoding contributes to sublexical neural readout, robustness, and interpretability. We evaluated a multitask Transformer-based sequence-to-sequence model for attempted speech decoding from area 6v intracortical recordings. The model jointly predicts phoneme sequences, word sequences, and auxiliary acoustic features. To address day-to-day nonstationarity, we introduced the Neural Hammer Scalpel (NHS) calibration module, which combines global alignment with feature-wise modulation. We further analyzed held-out-day generalization and attention patterns in the encoder and decoders. On the Willett et al. dataset, the proposed model achieved a state-of-the-art phoneme error rate of 14.3%. Word decoding reached 25.6% WER with direct decoding and 19.4% WER with candidate generation and rescoring. NHS substantially improved both phoneme and word decoding relative to linear or no day-specific transform, while held-out-day experiments showed increasing degradation on unseen days with temporal distance. Attention visualizations revealed recurring temporal chunking in encoder representations and distinct use of these segments by phoneme and word decoders. These results indicate that contextual sequence-to-sequence modeling can improve the fidelity of neural-to-phoneme readout from intracortical speech signals and suggest that attention-based analyses can generate useful hypotheses about how neural speech evidence is segmented and accumulated over time.

Michal Olak, Tommaso Boccato, Matteo Ferrante

Tether Evo

Sequence-to-Sequence ModelsNeural DecodingSequence ModelingTransformer
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Mar 10, 2026

The Radio-Frequency Transformer for Signal Separation

We study a problem of signal separation: estimating a signal of interest (SOI) contaminated by an unknown non-Gaussian background/interference. Given the training data consisting of examples of SOI and interference, we show how to build a fully data-driven signal separator. To that end we learn a good discrete tokenizer for SOI and then train an end-to-end transformer on a cross-entropy loss. Training with a cross-entropy shows substantial improvements over the conventional mean-squared error (MSE). Our tokenizer is a modification of Google's SoundStream, which incorporates additional transformer layers and switches from VQVAE to finite-scalar quantization (FSQ). Across real and synthetic mixtures from the MIT RF Challenge dataset, our method achieves competitive performance, including a 122x reduction in bit-error rate (BER) over prior state-of-the-art techniques for separating a QPSK signal from 5G interference. The learned representation adapts to the interference type without side information and shows zero-shot generalization to unseen mixtures at inference time, underscoring its potential beyond RF. Although we instantiate our approach on radio-frequency mixtures, we expect the same architecture to apply to gravitational-wave data (e.g., LIGO strain) and other scientific sensing problems that require data-driven modeling of background and noise.

Egor Lifar, Semyon Savkin, Rachana Madhukara +3

Massachusetts Institute of Technology (MIT).

Finite Scalar QuantizationTransformer
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Mar 10, 2026

Exclusive Self Attention

We introduce exclusive self attention (XSA), a simple modification of self attention (SA) that improves Transformer's sequence modeling performance. The key idea is to constrain attention to capture only information orthogonal to the token's own value vector (thus excluding information of self position), encouraging better context modeling. Evaluated on the standard language modeling task, XSA consistently outperforms SA across model sizes up to 2.7B parameters and shows increasingly larger gains as sequence length grows.

Shuangfei Zhai

Apple

Self-AttentionTransformerLanguage Modeling
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Mar 9, 2026

Adaptive Loops and Memory in Transformers: Think Harder or Know More?

Chain-of-thought (CoT) prompting enables reasoning in language models but requires explicit verbalization of intermediate steps. Looped transformers offer an alternative by iteratively refining representations within hidden states. This parameter efficiency comes at a cost, as looped models lack the storage capacity of deeper models which use unique weights per layer. In this work, we investigate transformer models that feature both adaptive per-layer looping, where each transformer block learns to iterate its hidden state via a learned halting mechanism, and gated memory banks, that provide additional learned storage. We find that looping primarily benefits mathematical reasoning, while memory banks help recover performance on commonsense tasks compared to parameter and FLOP matched models. Combining both mechanisms yields a model that outperforms an iso-FLOP baseline, with three times the number of layers, across math benchmarks. Analysis of model internals reveals layer specialization: early layers learn to loop minimally and access memory sparingly, while later layers do both more heavily.

Markus Frey, Behzad Shomali, Ali Hamza Bashir +3

Lamarr Institute · Fraunhofer IAIS · University of Bonn

TransformerMemory-Augmented Language ModelsImplicit Reasoning in Language ModelsRecurrent TransformersNumerical Reasoning in Language Models
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