Transformer Architectures

Gene regulatory networks (GRNs) capture transcription factor-target interactions and are central to understanding cell-state regulation and disease. Reconstructing GRNs from paired single-cell transcriptomic and chromatin accessibility data is promising but challenging: scATAC is extremely sparse, and most methods rely on fixed peak-to-gene links and weak supervision. We present EpiAwareNet, a prior-guided multi-omic Transformer framework that reconstructs GRNs from paired single-cell data using only lightweight biological priors. In Stage 1, EpiAwareNet learns joint gene-peak representations with a gene-peak cross-attention module, enabling data-driven, gene-specific aggregation of accessibility signals rather than hard-coded peak-to-gene assignments. In Stage 2, EpiAwareNet incorporates a bulk-derived GRN prior as noisy positive edges to provide weak supervision under label scarcity, refining regulatory scores while remaining robust to prior noise. In our experiments, EpiAwareNet improves GRN reconstruction over representative single- and multi-omic baselines and yields GRNs with greater biological plausibility, such as improved recovery of known regulatory interactions, suggesting that lightweight biological priors from bulk data can effectively guide single-cell GRN inference when combined with adaptive cross-modal representation learning. Code and data will be available at https://github.com/tianyang-x/EpiAwareNet_pub.

With the growth of Vision Transformers in safety-critical domains like autonomous systems and medical imaging, ensuring their reliability against soft errors is paramount. While ViTs offer state-of-the-art accuracy, their massive parameter counts render exhaustive fault injection campaigns infeasible. To bridge this gap, a statistical fault injection framework is presented, leveraging finite-population sampling theory to provide formal reliability guarantees. It is demonstrated that failure rates are bounded within a 1% margin at 99% confidence using only a few thousand samples, regardless of model scale. This methodology achieves up to a 10,700 times reduction in experimental cost compared to exhaustive approaches, while preserving the ability to localize vulnerabilities across architectural components. Through extensive evaluation of different architectures like ViT-Tiny and ViT-Small, a highly non-uniform reliability landscape is uncovered. It is shown that while only 3% of FP32 bit-flips result in failure, the vast majority of these events lead to catastrophic accuracy collapse. Specific vulnerabilities are localized to normalization layers and critical exponent bits within the IEEE-754 format, providing a mathematical foundation and actionable insights for the design of hardened, edge-deployed ViT architectures.

Transformers have achieved remarkable success across a wide range of applications, and a growing body of work suggests that part of their strength comes from their ability to learn and execute algorithmic procedures. However, our understanding of how transformers learn such algorithms remains limited, especially in the presence of layer normalization (LN). In this work, we study principal component prediction as a concrete testbed for understanding the training dynamics of transformers with LN. We prove that a looped linear transformer with LN, trained by gradient descent, converges to a solution that implements the power method, with each self-attention layer performing one power iteration. Notably, the model is trained only for principal component prediction, rather than being explicitly supervised to implement the power method. Our finding thus reveals an "algorithmic implicit bias" of looped transformers with LN: principal-component prediction can in principle be achieved by many mechanisms, yet gradient descent selects one that realizes the power method. We further provide a concrete comparison between transformers with and without LN: even with layerwise guidance from power iterations, a transformer without LN cannot exactly learn the power method, whereas the corresponding transformer with LN can, leading to a provable performance gap in principal component prediction. Our results provide, to our knowledge, the first theoretical analysis of the training dynamics of looped and single-layer transformers with LN, and shed light on the role of LN in transformer models.

Passenger count data from public transit systems reveals urban mobility patterns and is essential for planning, operation, and optimisation. However, non-linear spatiotemporal interdependencies across stops and lines make modelling and prediction challenging. Existing approaches often rely on fixed temporal, spatial, or stop-level formulations, limiting their ability to capture within-trip evolution and network context. This study proposes SMT-GraphFormer, a spatiotemporal multi-task graph transformer that frames trip-level transit prediction as sequence-to-sequence modelling. Given a line's stop sequence and trip-level context, the model predicts successive boarding and alighting counts, with delay and dwell time treated as encoder-side surrogate tasks. Key components include graph embeddings for multi-relational stop similarity, a context encoder for weather and temporal information, and a multi-gate mixture-of-experts module that produces task-specific decoder representations for boarding and alighting predictions. Evaluation on public bus transit data from Trondheim, Norway, shows that SMT-GraphFormer outperforms stop-level tabular benchmarks, with ablation studies examining each component's contribution. The sequential formulation yields substantial gains on alighting prediction ($+$0.24 in $R^2$) and consistent improvements on boarding, delay, and dwell, confirming the value of explicit trip-level sequential bias and inter-target dependencies. These findings demonstrate the potential of transformer-based sequence modelling for capturing complex spatiotemporal dynamics in public transit and underscore the value of architectures tailored to transit data rather than off-the-shelf tabular models. The proposed framework provides a horizon-agnostic basis for scenario analysis in digital twin environments, supporting informed decision-making by planners and transit operators.

We introduce \emph{universal transformers}: fixed transformers that can simulate any transformer in a given class via a suitable input embedding. Analogous to a universal Turing machine, the input embedding encodes a description of the target model while all internal parameters remain fixed. We provide explicit sparse constructions achieving universality when the embedding dimension is sufficiently large, and further show that universality is generic: randomly initialized transformers are universal almost surely, which aligns with recent empirical results of Zhong and Andreas (2024). We empirically validate our theory on the algorithmic tasks of parenthesis balancing and multi-hop reasoning. Our results suggest that much of a transformer's expressive power may reside in its input representation rather than its learned weights.

Tree search is a central abstraction behind many language-agent reasoning and decision-making tasks: agents must explore actions, remember failures, and backtrack toward promising alternatives. Yet, we lack a theoretical understanding of how transformer-based policies acquire such search capabilities from the training dynamics of reinforcement learning (RL). We study this question in a stochastic $k$-ary tree environment, where an agentic transformer observes only its trajectory history through interaction and receives a terminal reward for reaching a hidden leaf goal node. We first construct a two-head transformer that implements randomized depth-first search (DFS): one head tracks previous actions, while the other detects failure outcomes and triggers backtracking. We then analyze the training dynamics of policy gradient under a depth-wise curriculum, showing that this same DFS mechanism emerges in stages from sparse reinforcement feedback without expert demonstrations. The resulting policy exhibits depth generalization: after training only on depth-$1$ and depth-$2$ trees, it succeeds on deeper full trees. We further show that, under imbalanced goal distributions, discounting the return leads to a ranked DFS policy that prioritizes higher-probability branches. Overall, our results identify a mechanistic normal form for transformer-based search, in which attention heads specialize and cooperate to extract decision-relevant traces from context and convert them into agentic action selection via RL training.

Plain Transformers have become the de-facto architecture for processing text, audio, image, and video, offering a unified backbone for multimodal learning. However, state-of-the-art architectures for point cloud semantic segmentation remain dominated by U-Nets architectures where convolutions are interleaved with local or windowed attentions. In this work, we show how to effectively leverage vanilla, non-hierarchical ViTs for segmentation of large-scale automotive lidar scenes. We bridge the performance gap thanks to a carefully designed tokenizer, a lightweight decoder segmentation head, and tailored data augmentations. Our approach, VaViT for Vanilla ViT, matches or exceeds the performance of state-of-the-art methods while maintaining the simplicity of ViT architecture. We provide extensive evaluations on nuScenes, SemanticKITTI, and Waymo Open Dataset to validate the efficiency of our method. Code and models are available at https://github.com/valeoai/VaViT.

Analyzing attention weights has become a standard approach for interpreting the information flow of Large Language Models (LLMs). However, this approach has significant limitations as it neglects the geometric properties of the value vectors being aggregated. To address this gap, we introduce \emph{Contribution Weights}, a projection-based metric that quantifies a token's influence by accounting for it's attention weight, value magnitude, and directional alignment with the layer output. We demonstrate that contribution weights provide a more faithful measure of token importance, consistently outperforming attention-based metrics in identifying semantically critical tokens across different decoder-only models, tasks, and datasets. Further, our metric enables novel mechanistic analysis of \emph{attention sinks}. While previous work characterized sinks as passive repositories for excess attention, we reveal they serve an active functional role, suppressing information through a convex relationship between sink rate and output norm, stabilizing representations by opposing the semantic drift of low-confidence tokens.

This work addresses the problem of autonomous resource management in heterogeneous satellite cluster conducting Earth Observation (EO) missions including optical and Synthetic Aperture Radar (SAR) satellites. In autonomous operation mode, satellites are equipped with intelligent capabilities enabling real-time decision-making based on the latest conditions, while requiring minimal interaction with ground operators. Traditional scheduling approaches typically rely on mathematical models to represent satellite mission and resource management. Then, this problem is solved by using optimization algorithms. However, such solutions become less effective when the underlying models are not available, over complex, and inaccurate due to dynamic changes and uncertainties inherent in the space mission environment. A promising alternative is to reformulate the problem as a sequential decision-making process and apply model-free reinforcement learning techniques to enable adaptive and real-time resource management. To this end, we propose a novel transformer-based architecture tailored for heterogeneous satellite cluster autonomous EO Mission with relational observations-actions tokenization and differential attention mechanism. Our experimental results demonstrate significant performance improvements compared to the available baselines. Moreover, the proposed architecture exhibits strong adaptability and transferability with respect to varying numbers of satellite clusters.

Recent advancements in text-guided audio generation have yielded promising results in diverse domains, including sound effects, speech, and music. However, jointly generating speech with environmental audio remains challenging due to the inherent disparities in their acoustic patterns and temporal dynamics. We propose ImmersiveTTS, an environment-aware text-to-speech (TTS) model that generates natural speech seamlessly integrated within environmental contexts by explicitly modeling cross-modal interactions. Our model builds on a multimodal diffusion transformer and fuses transcript-aligned speech latent with text-conditioned environmental context via joint attention. To enhance semantic consistency, we introduce a domain-specific representation alignment objective tailored to environment-aware TTS, leveraging complementary self-supervised representations from speech and audio encoders. Experimental results show that ImmersiveTTS achieves higher naturalness, intelligibility, and audio fidelity than existing approaches across objective metrics and human listening tests.

We formulate data propagation through the Transformer, the machine learning architecture powering large language models, as a nonlinear control system on the space of probability measures. For the mean-field Transformer model with self-attention and affine feed-forward layers, we prove that Gaussian distributions remain exactly Gaussian along the induced flow. This invariance reduces the infinite-dimensional measure dynamics to a finite-dimensional bilinear control system governing the evolution of the mean and covariance, reformulates the expressive capacity of Transformers as a reachability problem for prescribed Gaussian moments, and reveals a novel connection with Riccati-type equations from classical filtering and control. For time-varying controls, we prove exact finite-time reachability of any target Gaussian distribution whose covariance matrix has the same rank as the initial one, this rank constraint being an intrinsic invariant of the dynamics. For time-invariant parameters, we derive explicit spectral conditions leading either to asymptotic stability toward positive-definite equilibria or to finite-time blow-up of the covariance. Numerical experiments complement the theory by showing that practical Transformers with Gaussian inputs remain close to moment-matched Gaussian distributions through early and intermediate layers, while Transformers with prescribed attention matrices reproduce the predicted covariance regimes: bounded evolution in stabilizing configurations and blow-up in destabilizing ones.

Real-time and accurate spatial audio generation is pivotal for delivering an immersive experience. However, existing spatial audio synthesis technologies are often encumbered by a tradeoff between generation quality and high inference latency, as well as difficulty in capturing precise spatial information from multimodal inputs. To address these challenges, we propose SwanSphere, a unified streaming framework for high-fidelity spatial audio generation from panoramic videos and text prompts. SwanSphere mainly makes the following contributions: 1) We introduce a causal autoregressive diffusion transformer architecture that enables streaming high-quality spatial audio generation. 2) We design a Spatial Video-Audio Contrastive (SVAC) learning strategy to align the video encoder with the acoustic domain, and further employ a multi-objective online direct preference optimization (ODPO) scheme, resulting in strong spatial perception and robust multimodal spatial audio synthesis. 3) To alleviate the current scarcity of spatial audio datasets, we also develop an automated annotation pipeline for generating detailed spatial captions. Experimental results demonstrate that SwanSphere achieves superior performance in both video-to-spatial and text-to-spatial audio generation tasks. Demos can be found at: https://swanaigc.github.io.

Chain-of-thought prompting and looped Transformers both give a fixed model more test-time computation, but they differ in what they remember. Chain-of-thought stores intermediate state in generated tokens that remain in the context, whereas a looped Transformer carries state through recurrent hidden activations. We argue that this persistent mutable memory is a central resource for test-time reasoning. We compare three memory regimes, the compressed latent loop, the full sequence-state loop, and the chain-of-thought scratchpad. Our main result shows that a compressed loop is limited by the size of its recurrent state. Running the loop longer adds computation but does not by itself create a growing scratchpad, so a loop with a small recurrent state remains a small-space reasoner even when run for many steps. Under a standard complexity assumption, such loops cannot decide problems that are P-complete under logspace reductions, whereas polynomial-length chain-of-thought can. The separation is specific to compressed loops, as full sequence-state loops carry state at every input position and live in a memory-rich regime closer to explicit scratchpads. Controlled pointer-chasing and associative-recall sweeps illustrate this memory-budget view, with performance sensitive to whether the persistent-state budget matches the task's working-memory demand.

Recent work describes what transformers can and cannot compute through connections to boolean circuits, but existing results lack exact characterizations and are sensitive to modeling choices. Padded transformers -- to whose input filler symbols such as ``...'' are appended -- emerge as a useful gadget for establishing equivalences to circuit classes by providing polynomial space for adaptive parallel computation. However, only a limited set of padded transformer idealizations has been studied, leaving open how robustly these equivalences hold under changes to attention type, model width, and uniformity. We find that, under practical assumptions, padded transformers are surprisingly robust to all of these, and identify numeric precision and model depth as the main factors affecting expressivity. Concretely, we prove that polynomially padded $\text{L-uniform}$ constant-precision transformers are equivalent to $\text{L-uniform AC}^0$, while growing-precision ones achieve $\text{L-uniform TC}^0$ regardless of width. Furthermore, looping enables sequential processing analogous to circuits: $\log^d N$-looped constant-precision transformers reach $\text{FO-uniform AC}^d$, and growing-precision ones reach $\text{FO-uniform TC}^d$. Interestingly, growing width or precision beyond logarithmic does not increase expressivity, and all our results hold for both softmax and average hard attention transformers.

We use a mean-field-based transformer model to theoretically investigate how auxiliary variables, such as positional encoding, prevent mode collapse of self-attention mechanisms. The use of mean-field transformers to analyze the properties of self-attention mechanisms has garnered significant attention in recent years due to their ability to comprehensively analyze token interactions. However, analysis of this simple model suggests that mode collapse, where token distributions degenerate to a single point, occurs during long inferences (i.e., many layers), indicating a discrepancy with reality. This study investigates this mean-field transformer model and demonstrates that the introduction of auxiliary variables, such as positional encoding, acts as a counterforce against theoretical mode collapse. Specifically, we show that in the theoretical scheme, the energy-maximizing distribution does not degenerate to a single point; instead, it is characterized by a pushforward of the auxiliary variable distribution, thereby avoiding concentration in the Dirac measure. Our main examples are the positional encoding and the fixed prompt insertion treated as a parallel auxiliary-variable mechanism. Furthermore, we demonstrate that positional encoding and prompt insertion possess universality of representation in the limit, meaning that the limit distribution of inference can exactly represent a wide class of distributions. We also analyze several key properties of positional encoding and metastability, and validate our theoretical results through mathematical experiments.

This work presents ViGeo, a feed-forward foundation model for recovering spatially dense and temporally consistent geometry from video sequences. Built upon a plain transformer architecture without task-specific architectural modifications, ViGeo supports streaming, full-sequence, and long-video inference within a unified model. The key design is dynamic chunking attention, which exposes the model to both bidirectional and causal temporal contexts during training and allows it to adapt its attention pattern at test time without retraining. To improve supervision quality, we further introduce a completion-based data refinement framework. This framework trains a video depth completion teacher that conditions on sparse and noisy annotations and exploits video/multi-view context to produce dense, temporally coherent, and geometrically reliable training targets. Beyond depth and point maps, ViGeo also predicts surface normals within the same framework. Trained solely on public datasets, ViGeo achieves state-of-the-art performance across online, offline, and long-video depth estimation, surface normal estimation, and video point map estimation.

Diffusion Transformers have become a powerful backbone for text-to-image generation, but their layered and cross-modal generation process makes safety control fundamentally different from prompt-level filtering or output-level detection. Harmful semantics may be weakly expressed in text representations, progressively bound to visual latents, and finally entangled with rendering dynamics. As a result, safety steering at a fixed layer can be unstable, and a steering mechanism learned from known risks may not transfer reliably to a shifted target risk domain. We propose SafeDIG, a safety steering framework that formulates DiT safety adaptation as position-aware sparse feature transfer. SafeDIG first constructs Sparse Autoencoders over functionally distinct DiT intervention positions and uses robustness-aware pre-training routing to prioritize intervention sites that are expected to remain stable under source-target risk shift. It then separates transferable safety features from domain-specific activation geometry by freezing the SAE encoder as a reusable sparse safety dictionary and adapting only the decoder to the target-domain activation manifold. During inference, SafeDIG combines Blend and Repel operations to steer unsafe activations toward transferred safety manifolds or away from harmful sparse directions. Experiments on FLUX.1 Dev and Stable Diffusion 3.5 Large show that SafeDIG consistently reduces target-domain and overall unsafe generation rates while preserving source-domain safety and image quality.

Transformer hidden states are often interpreted through local or low-order objects: neurons, sparse features, attention heads, residual-stream directions, or activation patches. This paper studies a complementary object: the rank-indexed geometry of relations among token tuples. I use Plucker sign entropy to test whether r-argument relations leave arity-matched orientation signatures in hidden-state space. Across Llama-family 8B, 70B, and 405B checkpoints, true relation tuples show stronger orientation-sign consistency at the expected rank k=r for r=3,...,6 than scrambled tuples under matched random-control audits. Multi-template audits show that the effects survive surface variation, with all tested 405B rows retaining positive expected-rank margins and 8B/70B retaining positive rows with constructor-specific mixed cells. I then ask whether the same relation geometry can be steered. In an edge-grid clean/corrupt intervention assay over 32 prompts, the row/column scaffold and answer format stay fixed while the YES/NO relation map changes, and the corrupt hidden-state relation frame is patched toward clean or placebo targets. In 70B and 405B, clean-targeted relation-frame paths recover clean-answer behavior and residual relation geometry, while centroid-only and equal-norm controls show negligible recovery. Site/order controls further separate marker-site importance from ordered clean-frame geometry: target clean shape and cross-prompt clean shape recover behavior and residual geometry at the marker interface, whereas corrupt-donor transfer, same-site permutation/reflection, wrong-site clean deltas, centroid-only motion, and equal-norm noise fail or remain far below clean-frame paths. The result is a controlled bridge from relation probing to relation-frame intervention: relation rank geometry can be detected, targeted, and behaviorally validated in transformer hidden states.

Decoding visual content from fMRI signals recorded while a person views images, and specifically answering questions about the seen images, is a long-standing challenge. While significant progress has been made in recent years in visual question answering (VQA) from fMRI, performance remains limited. Moreover, although recent models can make increasingly accurate predictions, they have rarely been used as tools for understanding the structure of visual representations in the brain. We present Brain-IT-VQA, a framework for visual question answering from fMRI. Building on the Brain Interaction Transformer (Brain-IT), our method decodes language tokens from brain activity and integrates them with a language model to answer visual questions. Our model substantially outperforms previous fMRI-based captioning and VQA approaches. We further introduce NSD-VQA, a new dataset and benchmark for visual question answering from fMRI. Unlike existing image-fMRI VQA datasets, which typically provide only a few broad and weakly controlled questions per image, NSD-VQA provides on average 20 question-answer pairs per image across 20 controlled question categories that disentangle multiple levels of visual understanding. This enables more reliable and interpretable evaluation despite limited fMRI test data. Together, Brain-IT-VQA and NSD-VQA provide both a strong predictive framework and a tool for studying brain representations. Using this benchmark, we quantify which forms of visual and semantic information can be reliably decoded from fMRI responses to natural images. We further analyze the contributions of different brain regions across question types.

The recursive quad-tree partitioning in High Efficiency Video Coding (HEVC) incurs considerable computational overhead, with exhaustive rate-distortion optimization for CTU partition prediction consuming the dominant share of encoding time. Although partition prediction through deep learning has emerged as a viable encoding accelerator, an architectural dichotomy remains largely unaddressed: CNNs are computationally efficient but spatially myopic due to their localized effective receptive fields, failing to capture long range semantic relationships and repetitive textures; conversely, transformer based architectures are better at capturing global context but incur prohibitive CPU latency, a critical liability that impedes deployment which is predominantly CPU-bound. This paper introduces Hybrid Fast Vision Transformer (HFViT), a hybrid architecture designed to accelerate HEVC intra-mode partition prediction. HFViT fuses a reparameterized depthwise-separable convolutional backbone with a Hierarchical Attention Transformer (HAT) mechanism, leveraging a carrier token scheme to enable efficient global information propagation at sub-quadratic complexity. Post-training structural fusion collapses batch normalization into preceding layers to further reduce latency. Comprehensive evaluation reveals the efficacy of HFViT in accelerating HEVC intra-encoding across resolutions. On standard JCT-VC test sequences, HFViT reduces the average VMAF BD-rate penalty by 2.4, 2.6, and 7.9 percentage points on Classes A, B and E, respectively, as compared to the competing ETH-CNN baseline while maintaining CPU inference latency within 8% of the CNN baseline and surpassing it on GPU by 40%, establishing practical viability for real-time encoder integration.

Instruction-based suppression is widely used to prevent language models from generating prohibited content, yet it remains unclear whether suppression reduces internal representation or merely suppresses expression. We investigate this question through representational probing, attention analysis, and behavioral semantic leakage experiments across multiple transformer models. We find that prohibited concepts remain highly recoverable from hidden representations under suppression, continue to influence attention routing, and measurably shape downstream generations despite successful lexical avoidance. These effects persist across pooling strategies, indirect semantic controls, and multiple model families. Our results expose a fundamental gap between behavioral and representational alignment.

Chain-of-Thought (CoT) prompting substantially improves the sample efficiency of transformers, reducing the complexity of tasks like parity learning from exponential to polynomial in the input length. However, generating explicit reasoning steps at inference is computationally expensive. Implicit Chain-of-Thought (ICoT) has emerged as a promising empirical remedy that trains models to internalize intermediate steps within their hidden states, but its theoretical foundations remain poorly understood. We give the first theoretical analysis of ICoT, proving that an $L$-layer transformer trained under our proposed Log-ICoT curriculum learns $k$-parity with $\mathsf{poly}(n)$ samples and $L = \log_2 k$ training stages. This matches the sample efficiency of explicit CoT while eliminating its inference overhead, and extends prior one-layer parity guarantees to multi-layer architectures. Compared to standard ICoT, which removes thinking tokens one at a time, Log-ICoT removes them in geometric chunks, reducing the number of stages from linear in $k$ to logarithmic. Experiments on multi-layer transformers confirm the theory and visualize how reasoning is progressively absorbed into deeper layers.

Many learning problems require predicting how populations evolve under an unknown transformation. A natural representation for such populations is a probability measure, with point clouds as a key example. In this work, we study the measure-to-measure (M2M) regression problem, in which one seeks to learn a map between probability measures from a finite collection of observed input-output pairs. In contrast to classical regression, where individual samples are transformed independently, M2M regression treats entire distributions as the data points. This perspective is vital in certain scientific applications, for example, cellular and molecular biology, where cells are known to evolve not as independent data points but as a collection. However, few existing approaches address the problem of M2M regression with sufficient expressivity and scalability. We present a formalization of nonlinear M2M regression and introduce two easy-to-use, expressive, and scalable approaches to learn such operators: transformers as static M2M maps and transformers as dynamic M2M velocity fields. Our approach leverages the natural measure-dependent and mean-field structure of transformers to learn nonlinear M2M maps on the space of probability distributions. We illustrate the effectiveness of our proposed method to generalize to unseen measures on synthetic experiments, interacting particle systems, and a large-scale patient-derived organoid dataset for predicting treatment response in colorectal cancer.

State-of-the-art learned image compression (LIC) schemes are increasingly based on hybrid CNN-transformer architectures. To further improve rate-distortion performance, we introduce channel-wise wavelet transforms into both the transformer and entropy-coding components. First, we propose a channel-wise wavelet-domain transformer attention (ChWDTA) mechanism. ChWDTA keeps the efficient windowed spatial self-attention used in modern LIC backbones, but computes the Q/K/V projections on channel-wise wavelet-transformed features before mapping the attention output back with the inverse transform. The resulting Channel-wise Wavelet-Domain Transformer Block (ChWDTB) therefore preserves the spatial tokenization pattern of windowed attention while sparsifying the channel covariance seen by the attention projections. Second, in the entropy-coding stage, we introduce a channel-wise wavelet packet (ChWP) decomposition that produces four equal-sized subbands, which better fit channel-wise slice-based autoregressive entropy modeling. When each channel-wise subband is divided into two slices, we use eight slices for entropy coding. With this configuration, the proposed scheme obtains BD-rate reductions of -17.82%, -19.15%, and -22.56% on the Kodak, CLIC Professional Validation, and Tecnick test sets, respectively. Even when each channel-wise subband is coded as a single slice, the scheme still retains most of the coding gains with lower complexity. The results confirm the advantage of introducing wavelet transform in CNN-transformer-based LIC schemes.

In-context learning \ -- performing tasks based on examples given in the prompt \ -- is an important capability that has emerged in large language models and has received significant attention in both theory and practice. Existing theoretical work often focuses on settings where the learning uses information purely from the prompt. However, many practical instances of in-context learning require the model to retrieve factual knowledge stored in the model's parameters, with the context serving to identify which knowledge is relevant. In this work, we study how in-context learning leverages factual knowledge recall. We formalize this behavior by introducing the \emph{in-context factual recall (IC-recall)} task, where a transformer is provided a context of (subject, answer) pairs generated from a hidden relation, along with a query subject, and must both infer this hidden relation and retrieve the corresponding answer. Factual knowledge is modeled by the transformer having access to a simple pre-constructed MLP associative memory storing (subject, relation, answer) triplets. We analyze the supervised fine-tuning dynamics of a one-layer transformer on IC-recall data and prove that the model successfully performs IC-recall by converging to a particular pairwise attention pattern. This fine-tuning stage requires a very small number of samples \ -- only polylogarithmic in the number of stored knowledge triplets. Experiments verify our theoretical predictions and show that the pairwise attention pattern emerges even when the MLP layer is pretrained instead of constructed.

Terrain understanding is fundamental for mobile robots operating in unstructured outdoor environments. Existing vision-based traversability estimation methods rely on robot-specific annotations or semantic class mappings, limiting transferability across platforms and requiring costly re-annotation when robot capabilities change, while standard semantic segmentation methods only focus on specific predefined classes, which do not capture the variety of terrains. In this work, we propose a transformer-based architecture that jointly performs class-specific semantic segmentation and class-agnostic terrain segmentation within a unified network, called Trinity. Terrain regions are segmented based solely on visual appearance, without predefined semantic labels or robot-dependent traversability scores. This formulation enables the learning of robot-agnostic visual terrain priors that can be combined with robot-specific experience for downstream tasks such as traversability estimation, visual odometry, and mission planning. To enable large-scale training with diverse terrain appearances, we extend the OAISYS simulator and introduce RUGDSynth, a synthetic dataset inspired by RUGD with class-agnostic terrain samples. Furthermore, we present the EXTerra Dataset, providing real-world images annotated with both class-specific and class-agnostic terrain labels. Experiments demonstrate the feasibility of the proposed task and the effectiveness of our joint segmentation approach in complex outdoor environments. Code and datasets will be released with this publication (after review).

We characterize the pre-softmax attention matrix $\mathbf{QK^\top}$ in transformers as an associative memory matrix encoding pairwise associations between input features. By decomposing this matrix into its symmetric and skew-symmetric parts, we interpret the symmetric component as governing the structure of the energy landscape, and the skew-symmetric component as driving circulation on that landscape. Leveraging the energy formulation induced by the symmetric component, we derive Hopfield-style stability measures that quantify the stability of retrieved features. We observe meaningful correlations between Hopfield-style stability measures and the fidelity-diversity trade-offs in generation. Finally, we propose a controllable knob to modulate this trade-off by modifying the circulation of the underlying dynamics. Code is available at our GitHub (https://github.com/hyeon-cho/Attention-Symmetric-Decomposition).

We study Latent Recurrent Transformer (LRT), a lightweight augmentation of autoregressive transformers that reuses a high-level source-layer hidden state from the previous token as recurrent memory for the next token. Because this state is already computed during ordinary decoding, LRT introduces a cross-token, cross-layer latent pathway while preserving the standard attention mechanism, KV-cache interface, and one model forward per generated token. To pretrain this recurrence without sequentially unrolling the full sequence, we introduce interleaved parallel training: one full-sequence initialization forward constructs a shared buffer, followed by sequential refinement of disjoint position subsets with parallel computation within each subset. This provides every token with recurrent-memory-aware supervision at approximately 2x ideal token compute. Across 1.3B- and 2.1B-parameter nanochat-style backbones and a wide range of training budgets, LRT improves both BPB and CORE under matched effective compute. Additionally, LRT outperforms two-forward PonderLM-2 and matches a three-loop Transformer in BPB, while retaining one-forward-per-token decoding with 9% latency overhead over the standard Transformer.

Prior-data fitted networks (PFNs) have recently emerged as a powerful approach for Bayesian prediction tasks, approximating the posterior predictive distribution (PPD) through in-context learning. Despite their strong empirical performance and ability to go beyond point predictions, theoretical understandings of the algorithmic capability of transformers to learn distributions in context are still lacking. Focusing on Gaussian process regression problems, we show by construction that transformers can implement a gradient descent algorithm targeting the posterior predictive mean and variance, followed by nonlinear mappings that yield binned probabilities of PPD. We study the error bounds of the approximated PPD in terms of attention depth and bin resolution. Based on these results, we further demonstrate the key role of normalization and the choice of attention depth in enabling the extrapolation abilities of transformers beyond the pretraining sample size range. We conduct simulations that corroborate our findings, providing insight into the expressivity of PFNs targeting PPDs and how architectural choices may influence generalization capabilities.

The inverse problem of multilayer thin-film optical coatings design represents a complex combinatorial-continuous optimization challenge. We present PRISM (Position-encoded Regressive Inverse Spectral Model), a unified decoder-only autoregressive transformer that streamlines this process by jointly predicting discrete material selection and continuous thickness regression within a single backbone. PRISM introduces two primary architectural innovations: (1) spectrum prefix conditioning, which utilizes standard prefix tokens for in-context target injection, and (2) cumulative-depth Rotary Position Embeddings, which encode continuous thickness directly into the positional representation to preserve the physical spatial relationships of the stack. Our benchmarks demonstrate that a PRISM-13M model reduces MAE by over 50% compared to other transformer baselines while utilizing only one-fifth of the parameters. Furthermore, a 44M-parameter variant achieves state-of-the-art performance (MAE = 0.010) on our in-distribution validation benchmark and operates significantly faster than simulated annealing, offering a highly efficient alternative to classical optimization methods.

Skin cancer is a common and fast rising malignancy worldwide. Early detection is critical for improving outcomes. Deep learning models trained on dermoscopic and clinical images can support automated and fast triage. However, many studies evaluate only a limited set of architectures. Experimental setups also vary across studies. In this paper, we present a unified evaluation of twelve deep learning models for binary skin cancer detection on the PAD-UFES-20 dataset. The models span four families: convolutional neural networks (CNN), vision transformers (ViT), hybrid convolution transformer backbones, and vision language models (VLM). Performance is assessed using AUC, the maximum F1 score with its precision and recall, and sensitivity at 80% specificity, reflecting screening oriented requirements. Our results show that well tuned CNNs already provide strong baselines, but transformer based families consistently improve discrimination. Hybrid models (MaxViT Tiny, CoAtNet0) and a SigLIP based VLM achieve the best overall trade off between ranking performance and clinically relevant operating points, while CLIP based model offers high precision. The full codebase for all experiments is publicly released. Together, these findings offer practical guidance on which model families are most suitable for real world deployment in skin cancer screening and establish a reproducible reference point for future work on PAD-UFES-20.

Modern deep learning offers powerful tools for automated retinal screening, but it remains unclear how different visual model families compare in realistic multi-disease settings and under domain shift. In this work, we benchmark twelve architectures across four model families: convolutional neural networks, vision transformers, hybrid CNN-transformer backbones, and vision-language models, using the Retinal Fundus Multi-disease Image Dataset (RFMiD). We evaluate two tasks: binary screening for any retinal disease and multi-label classification across 28 disease classes. Using standardized training, calibration, and evaluation protocols, we report AUC, F1, precision, recall, and sensitivity at a clinically relevant operating point with specificity near 80%. On RFMiD, all architectures perform well on binary screening, with AUC above 84%, but attention-based models perform best. SwinTiny and the hybrid CoAtNet0 and MaxViTTiny models achieve the strongest binary screening results and improve macro and micro F1 in the multi-label setting. Vision-language models, including CLIP ViT-B/16 and SigLIP-Base384, are competitive with CNN baselines but do not surpass the best transformer and hybrid backbones. In external validation on Messidor-2 for referable diabetic retinopathy, AUC ranges from 66.8% to 84.7%, with hybrid and transformer models again showing strong performance. These results provide a reproducible reference for model selection in multi-disease retinal screening and guide future automated screening tools for clinical deployment.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models for language modeling, yet the effective design of transformer architectures for MDMs remains underexplored. In this paper, we show that selectively looping the early-middle transformer layers significantly improves both training efficiency and model performance in MDMs. We call this approach LoopMDM(Looped Masked Diffusion Model), which brings two key benefits: looping layers at training-time yields a depth-scaling effect without adding parameters, while varying the number of loops at inference-time enables flexible compute scaling. Despite the simplicity, the results are striking: across multiple pre-training corpora, LoopMDM matches the performance of same-size MDMs with up to 3.3 fewer training FLOPs, while its final performance outperforms them on various reasoning benchmarks, including up to 8.5 points on GSM8K. It even surpasses deeper non-looped MDMs trained with comparable per-step compute, indicating that selective looping is more effective than naive depth scaling. Furthermore, LoopMDM can scale inference-time compute by increasing the number of loops. Adaptively adjusting the number of loops throughout the sampling process further yields additional gains in compute efficiency while maintaining performance. Lastly, with attention analysis, we provide evidence that looping is effective in MDMs by promoting interactions among masked positions. Our code and weights will be publicly released.

Humanoid parkour requires locomotion policies to coordinate whole-body dynamics across rapidly changing terrains such as stairs, gaps, slopes, and obstacles. Existing reinforcement learning policies are largely reactive, mapping observations directly to actions without explicitly modeling future body states. Such modeling becomes critical in agile locomotion tasks where successful motion execution depends strongly on anticipating upcoming contact transitions and body dynamics. We present ParkourFormer, a Transformer-based sequence modeling framework that reformulates humanoid locomotion as a future-conditioned decision-making problem. The current robot state queries historical sensorimotor trajectories through cross-attention, while a lightweight prediction head forecasts short-horizon future proprioceptive states. The predicted future states, trained with supervised signals, are fused with temporal features to generate actions, enabling the policy to jointly reason over motion history and anticipated future dynamics. We evaluate ParkourFormer on a diverse multi-terrain humanoid parkour benchmark including stairs, gaps, slopes, rough terrain, and obstacle traversal. Experiments in simulation and on a real humanoid robot show that ParkourFormer achieves a 93.85% average traversal success rate on highly challenging terrains, with improvements of up to 47.12% over strong MLP, MoE-based MLP, and vanilla Transformer baselines, while maintaining a single unified policy across all terrain types. These results demonstrate that explicit future-state modeling significantly improves robustness and generalization for agile whole-body locomotion.

Fine-tuning a language model on contexts whose correct completion has a near-synonym competitor often fails silently. The cross-entropy loss decreases monotonically while the correct token never overtakes the competitor in rank. We study this regime across five transformer architectures spanning two families and a fivefold parameter range, on ten hand-selected near-synonym contexts. We instrument these failures with an order parameter combining the predicted distribution and pairwise embedding overlaps. It decomposes additively into a signal, tracking the model's commitment to the correct token over its nearest competitor, and a background drag, set by how the embedding bulk leaks probability into the score. This isolates two failure modes. In kinematic failure the signal stays small. In structural failure the drag actively worsens as fine-tuning proceeds. We observe sharp catapult-like jumps in the order parameter that resemble a phase transition. A central negative result organises the paper. The transitions are phantoms. The spontaneous-symmetry-breaking interpretation is ruled out by direct measurement. Catapult-like jumps still appear under LoRA fine-tuning with the token embedding matrix exactly unchanged during training, where no geometric phase transition is possible. The discontinuity lives entirely in the softmax readout. A small number of dimensionless quantities organise the trajectory across architectures. One is consistent across all five under full fine-tuning. A second sorts architectures into two classes by bulk embedding distribution and predicts LoRA sufficiency. As a blind test, the framework predicts the critical learning rate of a held-out architecture, not used to fit any parameter, to within 2.1% of a subsequent learning-rate sweep. Findings concern the near-synonym mechanism only and should not be extrapolated without recalibration.

Distributing Transformer inference across embedded edge devices can alleviate individual memory and compute constraints, yet practical benefits on real hardware remain unclear: prior work relies largely on simulations that overlook hardware-specific communication overheads. We present a hardware prototype study on NVIDIA Jetson Orin Nano devices connected over WiFi. Our key finding is that the dominant bottleneck is not just network bandwidth but also the CPU-GPU staging during communication. Because Jetson's integrated GPU architecture lacks the PCIe/NVLink pathway that NCCL requires, all inter-device data communication should be routed through GLOO and staged in CPU memory; an overhead that scales with communication data volume and makes full-tensor exchange slower than single-device inference across the batch sizes for medium sized models such as ViT. We therefore evaluate Prism by combining Segment Means compression with lightweight offline profiling to adaptively select between local and distributed execution at runtime. Experiments show that this strategy reduces latency by 65%-77% and energy consumption by 34%-52% relative to full-tensor exchange in static distributed execution setup, demonstrating that profiling-driven adaptation is essential for practical distributed Transformer inference on embedded hardware.

This paper proposes StrTransformer, a source-wise structured Transformer framework for blind source recovery and branch-wise latent modeling. Instead of using an encoder to infer latent variables, StrTransformer directly optimizes the latent source matrix together with an observation-space mixer and source-wise structural Transformer branches. The mixer enforces reconstruction consistency, while each Transformer branch imposes a differentiable structural constraint on one latent source trajectory. Specifically, each source is converted into multi-scale patch tokens, randomly masked, processed by a locality-biased Transformer, and evaluated through a masked patch reconstruction energy. This energy acts as an implicit source-wise structural prior. To encourage different latent branches to specialize into different temporal regimes, StrTransformer further introduces an ordered multi-scale controller that learns branch-specific patch-scale weights, ordered scale centers, and locality attention slopes. The resulting objective combines observation reconstruction, source-wise structural regularization, and modular auxiliary penalties for separation and scale specialization. We analyze the decoupling and coupling structure of the objective, the regularized exact-reconstruction fiber, and the reduction of permutation symmetry induced by ordered branch descriptors. A controlled case study shows that the learned branches converge to distinct temporal-scale structures and recover source-aligned latent trajectories under post-hoc evaluation.

In the paper we show that there is an analogy between the operations occurring in a layer of a transformer (projections and layer normalizations, disregarding the feedforward neural network) and a step in the power method. Coherently with this analogy, we show that passing through a layer the tokens tend to be tilted towards the principal eigenvector of a matrix which is the product of the output and value weight matrices of that layer. In the special case of a transformer with shared weights (i.e., in which all layers have identical weights) then the alignment with this principal eigenvector is particularly evident empirically, and can also be shown analytically. The analogy also suggests a method to steer the output of the transformer towards an arbitrary desired direction in token space.

The growing interest in Temporal Graph Neural Networks (TGNNs) stems from their ability to model complex dynamics and deliver superior performance. However, TGNNs encounter fundamental challenges in capturing long-term dependencies and identifying periodic patterns. To address these limitations, we propose TGFormer, a novel Transformer architecture specifically designed for temporal graphs. Our model redefines temporal graph learning by establishing a trajectory framework that aligns with time series analysis principles. This approach allows TGFormer to derive node representations through systematic analysis of historical interactions, enabling granular examination of node relationships across sequential timestamps. Building upon stochastic process theory, we develop an auto-correlation mechanism that systematically uncovers periodic dependencies in node interactions. This innovation empowers TGFormer to perform dependency discovery and representation aggregation at sub-interaction levels, demonstrating superior efficiency and accuracy compared to conventional attention mechanisms. Experimental validation across six public benchmarks confirms the effectiveness of our approach, with TGFormer at most achieving 9.35% precision improvement compared to state-of-the-art approaches.

Transformer-based LLMs achieve strong results on many language tasks; however, long inputs remain challenging because context windows are finite, and prefill latency and memory grow rapidly with prompt length. Flat token-stream processing and chunk-based retrieval can therefore spend substantial computation and context budget on text unrelated to the query. Offline-indexed RAG additionally introduces external storage and index management overhead, and typically appends retrieved evidence as raw text, increasing prefill cost and latency. H^{2}MT makes long-context inference structure-aware: it builds a semantic hierarchy offline, computes a memory embedding for each node via bottom-up post-order aggregation, and routes queries coarse-to-fine at inference to prune irrelevant branches early. On LongBench QA (NarrativeQA, HotpotQA, QASPER) and two structured technical-document settings, H MT achieves favorable quality efficiency trade-offs, delivering competitive ROUGE-L and F1 (where applicable) with lower peak GPU memory and time-to-first-token (TTFT) than prompt compression, memory-token methods, and retrieval-augmented generation baselines.

Concept formation in transformer language models is depth-extended, not a single-layer event: concepts emerge gradually across a contiguous region of the residual stream. Mechanistic interpretability methods identify the single layer of peak class separation -- the "best layer" -- capturing a snapshot rather than the process itself. We introduce the Concept Allocation Zone (CAZ): the depth interval within which a concept becomes measurably separable, the region allocated to its geometric expression. We formalize the CAZ through three layer-wise metrics (Separation, Concept Coherence, Concept Velocity) and derive principled boundary detection without manual layer sweeps. A CAZ is not a concept: it is the depth region within which the model organizes its geometry to make a concept separable. A single concept typically participates in multiple CAZes; multiple concepts may share one. Empirical validation across 34 models from 8 architectural families and 7 concepts reveals that the separation curve S(l) is frequently multimodal. A scored detector uncovers "gentle CAZes" -- subtle allocation regions invisible to standard peak detection but causally active in 93-100% of cases under ablation (16 of 34 models; 26 in the companion validation paper). The framework generates seven testable predictions; four yield clear verdicts (two not supported, one partially supported, one supported), one had its precondition invalidated by the data, and two are underpowered -- with cross-architecture alignment confirmed as depth-matched rather than monolithic under leave-one-concept-out cross-validation. Reference implementation: rosetta_tools v1.3.1 (doi:10.5281/zenodo.20361433).

Muon is a recently developed matrix-aware optimizer that has shown strong results in transformer training, but its behavior in vision transformers (ViTs) is not yet well understood. We study Muon for ViT training, largely on ImageNet-100 and Pl@ntNet-300K, comparing against AdamW under standard vision recipes involving mixup, cutmix, smoothing, and random augmentation and erasing. Muon consistently outperforms AdamW, with especially large gains on long-tailed Pl@ntNet macro top-1. These gains are also recipe-dependent, where Muon benefits much more than AdamW from advanced and significant data augmentation techniques. To understand this interaction, we analyze the singular-value structure of matrix gradients throughout the ViT. Within Muon training runs, removing heavy data augmentation induces a late-training spectral concentration and mode collapse in gradient matrices, primarily in deep MLP-down blocks. Under a fixed "full" augmentation recipe, the clearest Muon-AdamW contrast appears instead in QKV gradients, where AdamW gradient energy remains concentrated in a much narrower basis while Muon spreads energy across substantially more singular modes. Muon in ViTs is therefore best understood as an optimizer-recipe interaction. Under a fixed recipe, Muon differs from AdamW most clearly in attention projections, where its gradients consist of a broader spectral basis. Within Muon, a full training recipe is important for preventing late spectral concentration and mode collapse in deep feedforward blocks. We further demonstrate efficacy in training ViTs on image segmentation and masked autoencoder models, where Muon outperforms AdamW in all settings considered.

Instruction-based video editing requires transforming a source video according to a natural-language instruction while preserving irrelevant content and remaining temporally coherent. We argue that existing Diffusion Transformer (DiT) editors struggle with this task for two structural reasons. First, conditioning signals are fed undifferentiated into all transformer blocks, forcing a single token stream to encode both global editing intent and fine-grained visual evidence. Second, the cross-attention patterns that govern the edit are supervised only indirectly through pixel-level reconstruction, leaving the model's internal reasoning process under-constrained. To address both limitations, we propose RVEDiT, an implicit Reasoning Video Editing DiT framework built around two complementary components. The first, Granularity-Routed Token Conditioning, introduces learnable editing tokens distilled from a multimodal LLM and routes them to shallow blocks, while reserving native visual and textual tokens for deeper blocks, thereby inducing a coarse-to-fine editing process inside the backbone. The second, Reference-Anchored Attention Alignment, employs a parameter-sharing reference branch during training and maximizes the mutual information between the attention features of the editing and reference branches, regularizing the model's internal reasoning without incurring any additional inference cost. Experiments on standard instruction-based video editing benchmarks show that RVEDiT consistently outperforms state-of-the-art baselines, with particularly strong gains on localized and compositional edits.

A sparse 8-layer code transformer develops dedicated neural circuitry for every Python construct tested, and that circuitry is organised by a clean computational principle rather than by semantic category. We extract neural circuits for 106 concepts (43 AST node types, 63 builtin objects) by marginalising across 63,800 controlled prompts, and decompose each circuit into concept-specific and token-driven components using contrastive checker prompts that present a keyword token without its associated syntactic structure. Three findings emerge. First, all 106 concepts produce non-empty universal circuits at every one of nine parameter settings, and the ranking of concept-specificity across constructs is stable across the sweep - survival is not an artifact of a permissive threshold. Second, AST circuits contain a genuine concept component distinct from token activation: concept-only neurons constitute up to 62.5% of the loudest-firing neurons at mid-to-late layers, while builtin circuits are almost entirely token-driven. Third, six computationally atomic constructs - Import, ImportFrom, Break, Continue, Pass, Assert - cluster together despite being semantically unrelated, sharing only the property of being single-statement constructs requiring no nested body; this atomicity super-cluster, together with a four-tier hierarchy organised by token ambiguity and structural distinctiveness, shows that the model's internal organisation tracks computational structure rather than meaning. The methodology, full decomposition data, and analysis code are released.

Independently trained transformers compute the same function in residual-stream bases that differ by a uniform random rotation on $\mathrm{SO}(d_{\mathrm{model}})$. We call this phenomenon polymorphism: same function, mutually unintelligible interior coordinates. One matrix multiplication per model pair removes it: an orthogonal Procrustes fit on a single batch of activations transfers sparse-autoencoder feature dictionaries and steering vectors between independently trained models, with no retraining. The phenomenon is invisible to the standard SAE universality metric. Decoder-column cosine similarity matches across seeds at 98%, the SAE-universality headline number, while an SAE trained on one seed reconstructs another seed's activations at negative explained variance, worse than predicting the constant mean. The decoder columns align; the encoder reads from a rotated frame. A single Procrustes rotation $R$ restores reconstruction to within 0.025 EV of the within-seed ceiling at every internal site. $R$ is Haar-distributed: $\|R - I\|_F$ matches the random-orthogonal prediction $\sqrt{2 d_{\mathrm{model}}}$ to 0.1% at $d_{\mathrm{model}} = 512$, and a Kolmogorov-Smirnov test of $R$'s eigenvalue spectrum against Haar $\mathrm{SO}(d_{\mathrm{model}})$ returns $p \approx 1.000$ pooled and per-pair. Diff-of-means steering vectors transfer in three regimes by alignment with $R$'s invariant subspace: clean when pinned by shared output weights, partial when overlapping the rotated subspace, inverted otherwise. With no shared I/O (Pythia), all three collapse to universally inverted. The same rotation account holds across training checkpoints within a single run. Validated on a 104k-parameter Dyck-3 transformer and nine independently-trained Pythia-70m seeds on The Pile, via a pre-registered four-bar operational framework. Frontier-scale (10B+) replication remains open.

The rapid growth of Electric Vehicle (EV) adoption challenges power distribution networks through peak load spikes, voltage instability, and transformer overloads from uncoordinated charging. While Model Predictive Control (MPC) and standard Reinforcement Learning (RL) methods have addressed these issues, existing approaches rarely treat real-time carbon intensity or fluctuating renewable energy (RE) availability as primary scheduling objectives, leaving substantial decarbonisation potential unrealised. This paper proposes an emission-aware RL strategy based on the Soft Actor Critic (SAC) algorithm, with a multi-objective reward that penalises carbon emissions, curtailed on-site renewables, and unmet user demand. The agent is trained within a unified benchmarking framework on the EV2Gym platform, incorporating behind-the-meter solar and wind profiles, time-varying EirGrid carbon intensity data, and realistic workplace EV behaviour across 25 Electric Vehicle Supply Equipment (EVSE) units. Nine control strategies, including heuristics, emission-aware MPC variants, and the proposed RL agent, are compared under five renewable penetration scenarios (0%-50%) over ten independent runs each. The RL agent achieves a carbon intensity as low as 23.96 grams of carbon dioxide per kilowatt-hour under 50% wind penetration, representing up to 87% emission reduction versus the uncontrolled baseline, and outperforms the external graph-based Power Distribution Network (PDN) benchmark. Transformer overload remains below 7 kWh across scenarios, against up to 1093 kWh for the As Fast As Possible (AFAP) heuristic, and renewable self-consumption reaches 52% under combined wind and solar supply. Embedding carbon intensity forecasts into the RL state and reward aligns charging with low-emission periods while preserving grid compliance and user satisfaction.

The residual update of a pre-norm Transformer layer admits an interpretation as one step of a first-order optimizer acting on a surrogate token energy, wherein the attention and MLP sublayers function as gradient oracles. Based on this observation, we build a family of optimizer-inspired Transformers (triple-momentum, Adam/AdamW, Muon, SOAP) and compare them under matched compute. In our main pretraining experiment, the triple-momentum TMMFormer achieves the lowest validation loss, outperforming the vanilla Transformer and prior architectural variants. A controlled ablation and supporting theory show that momentum, not preconditioning, is the main source of the gain. We further show that TMMFormer and other momentum-based designs reach flatter minima than the vanilla Transformer, which leads to less forgetting and better generalization.

Visual geometry transformers have become powerful architectures for multi-view 3D reconstruction, enabling joint prediction of multiple 3D attributes in a feed-forward manner. However, their computational cost grows quadratically with the input sequence length due to the global attention layers inside these models. This limits both their scalability and efficiency. In this work, we address this challenge with a simple yet general strategy: restricting the number of key/value tokens that each query interacts with during global attention. To achieve effective token selection, we introduce a two-stage framework. First, an inter-frame selection step operates at the frame level to identify frames that should be preserved. Second, an intra-frame selection step further discards more redundant tokens within the selected frames. Our analysis highlights the advantage of a diversity-based strategy for inter-frame selection, which ensures broad coverage of the scene. For intra-frame selection, we show that layer-aware sparsification is necessary, with the selection process guided by the entropy of the global attention pattern. Our approach offers a superior speed-accuracy trade-off compared to existing solutions. Extensive experiments show that it accelerates visual geometry transformers by over 85% for scenes with 500 images while maintaining, or even improving, baseline performance, which hints that how our token selection strategy can play a crucial role in future applications of visual geometry transformers. Our project website is available at https://zsh2000.github.io/good-token-hunting.github.io.

We introduce training-free looped transformers, in which a lightweight inference-time wrapper loops a contiguous mid-stack block of layers of a frozen checkpoint without additional fine-tuning, continued training, or architectural changes. Unlike prior looped transformer methods that train with the looped structure end-to-end, we retrofit recurrence onto pretrained models at test time. We show that naive block reapplication usually degrades performance, highlighting the importance of the loop application strategy. Motivated by viewing a pre-norm transformer block as a forward Euler step on an ODE, we instead treat looping as a refinement of the same approximation, replacing one large update with smaller damped sub-steps. Across seven dense, sparse MoE, and MLA+MoE model families, our method improves Qwen3-4B-Instruct by +2.64 pp on MMLU-Pro, Qwen3-30B-A3B-Instruct by +1.14 pp on CommonsenseQA, and Moonlight-16B-A3B-Instruct by +1.20 pp on OpenBookQA.

Vision Transformers (ViTs) can learn strong image-level representations while their patch representations become less effective for dense prediction during prolonged training. We revisit this dense degradation phenomenon and argue that it is not fully explained by high-norm artifacts alone. Instead, we characterize \emph{semantic diffusion}: an optimization shortcut in which global semantic information spreads through patch tokens beyond what is locally justified. Our analysis shows that dense representation quality is not captured by locality alone: shallow features can remain better aligned with foreground regions yet underperform deeper features, and \texttt{[CLS]} features remain complementary for dense prediction. These observations suggest that the goal should not be to remove global context, but to make token interactions more selective. We therefore study sparse attention as a minimal intervention, replacing softmax attention with entmax-1.5 while preserving global token connectivity. On DINOv1 ViT-S/16 trained for 200 epochs on ImageNet-1K, this change preserves ImageNet linear probing accuracy and substantially improves semantic segmentation performance: VOC mIoU increases from 42.80 to 48.78, ADE20K from 19.85 to 21.97, and Cityscapes from 36.79 to 37.87. These results suggest that selective token mixing is a simple and effective bias for improving dense ViT representations.

Distributed Acoustic Sensing (DAS) enables large-scale monitoring through optical fibers, but its high dimensionality and complex spatio-temporal patterns make event classification demanding. Existing deep learning approaches-CNNs, recurrent models, and Transformer variants-either fail to capture long-range dependencies or require processing raw DAS matrices at prohibitive cost. We propose DAStatFormer, a hybrid multibranch Transformer that combines compact multidomain statistical features with Gated Transformer Networks. Instead of raw signals, we extract 24 ANOVA-selected attributes per channel from the temporal, waveform, and spectral domains, reducing data size by orders of magnitude while preserving discriminative information. Each domain is processed via dedicated step-wise and channel-wise attention branches, fused by an adaptive gating mechanism. Experiments on the open $Φ$-OTDR benchmark and a real-scenario DAS dataset show that DAS-tatFormer achieves up to 99.4% accuracy and near-perfect real-world performance, while using significantly fewer parameters and lower inference cost than models such as DASFormer and DeepViT. These results demonstrate its suitability for scalable, real-time DAS-based monitoring. We release our code at https://github.com/MichelD-git/DAStatFormer

Mechanistic interpretability of transformers requires identifying not just which components matter but how they compose into the computational route that produced a prediction. Both attention and MLP follow a shared key-value template $φ(S)U$. We exploit this structure to develop Unpack, a backward recursion that decomposes credit through both sublayers, producing interaction strengths between any two components, named end-to-end paths with K/Q/V composition labels, and per-token attribution from a single forward pass, without intervention, gradients, or auxiliary training. We evaluate on the indirect object identification task. On GPT-2 small, the method recovers all three composition connections described by Wang et al. (2023), including the mode-specific routing of each connection (K, Q, or V). To test token-level attribution beyond trivial copying, we compare two occurrences of the same name in the same decomposition: the first mention retains strong credit while the duplicate-detection position is suppressed, a pattern absent in matched control prompts. Across the Pythia family from 160M to 6.9B parameters, this suppression pattern is consistently recovered at every scale, demonstrating that the method tracks mechanistic structure without ground-truth circuit labels. Code is available at https://github.com/Fun-Cry/unpacklm.

We present a three-step recipe for identifying attention-head circuits in pretrained transformers. A per-head spectral signal -- the time-integrated participation ratio of each head's attention output -- ranks heads doing sustained content-dependent computation without labels or attribution gradients. A task-pattern screen filters this general indicator into a task-specific candidate circuit, and group ablation against a matched-random control completes the causal claim. We validate across an 8x parameter range (51M to 1B-active / 7B-total), two architecture families (dense, mixture-of-experts), and four pretraining pipelines. The recipe ports: a 2-6 head induction circuit is causally necessary in every model tested, with a 94-100% drop in synthetic-induction top-1 after ablation. The spectral signal is predictive without supervision: on six independent seeds of a 51M-parameter probe model, the same computation identifies the seed-specific circuit on each seed. The fraction of heads doing identifiable specialized computation is conserved at 17-19% across the Pythia family (124M to 410M), while specific induction circuits stay 3-11 heads -- sublinear in total head count. This paper is the methodology anchor of a three-paper program; companion papers extend the recipe to developmental trajectories during pretraining and to composed-task circuits where pattern selectivity decouples from task-causal structure.

The Cognitive Categorical Transformer (CCT) is a 306M-parameter architecture that augments a pretrained GPT-2 Small backbone with cognitively grounded components derived from category theory and several inspirations from cognitive science. Under a matched-step protocol (215,000 optimizer steps, matched data, matched optimizer and schedule) on WikiText-103, CCT reaches 21.27 validation perplexity, compared with 24.19 for an identically fine-tuned GPT-2 Small baseline. The architecture therefore contributes a 2.92 PPL (12% relative) reduction beyond what in-domain fine-tuning alone provides. A retrain-from-scratch ablation that holds GT-Full simplicial message passing bypassed across the entire seven-phase activation schedule reaches 23.72 PPL, localizing 84% of the architectural improvement (2.45 of 2.92 PPL) to GT-Full. We present the first ablation-validated evidence that simplicial message passing improves language-model perplexity at the 306M-parameter scale on WikiText-103. Published GPT-2 Large reaches 22.05 zero-shot PPL on WikiText-103 with 6.2x more parameters than GPT-2 Small; this paper treats that number as an external published reference, not as the architectural benchmark. Three negative results on consistency-style categorical priors (sheaf smoothing, adjunction round-trip, curvature regularization) and the joint structural-prior result for GT-Full and PrecisionWeightedPP together support an empirical pattern termed the structure/consistency distinction, in which categorical priors that add new topology improve language modeling and those that enforce a consistency identity do not.

As state-of-the-art neural networks are deployed on reasoning and algorithmic tasks, exactness guarantees become increasingly important. However, high average-case accuracy can still mask inconsistent behaviors. This motivates exact certification, which asks for the smallest set of labeled examples needed to certify that a learned hypothesis equals the target. We show that while some hypotheses are easy to certify, even minimal overparametrization can make certification exponentially hard across several hypothesis classes. For threshold circuits of depth $\ge 2$, adding a single extra gate can force certificate sizes exponential in the input dimension. We show an analogous hardness result for log-precision Transformers with only constant architectural overhead. We also characterize approximate certification, showing that allowing only polynomially many mistakes still requires exponentially large certificates, whereas constant relative-error guarantees can hide exponentially many mistakes. Empirically, we study certification for constructed circuits and trained Transformers for recognizing binary addition. While the constructed circuits instantiate the exponential barrier for certification, the trained Transformer analysis shows that imperfect models can evade detection by large uniformly sampled certificate candidates.

Structured prompts require integrating components according to task-relevant relations. How a network implements this integration is often hard to judge in language or vision, where those relations are rarely specified precisely enough to define a candidate internal algorithm. Arithmetic offers a cleaner setting. We study a Transformer trained on base-digit extraction: given $N$, $B$, and $D$, it must report the coefficient of $B^D$ in the base-$B$ expansion of $N$. The closed-form solution, $\lfloor N/B^D \rfloor \bmod B$, provides explicit candidate algorithmic intermediates. Across three seeds, the model reaches 99.83% exact-answer accuracy on held-out number-base intersections, establishing reliable task competence. Linear probes decode the intermediates, making staged arithmetic computation plausible. Causal tests then separate representation from use: within the localized route from the stream with $D$ as input to the output positions, behavior depends on early $D$-selective communication, independent of $N$ and $B$. Relatedly, a sparse circuit search finds mostly separate $N$, $B$, and $D$ routes that combine late rather than the staged route suggested by the probes. Thus, the model represents the intermediates that make the closed-form solution plausible, but the identified localized causal route does not transmit them to the output stream. This case shows that probe-based conclusions can diverge sharply from causal observations, even when explicit algorithmic hypotheses are available.

We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively. We provide an upper bound depending on the length of the prompt, which we show empirically to be tight up to a factor less than 10, across architectures and model sizes. Our analysis also provides a theoretical explanation for previously observed empirical failures of transformers on simple sequence tasks, such as copying and cramming. Formally, we prove that (i) the maximal length of accessible sequences (those that the transformer can output for some prompt) grows linearly with the prompt length, (ii) beyond a critical threshold, the proportion of accessible sequences decays exponentially with sequence length, and (iii) the linear coefficient relating prompt length to accessible sequence length admits a theoretical upper bound. Notably, these results hold even with unbounded context and computation time.

Backtracking search underlies classical constraint solvers, planners, and theorem provers. Recent transformer-based reasoning systems explore search trees over their own intermediate steps. A common training recipe fits an autoregressive next-token loss on offline solver traces. The model's input at each step is a cumulative trace of all prior decisions. The optimal continue-or-backtrack predictor depends only on the current search state, since two trajectories reaching the same state admit the same viable continuations. We show that decoder-only transformers trained on cumulative traces fail this requirement in two ways: the trace can scatter state features across many positions (scattered retrieval), and the predictor can condition on the trajectory rather than the state (history entanglement). We address scattered retrieval with localization, a trace-level fix that rewrites each decision block to expose state features locally. We address history entanglement with Selective State Attention (SSA), a fixed attention mask that enforces state-based decisions structurally without modifying training data, objective, or parameters. We focus on reactive verification, after propagation has exposed a contradiction. We test SSA on 3-SAT, graph coloring, Blocks World, and backtracking parsing. On same-state pairs that differ only in prior history, SSA emits identical decisions while a cumulative-trained causal baseline does not. Our contribution is a diagnostic of transformer behavior on serialized trajectory data, paired with a structural fix. Pretrained language models that search over their own reasoning steps may face the same failure. Our analysis opens up inference-time context clearing as a candidate way to apply the same isolation without retraining.

Mechanistic interpretability often identifies circuits inside Transformer models, but explanations of those circuits are usually validated through examples, ablations, and manual reasoning. This leaves a gap between finding a plausible circuit and proving what the circuit does. We introduce Verifiable Transformers, a framework for converting task-localized Transformer circuits into bounded, solver-checkable claims. Given a behavior, a finite task domain, and a candidate-token projection, we extract a task circuit and verify properties such as projected functional equivalence, edge necessity, task-relevant invariance, and final-residual robustness. Direct verification encodes the extracted circuit itself into an SMT solver. When a circuit contains operators that are not exactly or tractably encodable, surrogate-mediated verification fits an SMT-encodable surrogate, validates it against the extracted circuit over the bounded domain, and verifies symbolic explanations against the surrogate. We instantiate direct verification with a GPT-style architecture using Signed L1 BandNorm, sparsemax attention, and LeakyReLU. On small symbolic sequence tasks, we train an SMT-representable Transformer, extract sparse circuits for quote closing and bracket type tracking, and exhaustively verify projected functional equivalence, content invariance, edge necessity, and final-residual robustness. At GPT-2 scale, the same operator stack trains stably on OpenWebText, although naive direct SMT verification remains intractable. We also demonstrate surrogate-mediated verification on task-localized circuits with hard-to-encode attention, showing both verified symbolic explanations and solver-generated counterexamples. The goal is not full-model verification, but a concrete path for turning mechanistic circuit explanations into formal propositions that can be proven or refuted.

Sentiment analysis, also referred to as opinion mining, primarily tries to extract opinion from any text-based data. In the context of movie reviews and critics, sentimental analysis can be a helpful tool to predict whether a movie review is generally positive or negative. It can be difficult for the ML models to understand the context or metaphysical sentiment accurately, as ML models rely largely on statistical word representations. The objective of this paper is to examine and categorise movie reviews into positive and negative sentiments. Diverse machine learning models are considered in doing so, and Natural Language Processing (NLP) methodologies are employed for data preprocessing and model assessment. The IMDb dataset is used. Specifically, Naive Bayes, Logistic Regression, Support Vector Machines (SVM), LightGBM, LSTM, and transformer-based models such as RoBERTa and DistilBERT were evaluated. After a lot of testing with accuracy, precision, recall, F1-score, and ROC-AUC, RoBERTa performed better than all the other models, with an accuracy of 93.02%. A soft voting ensemble that combined all the models also improved classification performance, showing that model ensembling works well for sentiment analysis.