Transformers

Rotation-based post-training quantisation commonly applies an orthogonal transform across an entire attention head to reduce outlier-induced error. RoPE instead partitions each head into two-dimensional frequency pairs, raising the question of whether a transform respecting this decomposition can improve on full-head mixing. Prior work has established the per-pair rotations that commute with RoPE. We state the converse result that, for distinct frequencies, no other single-head orthogonal map commutes with RoPE. For the head-shared parameterisation used in our experiments, we then derive the rotation angle that minimises the larger channel variance under a pooled-covariance, position-averaged surrogate and verify that the implementation attains its analytic minimum. The evaluated head-shared pairwise configuration does not improve accuracy in the tested dynamic W4A4KV4 setting. Across four checkpoints, replacing the full-head Hadamard with this configuration increases perplexity at both short and long context lengths. Composing the pairwise rotation with the Hadamard satisfies the selected $\pm0.05$-PPL interval criterion under the default estimator. Estimating the shared angle from K alone improves pairwise-only on every checkpoint but does not close its gap to full-head mixing. The analytic objective controls a position-averaged second moment of a pooled calibration covariance, whereas the dynamic quantiser sets its step from a tokenwise group range. The pairwise transform also has only two-channel mixing support. Along a controlled interpolation from two-channel to full-head mixing, K range, relative quantisation error, and perplexity degradation decrease as support increases. These results show that optimality for a structured surrogate need not reduce quantisation error when the surrogate and mixing support are misaligned with the quantiser's scale-setting statistic.

We ask whether language-model pre-training can be decomposed into smaller, independently trainable jobs that can later be recomposed into a coherent larger model. We introduce Mixture of Training (MoT), a scaffolded modular pre-training procedure that partitions a target Transformer into contiguous layer blocks, trains each block inside a frozen pretrained aligner scaffold, and then recomposes the trained blocks with an optional short end-to-end adaptation pass. On a 1.3B-parameter Gemma-style model trained on C4, MoT provides a small-scale proof of mechanism: independently trained depth slices can be recomposed into a usable language model, and a quality-parity schedule reaches the same reported perplexity as the monolithic baseline. This parity setting processes more aggregate tokens and has a shorter idealized layer-equivalent critical path after aligner preparation; its effective compute advantage depends on reusing the aligner across runs. We therefore present MoT not as a general replacement for monolithic pre-training, but as a small-scale framework for studying whether scaffolded sub-runs can act as reusable training units.

Large language model serving faces a critical memory bottleneck: the KV cache grows with sequence length and batch size. PagedAttention uses fixed-size memory blocks to reduce allocator-level fragmentation, but recent KV eviction algorithms operate at a token granularity finer than block-level management. This mismatch causes intra-block fragmentation, leaving a large fraction of allocated KV memory unreclaimable. We present vToken, a lightweight token-level virtualization layer that decouples logical token liveness from physical block placement. vToken maintains a stable logical token view through token-table indirection and realizes physical reclamation by repacking live tokens asynchronously. The design preserves PagedAttention kernels and CUDA Graph compatibility. We implement vToken in vLLM and evaluate it with H2O, Random, and Scissorhands across models. Compared with a paired Naive-Evict baseline, vToken reduces retained KV blocks per request by 27.2%--72.3% and improves SLA-constrained throughput by up to 1.37$\times$. Under a constrained active-KV budget, it extends the maximum feasible concurrency by up to 2$\times$, while reducing the per-policy integration footprint from 500+ lines to under 50.

Accurate modeling and forecasting of power transformer thermal behavior are critical for reliability, asset lifetime, and optimized power system operation. Numerical approaches such as finite element methods (FEM) and computational fluid dynamics (CFD) offer high fidelity but are computationally expensive, require complex mesh generation, and are often impractical for real-time or large-scale applications, particularly when transformer geometries are unknown. Lumped-parameter thermal models are more practical but depend on transformer-specific thermal constants and may fail to capture dynamic responses under varying operating and environmental conditions. Purely data-driven machine learning methods, including artificial neural networks, convolutional neural networks, and long short-term memory (LSTM) networks, have shown success in forecasting transformer temperatures but typically require large volumes of high-quality training data and may produce physically inconsistent or uninterpretable results. This paper develops a physics-aware Neural Ordinary Differential Equation (Neural ODE) framework for forecasting transformer thermal behavior from real-world time-series data. Neural ODEs model system dynamics in continuous time, providing smooth trajectory prediction and a natural representation of continuously evolving thermal dynamics. A key contribution is the integration of simplified heat-transfer equations directly into the Neural ODE formulation. The model is evaluated across datasets from fifteen transformers in different regions of Norway with varying designs and cooling mechanisms. The results demonstrate that the developed Neural ODE framework provides a standardized, physics-aware, and robust forecasting approach for heterogeneous transformer units.

Convolutional Neural Networks (CNNs) capture local features efficiently but struggle with global context due to their limited receptive field. On the other hand, transformers effectively capture global dependencies through self-attention but suffer from high redundancy and computational costs. Thus, to leverage the advantages of both CNNs and transformers, we propose a unified model (UniCon-Former) that aims to provide robust and efficient performance on dynamic hand gesture recognition. The unified approach helps the model to learn both local and global features. At the beginning of each transformer stage, the convolution projections help in decreasing the dimension of the input vectors of the transformer block. This creates a pyramidal structure at each transformer stage. These features enable the UniCon-Former to reduce resource usage than vanilla transformers, making it flexible for learning multi-scale and high-resolution features, which is required in hand gesture recognition. We have performed experiments with NVGesture and Briareo datasets and achieved state-of-the-art results with fewer parameters and MACs.

Vision Transformers (ViTs) demonstrate exceptional performance in computer vision but suffer from large parameter counts and quadratic computational complexity, severely limiting their deployment on resource-constrained edge hardware. While recursive weight-sharing reduces parameter counts and token merging mitigates computational and memory bottlenecks, integrating these two paradigms without costly retraining is non-trivial, leaving this intersection largely unexplored. We propose MergeOver, a post-training approach that integrates Token Merging (ToMe) into the recursively weight-shared Sliced Recursive Transformer (SReT). Through an Unmerge tracking stack, constraint-safe merge-rate adjustment, and synchronised token-mass tracking across spatial permutations, MergeOver resolves the spatial and merging constraints of this integration. We further employ a stage-wise single-shot schedule that performs token reduction at the first block of each stage and maintains a fixed sequence length throughout its subsequent recursive iterations. Benchmarked on ImageNet-1K, our selected configuration reduces top-1 accuracy by 1.47 percentage points. On the GPU, it reduces peak activation memory by 37.3% and 38.4% at batch sizes 1 and 16, while throughput decreases by 21.7% at batch size 1 but increases by 21.7% at batch size 16. On a Raspberry Pi 5 (ARM CPU), it reduces latency by 2.4% and 17.6% at batch sizes 1 and 16. These results show that MergeOver can recover a meaningful part of the throughput and memory cost that recursive weight-sharing introduces, without retraining, and provides a baseline for combining token merging with hierarchical recursive transformers.

Diffusion Transformer Text-to-Video models have achieved remarkable synthesis quality, yet fine-grained spatial controllability remains a significant challenge. While existing training-free methods produce solid overall results in spatially grounded generation, \ie, placing a specific object in a designated location, they rely on gradient-based optimization techniques that incur prohibitive computational overhead, a bottleneck amplified in modern large-scale architectures. To address this limitation, we present Gradient-free Analytical Trajectory Optimization Video Generation (GATO-Vid), a novel training-free and gradient-free approach for precise spatial guidance. Rather than relying on costly backward passes, we introduce an alternative cross-attention score and solve it analytically to obtain an exact, closed-form solution. To use our analytical solution, we propose an on-the-fly injection mechanism tailored to the topological manifold of the transformer's latent space. Our experiments demonstrate that GATO-Vid significantly outperforms existing baselines in localization accuracy while introducing minimal computational overhead.

Multimodal Diffusion Transformers (MM-DiTs) have demonstrated remarkable text-to-image generation performance, surpassing traditional U-Net-based diffusion models. Nevertheless, their powerful generative capabilities also raise significant safety concerns, as they may generate sensitive or inappropriate content. While existing concept erasure methods aim to mitigate such risks, most require modifying model parameters, which are often architecture-specific and impractical for deployed larger models. Several tuning-free approaches face challenges when applied to advanced large-scale MM-DiTs due to their deeply embedded knowledge, broad semantic space, and context-dependent text encoders. To address these challenges, we propose to erase concepts by directly manipulating the model's internal representations. Our key insight, derived from an in-depth analysis of MM-DiT's block-wise generative roles, is that text-conditioned semantic representations are most salient in the middle blocks of MM-DiTs. Based on this, we extract representations of an unwanted concept and a desirable safe one from the middle block, construct a steering vector from their difference, and inject this single vector into consecutive early and middle blocks. By operating exclusively on the sparse text-branch tokens and leveraging the straight sampling trajectory of rectified flow, our method achieves effective concept erasure with negligible overhead and without any training. Extensive experiments across MM-DiT models demonstrate that our method achieves state-of-the-art performance in erasing diverse concepts, enables effective control over the final output, and remains robust to adversarial attacks.

Diffusion Transformers (DiTs) incur quadratic self-attention cost over spatiotemporal tokens. Existing training-free sparse attention methods often construct sparse masks from block-level or cluster-level proxy scores, which can obscure fine-grained differences among keys and miss high contribution keys under aggressive sparsity. Moreover, such proxy scores may yield overly concentrated softmax distributions, causing Top-$p$ to retain too few keys for some query clusters. Although a fixed Top-$k$ minimum alleviates this failure mode, a shared value cannot adapt to variations across heads and inputs. To address both limitations, we propose SCOPE, a training-free sparse attention framework that combines 3D-RoPE-aligned key subspace clustering with online per-head Top-$k$ estimation for efficient video-DiT inference. SCOPE partitions post-RoPE keys into temporal, height, and width subspaces, clusters them independently, and aggregates the corresponding centroid scores through lookup tables to obtain per key proxy scores for each query cluster. Building on existing hybrid Top-$p$/fixed Top-$k$ selection, SCOPE derives a head-specific Top-$k$ value online by averaging the initial retained key counts within each head, weighted by query cluster size, and selects additional keys only for query clusters whose initial retained key counts fall below this value. Sparse attention is then computed over the selected original keys and values. Across six model--task configurations, SCOPE consistently outperforms existing training-free baselines in both fidelity and latency, achieving up to a $1.99\times$ end-to-end speedup on 720p HunyuanVideo with $28.46$ dB PSNR relative to dense attention.

Multi-layer transformers form the critical component of essentially all large language models (LLMs) in use today. Because of their ubiquity and computational capability, there is a rapidly growing body of work that aims to precisely calibrate the expressive power of transformers as language recognizers by comparing them against standard models of computation studied for decades by the theoretical computer science community. In this endeavor, circuit complexity has by and large emerged as the "correct" branch of computational complexity to analyze the expressive power of transformers; the reason is that parameterizing transformers by the various resources they use, such as attention and precision, leads to direct comparisons with different classes of circuits parameterized by resources such as type of gates, size, and depth. Here, we present an overview of selected results that delineate the expressive power of transformers using concepts and methods from circuit complexity.

Class activation mapping (CAM) is one of the most widely used visual explanation families in explainable artificial intelligence. Its purpose is intuitive: it converts internal model evidence into a heatmap that highlights the image regions, convolutional channels, tokens, or patches that support a target class or concept. Since the first CAM formulation in 2016, the field has moved far beyond global-average-pooled CNN classifiers. CAM-style methods now include gradient-based post-hoc explanations, gradient-free score and ablation methods, high-resolution upscaling, weakly supervised localization and segmentation, transformer token attribution, causal and debiasing methods, and foundation-model-era approaches that use CLIP, DINO, SAM, or feature-distribution comparisons. This review synthesizes a strict corpus of 57 method-centered papers published from 2016 onward. The paper develops a taxonomy that separates methods by attribution mechanism, architectural dependence, and evaluation objective. It then reviews gradient-based CAMs, recent and hybrid CAM-style methods, and model-based or architecture-aware methods. Across the corpus, the main trend is clear: the field is shifting from explaining one class score in one low-resolution CNN layer toward comparative, multi-layer, probabilistic, token-aware, and foundation-model-aware explanations. At the same time, evaluation remains fragmented. Faithfulness, localization, robustness, computational cost, and human trust are often measured with different protocols. The review therefore emphasizes not only what each method contributes, but also which gap it leaves open and which later methods attempt to close that gap.

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

Background: Accurate segmentation of the Left Anterior Descending (LAD) artery in 3D free-breathing, non-contrast CT is critical for cardiac dose sparing in thoracic radiotherapy. The LAD is extremely small, has poor soft-tissue contrast, and varies substantially across patients; even manual contours show limited inter-observer agreement, underscoring the ambiguity of the vessel boundaries. Purpose: To develop a transformer-based framework that improves LAD delineation in low-contrast, imbalanced CT through local-global context modeling and uncertainty-guided optimization. Methods: We propose NA-UNETR, a 3D transformer-based segmentation model whose Neighborhood Attention (NA) and Dilated NA (DiNA) blocks jointly capture fine structural detail and long-range context. Given the scarcity of annotated LAD data, the model is pretrained on 1,000 CTA volumes of general coronary anatomy and fine-tuned with LoRA-based parameter-efficient adaptation on 20 free-breathing institutional CT scans. A composite Dice-Focal and Hausdorff loss, dynamically balanced via homoscedastic uncertainty, improves overlap and boundary accuracy. Results: NA-UNETR reached 45.64% Dice, 38.16 mm HD95, and 10.01 mm ASD, improving Dice by 3.10 percentage points over nnU-Net and reducing HD95 by 2.96 mm relative to Swin UNETR, with the strongest boundary accuracy among all models and improved centerline stability. On ImageCAS it achieved 79.49% Dice, 8.89 mm HD95, and 1.02 mm ASD. Ablations confirmed that residual blocks, variable kernels, and uncertainty-weighted loss each contributed. Conclusions: NA-UNETR balances local precision and global context for thin, low-contrast LAD structures, offering a computationally efficient framework for substructure-level cardiac segmentation in radiotherapy planning.

Transformer-based methods have achieved strong performance in monocular 3D human pose estimation, but most existing approaches organise spatial and temporal reasoning as separate stages, which may weaken unified spatial-temporal interdependencies inherent in human motion and compress frame-level structural information before temporal modelling. In this paper, we propose HSTGFormer, a graph-enhanced Transformer framework that reformulates spatial-temporal reasoning as localised coupled graph aggregation over joint-time nodes. Specifically, HSTGFormer introduces a Hyper Spatial-Temporal Graph (HSTG), which decomposes global spatial-temporal reasoning into local spatial-temporal receptive fields around individual joint-time nodes by extending per-frame skeleton graphs into temporal neighbourhoods, thereby enabling structure-aware coupled reasoning while preserving local structural motion information. It further incorporates an Adaptive Dual-Scale Temporal Graph (ADSTG) to capture joint-specific temporal dependencies over complementary short- and long-range windows. A lightweight node-wise fusion module further adaptively integrates the two graph representations for each joint-time node. Experiments on Human3.6M and MPI-INF-3DHP show that HSTGFormer achieves strong accuracy with high computational efficiency.

Video diffusion transformers are costly to sample: every denoising step applies self-attention over a long 3D token sequence, a quadratic cost that dominates as resolution and duration grow. Sparse attention reduces this cost without retraining, but existing methods pursue aggressive sparsity, where further speedup costs disproportionately more attention fidelity. We target the opposite end of this trade-off: fix near-lossless fidelity by construction, and remove as much computation as this constraint permits. Two observations make this regime practical: roughly 40% of block interactions can be removed while retaining 99% of the attention mass, and the high-mass support remains stable across denoising steps. We propose LoSA, a training-free sparse-attention method that fixes a retained-mass threshold of 99% rather than a sparsity ratio: it measures exact block attention masses at one early dense step, keeps, for each head and query block, the smallest key/value block set meeting the threshold, and reuses the frozen block indices for all remaining steps. On Wan2.1-1.3B, LoSA alone gives a $1.36\times$ speedup with a 0.06-point VBench Overall drop. The benefit is largest under composition: combined with feature caching, LoSA reaches a $3.2\times$ speedup on HunyuanVideo at a 0.02-point drop, versus 0.32 points for the strongest sparse baseline at comparable speed. Across three video diffusion transformers and speedups up to $3.2\times$, LoSA consistently achieves the best training-free speed-quality trade-off.

Two accounts recur in explanations of the success of rotary position embeddings (RoPE). Expressivity studies associate periodic position information with modular predicates, whereas mechanistic and long-context studies emphasize positional anchors and local offsets. We formalize both accounts for fully uniform, finite-precision soft-attention transformers. We find that, if every rotary component is periodic, RoPE transformers recognize exactly the languages definable in past temporal logic with modular predicates. Conventional RoPE is different: The rotations it computes never repeat. This yields a precision-dependent bounded simulation of fixed-offset look-back operators, rather than an all-length modular characterization. Controlled experiments match this separation: Constructed periodic schedules length-generalize on modular languages, while conventional RoPE behaves more like a bounded locality bias and can impair tasks requiring position-invariant access to distant context. Altogether, our findings shed light on RoPE transformers, bringing theoretical expressivity characterizations closer to models used in practice.

Self-attention has become central to spiking vision transformers, yet its query-key scoring is still largely inherited from dense networks. Existing spiking variants either simplify dot product scoring or replace it with discrete operators, but spike timing, the native variable of a spiking network, does not directly define how tokens are related. We propose Lapis, a spiking attention mechanism that scores each token pair by the L1 distance between its query and key first-spike latency vectors under time-to-first-spike coding, and maps this distance to an affinity through a Laplacian kernel. The kernel's exponential decay matches the impulse response of a leaky integrate-and-fire membrane, so the accumulated latency difference determines the decay of a membrane trace, while row normalization reduces to a bit shift under power-of-two rounding. Scoring therefore needs only subtraction, absolute value, and accumulation, and removes all multiplication between query and key channels. Under a matched backbone and training schedule, Lapis reaches 96.56% top-1 accuracy on CIFAR-10, within 0.53 points of dot-product scoring. On ImageNet-1K, it reduces the estimated arithmetic energy of the attention path by 14.5x relative to dense dot-product attention. The deployed 6-bit model attains 83.25% top-1 accuracy at an estimated arithmetic energy of 3.28mJ per image.

Scaling laws promised cost-effective experiments; six years later, they have yet to fully deliver. Instead, researchers have found them unreliable at small scales (starting at 4M parameters) and concluded that sizable models cannot be avoided. We show this is not the case: the confounding factor is hyperparameters. Small models are highly sensitive, but hyperparameter sensitivity fades with scale. This small-scale sensitivity makes scaling laws easy to miss because they only emerge on the fully tuned frontier, and reaching that frontier requires an extensive search far beyond what most ever run. By ablating the basic scaling law recipe, we show well-tuned hyperparameters matter more than any other ingredient. Further, we reveal why those hyperparameters become easier to find: as scale increases, the hyperparameter loss surface becomes lower dimensional. Nevertheless while scaling laws exist in small models, extrapolation hits statistical limitations. A holistic approach is required. Synthesizing our insights with the recent literature, we develop a new methodology for model-centric research and demonstrate it on a question that once took the field years to settle: where to place normalization layers in the transformer architecture. From small-scale experiments, we recover the large scale result: pre-normalization works better as models grow in size. With the right tools and a better understanding, small-scale experiments can deliver on scaling laws' long-awaited promise.

Financial text is produced and interpreted within a market environment, yet financial text classifiers almost always receive text alone. We study whether financial time series are useful as an additional input on the task of classifying sentences from Federal Reserve communication as hawkish, dovish, or neutral. Our system, \lfts{}, extends the \lf{} architecture with this modality: a small voting network combines three independently trained components, a fine-tuned RoBERTa encoder, a prompted large language model (LLM), and a fused ensemble of time-series transformers over the market series of the months preceding publication. Because only about a thousand annotated sentences are available for training, the RoBERTa encoder is first pre-trained on sentences annotated automatically by the LLM and only then fine-tuned on the human labels. Trained on Federal Open Market Committee (FOMC) communication up to 2015 and evaluated on 2015--2022, the fused system achieves 70.2% weighted F1 -- against 64.1% for the zero-shot LLM -- and overtakes it with as few as 240 human-labelled sentences. We take this as initial evidence for market time series as an input modality in financial text classification.

The prevailing recipe for Vision-Language-Action (VLA) models couples a pretrained VLM with a separately trained flow-matching action expert. This makes the VLM a context encoder rather than a decision-maker. We introduce G0.5, a pretrained autoregressive VLA in which a single transformer decoder emits reasoning and action tokens under a single objective. Three components make this tractable at foundation-model scale: a learnable cross-embodiment action tokenizer that maps heterogeneous robot actions into a shared vocabulary; a native chain-of-thought stream interleaving task decomposition, object grounding, and action hints with action tokens; and a visual memory module that injects multi-second history through the vision encoder. Because reasoning and action share a single set of weights, the pretrained VLM's capabilities carry over to physical behavior: the model follows instructions closely, and prompts directly steer action granularity, task horizon, and out-of-distribution scene handling without further training. Pretrained on a large collection of robot datasets together with VQA samples, G0.5 surpasses state-of-the-art models across 7 independent regimes: real-world fine-tuning on R1lite and R1pro robots (76.7% vs.\ 53.3% for $π_{0.5}$ and 24.4% for GR00T-N1.7), the 2025 BEHAVIOR Challenge on 50 long-horizon household mobile manipulation tasks using a generalist policy (31.4% vs.\ 26.3% for $π_{0.5}$ and 26.1% for the challenge winner), DROID post-training followed by zero-shot transfer to an unseen environment and objects (82.5%), a language-following Pick-and-Place benchmark, LIBERO (98.9%), RoboTwin 2.0 (93.3%), and SimplerEnv-Bridge (87.3%).

A multiplicative dual-encoder network computes a real-valued output for a pair of inputs as the inner product of their separate encodings. This architecture has been developed independently in operator learning, bipartite matching, contrastive vision-language models, retrieval, and other areas, yet no unified theory guides the basic design decisions: how many interaction modes to represent, how to normalize the encoders, and when the architecture should be avoided. We provide such a foundation by introducing the class of functions of low interaction rank, a class whose intrinsic complexity is measured by its interaction spectrum. Within this framework, approximation error decomposes into a spectral truncation term and an encoder-realization term; sample complexity is governed by the sum of the two encoder complexities rather than their product; and a usability criterion based on spectral decay determines when the architecture can succeed. The same framework exposes a central identifiability problem: the encoders are defined only up to a linear gauge symmetry that leaves the learned coordinates arbitrary. We show that normalization is gauge fixing and that whitening pins the interaction modes up to permutation and sign, thereby explaining the uninterpretability of contrastive dimensions and providing a constructive remedy. Experiments on synthetic kernels, operator learning, and CLIP models validate the theoretical predictions: spectral decay rates match the predicted scaling, whitening recovers the true modes, and independently trained CLIP models are related by a single rotation which, after removal by whitening, exposes interpretable concept axes. The code of this paper is provided at https://github.com/RS2002/Mul-Net .

Full attention exposes every token pair, whereas kernel attention compresses a sequence into a fixed-dimensional sketch. We show that this distinction becomes exponential at the first context length containing two competing candidates. On Min-IP over Boolean inputs, rank-one normalized kernel attention solves every sequence of length at most two exactly. In contrast, any single normalized nonnegative kernel-attention head that succeeds on all three-token sequences with error strictly below $1/2$ requires $2^{Ω(m)}$ features, even with arbitrary finite-dimensional tokenwise values and an arbitrary query-dependent affine readout. Dense softmax solves the same task with $m$-dimensional scores and constant temperature. The conclusion survives position-dependent token maps and a causal final query. As context length grows, the lower bound approaches the exact $2^m$-feature realization. Separately, for deterministic multihead, multilayer sketch models whose cross-token channels have finite alphabets, we prove a transcript lower bound linear in the number of independent answers and logarithmic in their alphabet size.

Sign language translation has achieved strong results with Transformer architectures, yet recent improvements largely rely on scaling model capacity at the cost of increased computation. We propose a parameter-efficient alternative that improves expressiveness without increasing model size. Rather than scaling capacity, we focus on enhancing the update dynamics of iterative refinement decoders, where each refinement step corresponds to one internal decoder iteration that progressively improves the latent representation before translation generation. We reinterpret residual refinement updates from an Ordinary Differential Equation (ODE) perspective and replace them with higher-order numerical integration schemes, namely Runge--Kutta methods (RK-2 and RK-4). These methods perform multiple function evaluations within each refinement step to produce more accurate and stable representation updates without adding decoder parameters. To the best of our knowledge, this is the first application of ODE-inspired update dynamics to sign language translation. RK-2 achieves 22.96 BLEU-4 on the PHOENIX-2014-T test set and 19.34 BLEU-4 on the CSL-Daily test set, outperforming the IPSLT baseline on both benchmarks, with fewer decoder layers and refinement iterations on CSL-Daily. These results suggest that stronger refinement dynamics can improve translation performance under parameter-efficient decoder designs, providing a complementary alternative to conventional model scaling.

The attention mechanism forms the foundation of many modern AI models such as the Transformer. In one subclass of problems where attention is used, inputs and outputs are bound to the probability simplex so that all outputs sum to one. In this setting, softmax attention admits an exact, component-by-component quantum realization. Attention scores are Hadamard-test statistics on block-encoded projections of amplitude-encoded inputs. The exponential softmax is the interior of a cosine-squared family generated by Born-rule measurement under an exact bijection, whose boundary expresses sparse attention with exact zeros at finite parameter values. The softmax temperature is a repetition count where post-selected measurement rounds realize discretized inverse temperature exactly. Value aggregation is a deterministic column-loading channel that dilates the column-stochastic value matrix. The gated residual is the preparation angle of a single ancilla, with the additive identity at a mixing angle of π/2. Every learnable parameter is a rotation-gate angle. The composed layer is exact in the infinite-shot limit with one measure-and-reload step per attention score; a fully-coherent variant is ε-approximate via quantum singular value transformation in the infinite depth limit. The algebraic core is machine-checked in Lean 4.

The strong performance of foundation models for tabular tasks comes at substantial inference costs. Distilling models into task-specific architectures reduces model size and computational demands but also sacrifices in-context adaptability. Here we introduce TACTICL, an automated task-aware compression framework for tabular in-context learning models that jointly prunes transformer layers and replaces them with lightweight adapters trained on downstream tasks, thus blending in-context with in-weight learning. We study TACTICL on 47 benchmark datasets and show that we can substitute up to 85% of layers without substantial performance drop on a given downstream task. We further show that TACTICL maintains robustness to data shifts, leaving its in-context ability intact. Overall, TACTICL provides a robust framework for exploiting the depth-wise redundancy of tabular foundation models by combining task-specific adaptation and structured compression. We provide the code at: https://github.com/Hebog/tfm_compression

Vision-Language-Action(VLA) models map camera images and language instructions directly to motor commands through a single autoregressive transformer. In real-time control, they still spend substantial compute recomputing key-value(KV) representations for visual tokens that barely change across neighboring frames. Recent work such as VLA-Cache reduces that cost by reusing KV states for visually static patches, but its policy relies only on observation-space heuristics and does not account for the model's own uncertainty. We propose Gated VLA-Cache, a lightweight, training-free extension that augments visual-similarity caching with neural introspection. The method monitors the logit margin between the top two predicted action tokens, a zero-cost confidence signal available during decoding. When the margin drops below a threshold, the cache is invalidated and a full recompute is triggered. Evaluated on four LIBERO benchmark suites with both OpenVLA and OpenVLA-OFT, Gated VLA-Cache improves reliability when blind caching hurts. On LIBERO-Goal and LIBERO-Long, it recovers over 100% of the lost accuracy while retaining 80% of the compute savings.

Reliability estimation of large language models is in many cases as crucial as their accuracy, as reliable models are more trustworthy, robust, and suitable for practical applications. Recent advancements in natural language processing (NLP), particularly those based on transformer architectures, have significantly accelerated progress across various NLP tasks. This study focuses on the reliability of transformer-based question answering (QA) models, specifically BERT models and its variants (RoBERTa, ALBERT, DistilBERT). These encoder-only pretrained transformers have demonstrated remarkable accuracy in QA tasks that can be treated as classification tasks. However, their reliability remains underexplored. This study evaluates the reliability of four BERT-based models by assessing response stability under two conditions: (1) internal model variations induced via Monte Carlo Dropout (MCD) and (2) input perturbations through paraphrasing. Using the SQuAD and QuAC datasets, we investigate how dropout rates affect prediction consistency and whether lexical changes impact answer stability. Our findings reveal that RoBERTa maintains higher reliability, whereas AlBERT and DistilBERT exhibit significant inconsistencies. Statistical analyses confirm that enabling MCD during prediction does not disrupt inference dynamics, validating its effectiveness as a reliability metric. These findings underscore the importance of evaluating both accuracy and stability in QA models to ensure stability in real-world applications.

A transformer's answer lives on one axis: the direction its unembedding reads. Its intermediate states largely do not, and that off-axis position is usually treated as an obstacle to interpretation. We show it is functional. A 12-layer model computes in two phases. Through the first, every sublayer writes into a subspace held near-orthogonal to the read-out, attention 75 to 96 degrees off it at every depth. Moving attention's values onto the read-out is 64 to 84 times more damaging than a matched random rotation, and the damage is entirely in cross-token mixing: the subspace insulates composition from the vocabulary. Beneath it the frame itself turns rigidly with depth. In the second phase the answer arrives on-axis, late, and by addition rather than by turning accumulated content onto the read-out. Pressing every layer onto the read-out instead, as training for early exit does, matches the baseline on perplexity, LAMBADA and BLiMP while cutting the concept-phase workspace from about twenty-five effective dimensions to fourteen, a change none of those benchmarks register. The geometry can also be imposed, though not by asking for it. Prescribing it through the loss is a lottery: six of eight seeds collapse, because a model told to null its read-out projection obeys most cheaply by discarding dimensions. Inserting one fixed rotation at the phase boundary lands it instead, at baseline quality. A sparse rotation the surrounding weights can absorb converges on all nine seeds, against five of nine for ordinary training. Which rotation is immaterial: twenty-five runs across thirteen distinct ones reach the same quality, and two baselines from different seeds hold their concepts in near-orthogonal frames while agreeing on their read-outs. That freedom is usable: a basis drawn at random and prescribed before training is adopted across the concept phase, with quality unchanged.

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

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

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

We present a linearized form of 2-simplicial attention by rewriting the trilinear score as an inner product between a composite query and a key, so that the sum over one token axis takes the same form as ordinary softmax attention. We then approximate this sum with positive random features and store the entire past in a fixed-size state, while the second axis stays explicit over a short window of recent tokens. This enables us to achieve linear cost in sequence length combined with a global reach that windowed 2-simplicial attention lacks. We implement it with custom Triton kernels and combine it with Kimi Delta Attention to build a model with no softmax attention at all. Under matched compute, this model achieves the highest mean downstream accuracy among the compared architectures, and at 16k context it improves mean accuracy over a KDA hybrid while lowering LAMBADA perplexity from 715.6 to 602.6.

Query-Key Normalization (QK-Norm) improves the training stability and quality of modern Large Language Models (LLMs). However, under Tensor Parallelism (TP), layerwise QK-Norm introduces additional cross-GPU communication because the normalization factor depends on the full hidden vector. We present SwiftQK, a multi-GPU RMSNorm kernel that exchanges only scalar normalization statistics and overlaps the remaining Peer-to-Peer reduction with independent element-wise computation in a deadlock-safe persistent kernel. Evaluations on recent LLMs show that SwiftQK reduces QK-Norm latency by 81.4--93.9% relative to the standard TP QK-Norm using full-vector All-Gather. In end-to-end serving, SwiftQK reduces TPOT on average by 29.5% over the All-Gather-based baseline and by 14.3% over an optimized scalar-aggregation implementation.

Autoregressive transformers compute along two axes: horizontally across generated tokens, and vertically through model depth. Dense attention gives each token broad horizontal access to the past, but the vertical feedback channel between decoding steps remains narrow: only the sampled token returns to the bottom of the stack, while the top-layer hidden state is discarded. We introduce the \emph{full-bandwidth transformer}, which widens this channel with \emph{latent feedback}: at each decoding step, the previous top-layer hidden state is fused with the sampled token embedding through a gated linear unit and fed back as the next input. Latent feedback lets non-verbalized computation re-enter the stack with a renewed depth budget, while preserving the standard transformer architecture, KV cache, and language-modeling objective. To train full-bandwidth transformers without losing parallel teacher forcing, we use a scheduled multi-pass objective that introduces latent feedback late in pretraining and mixes a small fraction of deeper feedback passes for stability. We train 1B-parameter full-bandwidth transformers up to 400B tokens and find that latent feedback improves validation loss, 5-shot language-model evaluation, math and coding generation, and instruction-tuned performance. With negligible per-token decoding overhead, full-bandwidth transformers match or approach standard transformers trained with roughly $1.5\times$ more tokens, and manage to produce shorter reasoning traces at equal or better accuracy.

Transformer-based large language models (LLMs) achieve strong performance across many tasks, but their Key-Value (KV) cache grows linearly with sequence length, creating a severe memory bottleneck for long-context inference. Existing heuristic eviction methods (e.g., H$_2$O and SnapKV) rely on static attention or positional signals that often fail to capture a token's future predictive influence. We propose DistillCache, a reinforcement learning framework that formulates KV-cache eviction as a sequential decision problem. DistillCache learns a lightweight policy network using rich internal model signals (attention statistics, value norms, entropy, and position) and trains it with REINFORCE via a per-step KL-divergence reward to preserve the full-cache output distribution. On a 7B-parameter instruction-tuned Transformer (Mistral-7B-Instruct-v0.3), DistillCache retains 94.2% of full-cache accuracy on LongBench at a 25% cache budget, outperforming both strong heuristic baselines (H$_2$O, SnapKV) by up to 2.7 absolute points and, under our re-implementations, concurrent RL-based methods (ForesightKV, RLKV) by up to 1.4 points on long-context tasks. On reasoning benchmarks, DistillCache is competitive with the best concurrent method and surpasses it under aggressive compression. It also delivers up to 2.1x full-cache throughput while maintaining competitive practical efficiency. These results highlight the effectiveness of learned, distribution-aware policies for memory-efficient long-context LLM inference.

Activation steering edits the behaviour of a frozen language model by adding a learned vector to its residual stream, and current practice fixes the injection layers globally per task. We argue that the best layers are an instance-level decision, and we make per-instance, multi-layer selection both well understood and deployable. On two open-weight 8B models and six binary persona traits, a per-instance oracle over layer subsets shows that the best layers vary from one input to the next: on most trait-model pairs, no fixed global layer set recovers the per-instance benefit. A greedy rule that ranks layers by single-layer marginal effect recovers nearly all of the oracle's benefit, but both must score candidate layers against the gold answer, so neither can run at deployment; the rule instead becomes the target a prompt-only predictor is trained to reproduce. Our deployable recipe needs no label at inference: a per-instance layer ranker read off the prompt embedding, a classifier that infers the steering direction, and an adaptive gate that scores short steered passes against that inferred direction and steers no more layers than necessary. The recipe recovers most of the oracle's lift (the bulk on the stronger model, a clear majority on the harder one), never drives any trait-model pair below its unsteered alignment baseline on average, and largely avoids the fluency collapse that strong global selection incurs at higher layer counts. A mechanistic account, "direction over magnitude", explains the behavioural flip under a mis-directed global set, the output collapse from steering too many layers, and the ceiling of unsteerable inputs.

Long-context LLM inference is bottlenecked by KV cache memory, yet distributing a limited cache budget across layers remains challenging. Existing methods rely on proxies such as layer depth, attention statistics, or representation change. These proxies do not measure how perturbations at each layer propagate to the output and may therefore cause sensitive layers to be underallocated while tolerant layers are overallocated. To address this issue, we propose RippleKV, which allocates cache across layers by estimating how perturbations to each layer's value cache affect the final predictive distribution. RippleKV independently injects norm-adaptive perturbations into each layer's value cache and measures the induced KL divergence at the model output over a small calibration set. Averaging these responses yields a sensitivity profile specific to the model that need not vary monotonically with depth. RippleKV then converts the sensitivity profile into layer budget multipliers by normalizing the sensitivity scores and applying an exponential mapping. A ratio parameter controls the allocation disparity between sensitive and tolerant layers, while a final normalization preserves the KV cache budget. Experiments on LongBench demonstrate that RippleKV achieves the highest average performance among the evaluated KV cache compression methods under matched cache budgets.

Self-attention models content-dependent interactions between tokens but does not by itself encode token order. Position encoding addresses this limitation by introducing absolute coordinates, relative distances, or position-dependent rotations into Transformer representations and attention scores. This technical survey develops a unified account of sinusoidal and learned absolute position embeddings, Shaw-style relative position representations, Transformer-XL, T5 relative position bias, ALiBi, and Rotary Position Embeddings (RoPE). We derive how RoPE converts absolute position indices into relative phase differences in Query-Key inner products and compare these methods in terms of where position is injected, computational cost, compatibility with KV caching, and length extrapolation. We then examine long-context extensions, including Position Interpolation, RoPE scaling laws, NTK-aware scaling, Dynamic NTK, NTK-by-parts, YaRN, LongRoPE, and LongRoPE2, with emphasis on frequency allocation, attention rescaling, training length, and target context length. We also summarize implementation considerations, evaluation protocols, and position-encoding choices in representative large language models. A central conclusion is that the ability to compute positional features beyond the training length does not imply reliable long-context generalization; context extension must be evaluated through short-context retention, position-wise perplexity, retrieval, reasoning, and long-context code tasks.

The CVPPA@ECCV 2026 BuzzSpot Challenge asks us to detect bees, bumblebees, hoverflies, and moths in 1920x1080 field keyframes. Its annotations carry 2 difficulties: the median box occupies 0.16% of a frame, and bees account for 80% of the labels. To cope with the small boxes, we compare 10 recorded detector configurations on held-out keyframes; plain Co-DINO with a Swin-L backbone has the highest mAP in this comparison, so we select it. Training then addresses the bee dominance in 2 ways: fine-tuning on a crop-mosaic pool in which the combined annotation share of the 3 rare classes rises from 19.9% to 55.1%, and a class-weighted simplex equiangular tight frame (ETF) loss that pulls the projected states of matched decoder queries toward fixed class directions. The full schedule spans 12+3+2 epochs. Without inference-time ensembling or test-time augmentation, we rank first on FinalTest at 0.5062 mAP@[.5:.95].

Spiking Transformers provide a promising paradigm for efficient visual processing with spike-driven computation, yet their Softmax-free Spiking Self-Attention (SSA) struggles to establish spatially localized token interactions. Although existing locality-enhanced SSA methods improve accuracy, it remains unclear whether they consistently induce spatial locality across layers and different Spiking Transformer architectures. Through Mean Attention Distance (MAD) analysis, we reveal that computational locality does not necessarily translate into spatial locality and show that uniformly applying the same locality enhancement overlooks architecture-dependent deployment requirements. Motivated by these observations, we propose Spatially Contiguous Local Attention with Boundary Continuity Pathway (SCLA-BCP). SCLA computes attention within non-overlapping regions of spatially adjacent tokens, while BCP facilitates cross-boundary information exchange through a lightweight convolutional pathway. Furthermore, we develop a hierarchical locality deployment strategy to effectively apply SCLA-BCP across the two major Spiking Transformer architectures. Extensive experiments on seven static and neuromorphic datasets covering classification, detection, and segmentation demonstrate consistent improvements with limited parameter and energy overhead. Notably, our approach improves mAP@50 by up to 9.50% on COCO 2017 and mIoU by up to 3.42% on ADE20K. Visualizations, MAD analysis, and ablation studies further validate its effectiveness.

Transformer models are increasingly used for whole-slide image analysis in computational pathology. Yet, WSIs differ fundamentally from natural images: neighbouring patches often contain highly similar tissue type, stain, texture, and cellular composition. We identify this local spatial redundancy as a pathology-specific failure mode of self-attention, where dominant neighbourhood features can be repeatedly mixed into patch-tokens and weaken subtle diagnostic or prognostic deviations. We propose Gated Spatial Redundancy Projection (Gated SRP), a lightweight drop-in correction module for self-attention layers. For each patch token and attention head, Gated SRP estimates a local redundancy axis from neighbouring value vectors, projects the attention output onto this axis, and applies a learned signed gate to correct the redundancy-aligned component geometrically. Across five TCGA survival cohorts, Gated SRP obtains the highest mean C-index among the compared attention variants in all cohorts, with an average improvement over the base attention, while adding only +0.02% parameters. Across five slide-level classification datasets, it improves the base attention on 12 of 16 reported metrics and achieves the best AUC on three datasets. Code is publicly available at https://github.com/AtlasAnalyticsLab/GatedSRP.

Large mixture-of-experts (MoE) language models with 26--120 billion parameters exceed the memory capacity of consumer devices through three simultaneous pressures: resident weight matrices, key-value (KV) cache state that grows linearly with context, and dozens of expert sublayers that must be paged on demand. We present RotaryQuant, a three-axis compression system that addresses all three. Mixed-precision weight quantization assigns bit-widths by architectural role: 4-bit for dense layers, 2-bit for routed experts, and 8-bit for the shared expert whose high activation kurtosis resists aggressive compression. LRU expert offloading pages non-resident experts to disk under genuine memory pressure. The novel axis is IsoQuant, a KV cache compression method that applies a Walsh--Hadamard transform followed by block-diagonal SO(4) rotations to isotropize activation distributions before 3-bit scalar quantization, requiring $O(d \log d)$ operations and 256 stored parameters per head versus $O(d^2)$ and 16{,}384 for dense rotation methods. A fused four-kernel Metal GPU pipeline performs attention directly on packed 3-bit tensors without materializing full-precision KV state---a different execution model, not just a quantization scheme. The combined system fits Gemma 4-26B-A4B and Qwen3-30B-A3B within a 16,GB budget and Nemotron-H 120B within 32,GB, running interactively at 9--19 tok/s with near-zero perplexity degradation ($Δ$PPL $\leq +0.0012$) and 100% retrieval accuracy at 32K context.

We apply Marchenko-Pastur (MP) random matrix theory to pre-trained attention weights in order to separate each projection matrix into a random-like bulk and a set of spectral outliers. We validate this decomposition causally: zeroing the MP-identified outliers (signal) in Mistral-7B drives HellaSwag, MMLU, and PIQA close to random-chance performance, whereas zeroing a count-matched subset of bulk singular values causes smaller but non-negligible degradation. Across 11 pre-trained transformers we identify five recurring patterns: spectral outliers encode a dominant component of the learned structure; Q projections carry the most outliers; V projections under grouped-query attention lack a clean signal/noise separation; entry-level outliers form structured row-bands in Q and column-bands in O; and specific residual-stream dimensions persist as band outliers across layers in K and O. We close by outlining how these observations could inform parameter-efficient fine-tuning and structured pruning.

Transformers have had a profound impact on the world of language processing and computer vision. As efforts to answer the million-dollar question of ``How does a Transformer learn?" have been increasing, existing interpretability studies primarily analyze representations at isolated layers or the network as a whole, while the developmental evolution of individual representations and its manifolds across transformer layers remains underexplored. With this work, we aim at providing a comprehensive analysis of the evolution of representations as the representation point cloud transforms across the layers; thereby attempting to isolate layers or establish a trend which comes closer to justifying how and when raw input representations evolve into task-relevant feature representations. Thus, Transformer Geometry Observatory-TGO-IV introduces a topological framework for analysing the evolution of Transformer representations through the lens of Persistent Homology. Rather than studying local geometric properties alone, TGO-IV constructs Vietoris--Rips simplicial complexes from token-level representation point clouds and investigates the evolution of their persistent topological signatures across Transformer layers. The proposed framework comprises complementary topological observatories including Persistence Diagrams, Barcode Diagrams, Betti Curves, Persistence Landscapes, Bottleneck Distance, and Wasserstein Distance, enabling a comprehensive analysis of how the global topology of representation point clouds develops throughout the forward pass.

Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive. Recent advances, such as Diffusion Graph Networks (DGNs), have combined diffusion models with graph neural networks to sample equilibrium states directly from unstructured meshes, enabling distributional accuracy even from short simulations. However, graph-based diffusion approaches suffer from hand-crafted architectural constraints, limited receptive fields in message passing, and costly multi-scale designs, which restrict scalability to larger and more complex domains. We propose Fluid-DiT, a Graph-Free Diffusion Transformer that replaces graph message passing with attention-based denoising, eliminating explicit graph design while preserving the ability to model distributions of chaotic flows. Our framework introduces a latent-space formulation that disentangles geometric fidelity from distributional learning, reducing high-frequency artifacts and accelerating sampling. By leveraging the transformer's global receptive field, Fluid-DiT naturally captures both local flow structures and long-range correlations without requiring hierarchical graph coarsening. On canonical benchmarks including laminar cylinder wakes, ellipse-flow systems, and turbulent 3D wing experiments, Fluid-DiT consistently outperforms graph-based diffusion baselines in both sample quality and distributional accuracy, achieving higher $R^2$ correlations and lower Wasserstein distances. Moreover, it generalizes robustly from short, incomplete trajectories to unseen Reynolds numbers and geometries, demonstrating strong scalability.

The Tower of Hanoi is a simple planning puzzle that in prior work has proven challenging for large reasoning models (LRMs). Current models solve the standard formulation of the puzzle, but still struggle with the flat-to-flat variant (where initial and goal states are not restricted to have all rings on a single peg). This paper presents an in-depth study of how both small, in-house Transformers and large, third-party LRMs solve this task. To understand the failures mechanistically, we first train small Transformers from scratch on precomputed solution traces. Using a variety of interpretability techniques, we show that these Transformers develop an emergent world model: a linearly decodable, geometrically faithful representation of the puzzle's state space (the Sierpinski triangle), that is causally involved in solving the puzzles. Second, we return to the large LLMs and apply our techniques to two frontier reasoning models, Qwen3.6-27B and DeepSeek-R1-Distill-Qwen-32B, that attempt to solve the task through extended chain-of-thought. Surprisingly, we find that both models encode the Sierpinski world model near-perfectly at the end of the prompt, and yet fail at the majority of tasks when there are more than 3 rings. We locate the source of this failure in the decaying representation of the world model. We probe for the representation at different stages during planning, and establish causality by showing that performance can be improved by injecting the prompt-time representation at inference. The failure of the models is thus one of maintenance of the required representations, not their absence, and performance is at least partially recoverable. These results thus reframe the reported collapse in performance from prior work: current Large Reasoning Models build a world model, and then lose it.

Long-context LLM inference is bottlenecked by quadratic attention computation and growing KV-cache costs. Existing sparse attention and KV-compression methods typically decide which tokens or heads to preserve from runtime attention scores, observation windows, calibration prompts, or learned gates, making head diagnosis input-dependent and costly to deploy. We propose Autonomy-of-Heads (AoH), a data-free method that identifies retrieval and streaming heads from the spectral geometry of query-key projections. AoH defines the kernel attention operator $M_h = W_K^{h\top}W_Q^h$ and uses its effective-rank as a weight-space measure of head function: concentrated spectra indicate a small number of dominant query-key matching directions and are associated with retrieval heads, whereas diffuse spectra indicate the absence of a dominant global matching direction and are associated with streaming heads. We further derive an efficient $d_\text{head}$-dimensional computation that avoids constructing the full $d_\text{model}\times d_\text{model}$ matrix. We conducted extensive experiments across models demonstrating that at 50% sparsity, AoH retains 96.5% of Full Attention performance on average while reducing prefill and decode latency by up to 41.4% and 66.0%, respectively, and KV-cache memory by 50.0% at 256K tokens.

We test whether a parameterized quantum circuit (PQC) improves a hybrid quantum-classical model's performance on classical datasets, using an interface-matched classical map as the control while holding all other components fixed. Our architecture, Quantum-Embedded Attention (QEA), uses a learnable projector to compress backbone features into an $n_q$-dimensional angle vector, a shallow PQC to map those angles to one- and two-qubit Pauli expectations, and a classical attention decoder to produce class logits. We hypothesized the PQC would improve accuracy or seed-to-seed stability over a classical map with matched input/output dimensions. We test this with an interface-matched $2\times2$ factorial on Breast Cancer Wisconsin at $n_q\in\{4,8\}$, independently swapping the PQC for a classical map and the attention decoder for a linear head, across five paired seeds per cell. Three of four paired quantum-minus-classical $95\%$ confidence intervals include zero; the fourth, a $+1.63$ percentage-point contrast for the attention decoder at $n_q=4$, reverses sign at $n_q=8$ and does not survive correction across the four contrasts. The experiment thus shows no consistent PQC contribution and cannot establish equivalence. A five-dataset cross-modality grid shows comparable accuracy on AG~News, Breast Cancer Wisconsin, and BirdCLEF but a large deficit on CIFAR-10; these cells are not interface-matched and are interpreted descriptively. We report all planned canonical runs, distinguish current Pauli-readout results from legacy probability-readout experiments, and analyze bottleneck, simulation, finite-shot, and noise limitations. The results do not establish a quantum advantage; they demonstrate why controlled component attribution is necessary before crediting a hybrid model's performance to its quantum layer.

Transformers provide a powerful architecture for global content-based matching, but reasoning problems may benefit from a stronger inductive bias toward iterative traversal of latent relations. We introduce Graph Machine, an architecture with two explicit edge-based mechanisms: Edge-augmented attention, in which edges modulate attention between nodes, and edge-centric referral, in which nodes exchange addresses to update their edges. Conceptually, this enables the model to dynamically and differentiably construct and revise relational graphs across layers. We study this inductive bias using Sudoku under controlled settings and find that Graph Machine outperforms Transformer baselines, with ablation studies and mechanistic analysis attributing the gains to the edge mechanisms. Surprisingly, we found that the model discovers a compact edge-based construction for Sudoku geometry. Our results support explicit edge mechanisms as a promising architectural design, motivating broader evaluation.

A standard self-attention layer consists of two interacting circuits: the query-key circuit that governs attention allocation, and the output-value circuit that maps attended representations to predictions. Collapsed and factorized parameterizations of the query-key and output-value circuits lead to qualitatively different attention patterns. In particular, some parameterizations give sharper attention to task-relevant tokens, at a similar training loss. We analyze how the parameterizations of these circuits shape the parameter trajectories in single-layer self-attention models trained for next-token prediction. Through gradient-flow analysis, we show that factorization induces implicit rescaling of the two circuits' learning rates. We derive closed-form dynamics showing that output-value and query-key parameters move along a line, with relative speeds determined by their learning rates. Faster query-key learning relative to output-value learning thus produces sharper attention, as the model compensates for slower output-value learning by increasing attention mass on relevant tokens. Experiments show that differences in the relative learning rates of the two circuits govern attention concentration. This improves attention interpretability proxies while maintaining comparable predictive performance.

Vision transformers face significant computational overheads in high-resolution dense prediction due to the quadratic complexity of self-attention. Linear attention offers efficiency but sacrifices local context modeling. We propose \textbf{HSMLA (Hierarchical Softmax Multi-scale Linear Attention)}, which combines ReLU-based linear attention for global context, selective softmax refinement for critical local features, and multi-scale token representations via depthwise convolutions. HSMLA achieves superior accuracy-efficiency trade-offs: up to $4.2\times$ inference-time speedup across dense prediction tasks, $87.3$ Dice with $3.2\times$ speedup on CT organ segmentation, and $94.2$ AUC with $4.1\times$ speedup on pathology WSI.

Diffusion language models (dLLMs) offer a promising alternative to autoregressive models by accelerating inference through parallel decoding. Recent dLLMs commonly use blockwise semi-autoregressive decoding, generating blocks autoregressively while denoising tokens within each active block in parallel. However, despite KV caching, each denoising step still attends to all previous blocks, repeatedly incurring prefix-attention cost. Motivated by this bottleneck, we ask whether dLLM inference can be further accelerated by linearizing attention over previous blocks. We introduce block-hybrid attention, which retains exact softmax attention within the active denoising block while applying linear attention over previous blocks. We show that this hybrid attention can be retrofitted into a pretrained dLLM with minimal post-training: LLaDA-Hybrid replaces 6 of the 20 attention layers in LLaDA~2.1, a 16B open-source dLLM, largely following LoLCAT (Zhang et al, 2024). The conversion takes only approximately 60 hours while preserving benchmark performance: 72.0% vs. 75.6% on HumanEval, 63.0% vs. 57.7% on MBPP+, and 86.7% vs. 88.3% on CMATH. With a Triton implementation, LLaDA-Hybrid achieves up to $1.7\times$ higher decoding throughput and supports more concurrent requests before exhausting memory, showing that pretrained dLLMs can be efficiently linearized for faster inference. Our code is available at: https://github.com/Diuven/LLaDA-Hybrid.

In a feature-tokenized transformer (arXiv:2106.11959) such as BiomeGPT (doi:10.64898/2026.01.05.697599), each input token is built by fusing a fixed identity with a sample-specific measurement: a fixed species and a variable abundance, T = S + A. To interpret downstream classification in such models, prior work inspects the attention weights of the special [CLS] token (arXiv:2106.11959, arXiv:1810.04805, BiomeGPT) to rank sample tokens by importance. These weights have two critical limitations: they are nonnegative, so they cannot separate disease-supporting from health-supporting evidence (arXiv:2201.12114), and they act after token fusion, obscuring how the input sources S and A each affect the output. To address this we use Integrated Gradients (arXiv:1703.01365), a signed, fusion-aware attribution method, and propose a source-derived baseline T' = S + A_0 for feature-tokenized models such as BiomeGPT, which preserves species identity as a fixed biological coordinate while isolating the effect of abundance variation. Applied to a disease-versus-health decision margin, it yields polarity that explicitly separates pathogenic from protective microbial signals. We show that this gradient-based approach uncovers species-abundance directional relationships and sensitivity diagnostics entirely obscured by unsigned [CLS] attention weights. We further recommend second-order Integrated Hessians (arXiv:2002.04138) to expose microbiome community interaction rules: how a perturbation in one member alters the model's sensitivity to another, and which other species drive ambiguous cases toward disease or health at a given abundance level. This provides a principled approach to explainability in BiomeGPT that generalizes to other smooth and differentiable feature-tokenized transformers. Code is available at https://github.com/nohren/token-source-attribution

Inspired by recent evidence that transformer architectures benefit from Self-PreTraining (SPT) on long-context benchmarks, we investigate whether similar gains extend to multimodal, multivariate, and even simple univariate medical time series. Our objective is to assess the impact of SPT on the performance and scalability of transformer-based models across diverse medical applications, particularly under limited data conditions. We evaluate transformer architectures on three representative medical time-series tasks: rehabilitation robotics (Camargo dataset), stress detection (Non-EEG Stress), and Parkinson's disease detection (Gait Parkinson's Disease). Models are trained either from scratch or through SPT using four masking-based objectives designed to promote temporal and cross-modal representation learning, and we systematically vary model depth to examine how capacity interacts with pre-training benefits. Across datasets and configurations, SPT consistently improves classification accuracy by 0-6 percentage points depending on masking strategy, dataset and architecture, with gains observed not only in multivariate settings but also when models are restricted to simple univariate inputs. The improvements increase for deeper models that can better exploit the enriched temporal representations learned during pre-training. These findings indicate that SPT is a simple and general strategy that enhances transformer performance on medical time-series tasks without requiring task-specific architectural changes, supporting its potential to improve robustness and accuracy in data-limited clinical settings.

Positional embeddings (PE) in Transformers encode token distance and order but are largely agnostic to \textit{syntactic structure}. We introduce \textbf{S}yntax-\textbf{i}nformed \textbf{P}ositional \textbf{E}mbeddings (\textbf{SiPE}), which learns a lightweight syntactic prior from dependency parses during pretraining and injects it across all three dominant PE families (absolute, relative, rotary), for both encoders and decoders, leaving self-attention and the rest of the architecture untouched. We isolate \emph{where} and \emph{how} the prior should enter the model, and find it depends on the architecture: for autoregressive decoders that use relative PE, the prior is strongest when coupled multiplicatively with the relative-position term of the attention score, outperforming injection into the input embeddings, into self-attention, or into the positional and attention terms jointly---while for encoders it is best added directly to the input embeddings, composing with each encoder's native positional mechanism. We find that models pre-trained with SiPE improve on the SyntaxGym benchmark by up to $10.3\%$ while simultaneously reducing perplexity by $9.0\%$ over a base model with no syntactic supervision---a metric nearly every existing syntax-injection method instead degrades. Crucially, these gains extend beyond syntactic generalization: SiPE also improves real-world language understanding, raising scores on the GLUE benchmark by up to $8.2\%$ over a model trained without it. Unlike existing syntactic language models that marginalize over many parses at inference or discard syntax at runtime, SiPE conditions on a single parse, establishing a new Pareto frontier between syntactic supervision and inference cost.

Standard Large Language Models (LLMs) execute layers sequentially. Dynamic layer routing, i.e. search for a different execution path through layers involving layer repetitions, skips and other moves, can improve performance. Existing routing approaches often require updating model weights, running expensive search loops per test instance, or demand ground-truth labels during inference. In this work, we propose Markov Chain Routing of Transformer Layers (MACRO), a framework that learns task-specific routes over LLM architectures without modifying underlying parameters. MACRO models layer routing as a context-dependent Markov policy conditioned on layer indices, computation budget phases, directional displacements, and operator context, supporting skip, repeat, and residual hidden-state addition operations. The Markov route distribution is updated via feedback on training data and decoded using a top-k Viterbi algorithm to isolate high-probability candidate programs. We evaluate MACRO across diverse reasoning and knowledge benchmarks on multiple open-weight LLMs. MACRO achieves a +5.0% average accuracy improvement over the unrouted baselines, with largest gains on small models. We outperform the best dynamic routing approach Dr. LLM by +7.2%, while reducing route-search time 9.4x (from 14.8 to 1.6 hours). Our code is publicly available at https://github.com/Batorskq/MACRO.

Modern models no longer keep a plain KV cache: latent caches, learned sparse selectors and recurrent states each carry the model's memory in a different form, and each fails differently under compression. We give a runtime observability contract that covers all four memory classes with three operators, instantiate it on six model configurations across five architecture families, and compose the per-stage bounds into an executable request-level risk ledger. Contracts carry their error metric as a type -- composition is only defined when metrics match, and this check rejected our own first composed chain; the repaired chain crosses metrics through two proved bridges, and whatever no formal system can certify is measured instead, dropping the composed tier to empirical automatically: every claim is certified, partially certified, or empirical, composition inherits the weakest tier, and the tier is decided by the machine. Replayed over $12.4$M entry reads and run under eight-way concurrency with per-request budgets and fail-closed identity attribution, the ledger quantifies the honest trade-off on today's witness and holds its risk budget with zero violations. A fused always-on probe observes a declared one-layer subset under CUDA graphs inside the serving noise floor. Applied to a served DeepSeek-V4 stack with a packed compressed-KV prototype, the same machinery localizes a silent corruption to a precise structural boundary -- exact in the eviction-free, identity-isolated regime, with every observed failure in an eviction or slot-reuse regime -- through a machine-adjudicated discrimination campaign whose calculus rejected two of our own confounded inferences along the way. All artifacts, guards, and the Lean development are released at https://github.com/metask-ai/witprobe-attention-memory; every number in this paper regenerates from the shipped artifacts by one command.

Frame selection is essential for applying Large Multimodal Models (LMMs) to long videos due to severe frame redundancy and limited context windows. Since the appropriate frame budget varies with the downstream LMM, reasoning demands, and latency constraints, a practical selector should serve multiple budgets. However, existing methods typically optimize an isolated frame subset for each predefined budget: when the budget changes, previously selected evidence may be replaced rather than progressively augmented. Ranking frames by a fixed score would allow prefix reuse across budgets, but it ignores the distinct roles of different ranking positions. In this paper, we formulate long-video frame selection as a Matryoshka ranking problem: constructing a single priority sequence whose small prefixes concentrate query-conditioned evidence, while progressively larger prefixes preserve this evidence and add broader temporal context. Efficiently constructing such a ranking is itself challenging, as densely sampling long videos and evaluating frame-query relevance incurs substantial overhead. We therefore introduce Matryoshka Evidence-to-Context (MEC) Frame Selection, a training-free framework that builds a reusable sparse video index, discovers candidates through sparse probing and local zooming, and greedily constructs a position-adaptive ranking: early positions emphasize evidence; later positions progressively favor temporal coverage while preserving visual diversity. A single ranking can thus be truncated to any target budget without rerunning the selector. Across four benchmarks and six frame budgets, MEC improves average accuracy over uniform sampling by 3.77 percentage points, matches strong state-of-the-art selectors, and reduces end-to-end selection latency by 47.37-51.19%.

Autoregressive large language model inference is increasingly constrained by the memory footprint of the Key-Value (KV) cache. A dominant line of work reduces this footprint by evicting tokens that appear unimportant under attention-derived scores. However, such policies make an implicit irreversible decision: once a token is evicted, it cannot become useful again. We show that this assumption is brittle during decoding. Token and window importance drift as generated queries evolve, causing standard eviction policies to permanently discard states that later receive substantial attention under the full-cache model. To characterize this behaviour, we introduce Future Missed Mass and Global LIR, two diagnostics that measure future attention assigned to discarded states and the reactivation of historically inactive regions. We propose QEvict, a three-tier KV-cache management scheme that replaces binary retain-or-delete eviction with recoverable eviction. QEvict maintains high-confidence windows in full precision, stores intermediate windows in a quantized recoverable tier, and deletes only the lowest-confidence windows. During decoding, cumulative attention scores update window importance and when a quantized window becomes important again, it is dequantized and promoted to the full-precision. Under a fixed memory budget, this design preserves broader historical context while retaining exact full precision for the most important regions. Across long-context understanding, retrieval, and reasoning benchmarks, QEvict consistently improves over representative eviction and quantization baselines, reducing missed attention and improving information retention

Structured input files such as JSON, DOT, OBJ, INI, S-expression, and TinyC are widely used in software systems, but small corruptions can cause parsers to reject otherwise useful data. Repairing such inputs is important because malformed configuration, program, and data files can interrupt testing, analysis, deployment, and downstream automation even when most of the original content remains intact. Existing repair techniques can produce structurally valid inputs, but they often rely on deletion or repeated search, which may lose original content and result in semantic incorrectness. This paper presents RepairFormer, a transformer-based framework for structured input repair. The approach formulates repair as a supervised sequence generation task and uses format tags, oracle validation, and boundary-localized repair to generate valid outputs while preserving content. The boundary workflow focuses generation on the detected fault region, reducing the input size, and supporting repair of longer files. In evaluation, RepairFormer achieves a 88% in repair and 94% in recovery, showing strongest content preservation when repairs are successful. Additional experiments on our benchmark shows RepairFormer repairs 97.57% and recovers 94.29% with 5x faster runtime compared to state of the art.