Transformers

Vision Transformers (ViTs) increasingly rely on input-adaptive inference, such as token pruning and early halting, to meet energy and latency budgets. This survey examines a recent class of adversarial efficiency degradation attacks that target these mechanisms to increase computation without necessarily degrading accuracy. We unify and compare two representative attacks, SlowFormer (a universal adversarial patch) and DeSparsify (per-image perturbations), across three popular token-pruning frameworks: A-ViT, ATS, and AdaViT. We standardize reporting using GFLOPs, accuracy loss, and an Attack Success (AS) metric that measures how much of the model's compute savings the attack takes away. Understanding these attacks is crucial for designing countermeasures that not only mitigate risk but also remain lightweight, since deployment often occurs in low-power settings such as mobile or embedded devices. To organize our analysis, we focus on three questions: how input-adaptive optimizations (e.g., token pruning and early halting) create attack surfaces for efficiency degradation; how such attacks operate in practice and which optimizations are most vulnerable; and which defenses exist today and whether they meaningfully restore efficiency under attack.

Long-context large language models (LLMs) are increasingly deployed in real-world applications, yet self-attention remains a major efficiency bottleneck -- especially during decoding -- due to the necessity of repeatedly processing ever-growing key-value (KV) caches. Existing sparse attention reduce computation by attending to fewer KV pairs, but often suffer from substantial accuracy degradation, require additional training, or rely on expensive hashing. In this work, we present BinaryPC, a training-free, data-aware hashing-based sparse attention for long-context LLMs. BinaryPC constructs compact binary hash codes and corresponding hash function by computing binary principal components of data. Unlike Locality-Sensitive Hashing (LSH) with data-independent random projections or learned non-linear hashing methods, BinaryPC constructs binary codes that explicitly preserve the structural information of data without requiring gradient-based training. Comprehensive experiments across multiple model families and long-context benchmarks show that BinaryPC preserves accuracy relative to full attention while achieving superior performance among sparse and hashing-based baselines. On modern GPUs, BinaryPC improves end-to-end decoding throughput by 3.56$\times$ over the FlashAttention kernel. Our code is available at https://github.com/yudaohai666/BPC.

Multi-head attention layers produce vector representations that support multiple downstream tasks. We establish bounds on the number of heads required in two simple and concrete multi-task scenarios. In the first scenario, a vector representation is sought so that linear predictors can compute both the smallest and largest numbers in a given list. In this case, it is known two attention heads with small embedding dimension and bit precision level suffice. We prove that a single attention head requires exponentially higher embedding dimension or precision level. In the second scenario, a vector representation is sought so that a polynomial threshold function can compute the XOR of a given string of $n$ bits. This scenario is analogous to the first one for $n=2$, since XOR is readily computed by a linear function using a vector representation that encodes both the AND and the OR of the two bits. We observe that $n$-bit XOR requires the product of the number of heads and the polynomial degree to be at least $n$, and we construct multi-head attention layers that match this lower bound. These results generalize to arbitrary (symmetric) Boolean functions, where the bound is given in terms of the threshold degree.

Existing studies on self-supervised learning for white-box networks typically decouple the derivation of white-box networks via optimization algorithms from self-supervised learning paradigms. In this work, we instead revisit the two components from a joint perspective. The LeJEPA-based self-supervised framework assumes an isotropic Gaussian distribution as the optimal embedding distribution for downstream tasks, which is conceptually equivalent to the expansion term $R(Z)$ in the sparse rate reduction objective guiding white-box Transformer optimization. Building on this observation, we use the LeJEPA self-supervised paradigm to optimize $R(Z)$, and derive the remaining terms $R^{c}(Z\mid U_{[K]})+λ\lVert Z\rVert_{0}$ via the alternating direction method of multipliers (ADMM) into an attention-only Transformer that dispenses with the ISTA structure or MLP layers of the original design. Experimental results demonstrate that our attention-only white-box Transformer achieves classification accuracies of $88.88\%$ on CIFAR-10 and $63.54\%$ on CIFAR-100 at the Base scale under the LeJEPA self-supervised paradigm, while the original white-box Transformer CRATE achieves classification accuracies of $89.18\%$ on CIFAR-10 and $63.56\%$ on CIFAR-100. Our model achieves competitive performance while reducing the parameter count by roughly $31\%$. Beyond the white-box setting, we further investigate standard ViTs and find that replacing all MLP blocks with ReLU activations under knowledge distillation removes approximately 66% of the parameters while preserving competitive accuracy, motivating further investigation into the potential redundancy of MLP modules in standard ViT architectures.

Modern large language models - transformers and diffusion language models - are built around two canonical algorithmic tasks: prediction and generation. We prove unconditional separations between low-depth quantum computation and the corresponding bounded-resource classical language-model architectures in both regimes. Concretely, we exhibit the following: 1. Distributional separation. We give a distribution that is sampleable by $\textsf{QNC}^0$ circuits (i.e., a family of constant-depth quantum circuits consisting of bounded fan-in gates) that no constant-round diffusion language model ($\textsf{DLM}$) with shallow scheduling and denoising can sample within constant distance, even when allowed sublinear chain-of-thought and output-token revision/remasking events, the very features modern $\textsf{DLM}$s rely on. 2. Functional separation. We exhibit a function computable in $\land \circ \textsf{QNC}^0[\log\log n]$ (i.e., a family of O$(\log\log n)$-depth $\textsf{QNC}^0$ circuits, where $n$ is the input length, followed by a single classical $\mathsf{AND}$ gate) such that any constant-depth decoder-only transformer computing the function must be large: it would have to have width $n^{Ω(1)}$. Together, our work initiates the study of quantum advantage in the era of large language models.

Bimanual manipulation policies trained with imitation learning are typically evaluated on workstation or datacenter-class GPUs, leaving the cost of deploying them on embedded hardware largely uncharacterized. We present a bimanual SO-101 system running entirely on an NVIDIA Jetson Orin Nano Super (8 GB), the entry-level tier of NVIDIA's embedded line, using a desktop GPU (RTX 3070) only for offline training, evaluated on pick-and-place of a deformable beanbag. First, we build a GStreamer capture pipeline backed by NVMM buffers that removes redundant host-device copies from three-camera sensing. Contrary to expectation, the conventional path fit the memory budget and dropped no frames; what zero-copy sensing recovers is CPU headroom (peak single-core utilization 98.0% to 77.0%) and worst-case latency (117.31 ms to 101.52 ms). Second, we train ACT and Diffusion Policy on identical demonstrations, each at its own reference budget (100k gradient steps for ACT, 200k for Diffusion Policy). ACT converges to a task-competent policy (19/20 trials) while Diffusion Policy does not converge to a usable one (0/10) even at twice the step count, which we attribute to differing convergence costs rather than an accuracy ceiling. Third, we convert ACT to TensorRT. FP16 reduces mean inference latency from 114.02 ms to 17.93 ms (6.4x) and INT8 to 12.65 ms (9.0x), with task success preserved at all three precisions (19/20, 18/20, 19/20). We report two findings not previously documented for ACT: TensorRT's general-purpose INT8 calibration quantizes the ResNet18 backbone but accepts zero of 145 transformer layers, explaining INT8's negligible size reduction over FP16 (0.9%) despite a further 28% latency gain; and the need for quantization is conditional on ACT's action-chunking configuration, feasible in full precision at n_action_steps = 100 but not at the per-step re-prediction temporal ensembling requires.

Engineered Skeletal Muscle Tissues (ESMs) have become a key structure for biomedical disease modeling and pharmacological screening, yet their functional characterization often relies on simplistic metrics like peak force, discarding critical kinetic information. This is partially due to the high level of mathematical complexity which mechanistic models introduce to capture these dynamics. Hence, exactly the complexity prevents scalable application and widespread adaptation in the field. Here we present a Physics-Flavored Neural Network (PFNN) that automates the kinetic phenotyping of ESMs. Our architecture integrates a stretched-exponential physical model into a CNN-Transformer, enabling the extraction of physically meaningful parameters directly from force-time profiles. To address the scarcity of labeled biological data, we employ a hybrid training paradigm: the model develops a "physical intuition" on synthetic data before undergoing unsupervised self-alignment on unlabeled real-world measurements. Our results demonstrate that this physics-flavored approach achieves high-fidelity parameterization across diverse contractile phenotypes and cell lines, including Duchenne Muscular Dystrophy models. Our scalable, self-improving pipeline bridges the gap between idealized biophysics and noisy \emph{in vitro} data, providing a robust tool for high-throughput biophysical research.

We reinterpret Transformer inference by developing a functionally equivalent mechanical-structural description of its functional architecture. Parameterized transformations of token representations, or transforming concepts, are identified with simple neural networks organized through output-input and output-weight interconnections. This redescription makes explicit an organizational feature that is not equally salient in the standard matrix description: during inference, the outputs of some networks determine the weights, and hence the transformations, of others. These output-weight interconnections generate prompt-dependent dynamic transformations and give rise to Sequence-level Interactive Dynamic Parallel Processing (SIDPP). We show that the number of dynamic parameters grows linearly with prompt length and may become comparable to, or exceed, the number of static parameters fixed through training, a phenomenon we call strong prompt sensitivity. Philosophically, this shifts the conceptual picture of the Transformer from one centered on the static structure acquired through training to one that also treats the prompt-dependent transformations dynamically constructed during inference as constitutive features of its operation. GPT-4.5's recent Turing test results provide a behavioral illustration of this phenomenon. Finally, we identify biological mechanisms morphologically and functionally correspondent to output-weight interconnections, supporting the in-principle neural realizability of SIDPP and motivating Conjecture T: human neural systems may realize a functional architecture relevantly similar to that of the Transformer.

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

Dense pretrained transformers do not naturally expose interpretable units for circuit extraction. Existing approaches obtain such units by learning auxiliary sparse representations or training sparse models, incurring substantial additional computation while potentially introducing a fidelity gap between the representation being analyzed and the original pretrained model. We propose Sparse Weight Decomposition (SWD), which reparameterizes pretrained linear projections by factorizing each weight matrix into two sparse factors whose shared intermediate coordinates serve as individually addressable circuit units. Without training a separate replacement network, this parametric representation supports the same scoring, selection, and ablation circuit extraction workflow used for methods that learn sparse features. Across single-matrix replacements, SWD matches the held-out fidelity achieved by Transcoder and other strong baselines while using less than 1% of the data that those baselines use to train their replacements. For matched replacement fidelity, SWD reaches the same circuit sufficiency and necessity targets with fewer active read/write edges and selected units across tasks on GPT-2, Qwen2.5, and Qwen3.5-27B. We further show that SWD remains effective for full-model replacement of all attention and MLP weight matrices after fine-tuning the nonzero factor values. Finally, SWD also features a zero-data variant, allowing broader use of mechanistic interpretability analysis (e.g., per-step analysis).

Production deployments often swap between different-sized models in a family for cost-quality cascading, mid-conversation switching, and routing, and each swap forces the receiver to repay the prefill from scratch. We propose cross-model KV cache transfer, where the receiver reuses the source's KV cache, skipping prefill. We find that cross-model KV has substantial linear structure across matched-KV pairs, where source and target share KV head count and per-head dimension. On Qwen3 14B->32B, one source layer explains 56% of variance in the target's keys and 32% in values, rising to 79% and 65% with multiple source layers. Building on this, we design a closed-form ridge mapper that operates per head and proceeds in three steps. First, for each target layer we select the top-k most predictive source layers and concatenate their KV as input. Second, we strip RoPE from the keys before mapping, so the fit is position-free and reusable across context lengths. Third, we fit ridge regression on a small calibration set of 500 FineWeb-Edu sequences of 1,024 tokens each. Surprisingly, across six pairs in three families, this linear mapper retains 73-98% of the receiver's standalone-prefill accuracy on four pairs, while two degrade sharply. A nonlinear MLP recovers up to +37 pp HellaSwag retention on the failures. The mapper runs 2.7-25x faster than re-prefill and remains stable across multi-turn handoff, making cross-model KV cache transfer practical.

Long-context LLM decoding reads the key-value (KV) cache at every step. Loading it takes longer than computing attention over it, so throughput is bandwidth-bound. Hence, reducing the cache size can raise both decoding speed and serving capacity. The challenge is to reduce cache size while preserving the attention products, keeping reconstruction cheap, and using a fixed per-token bit count. At two bits per element, the most competitive methods rely on orthogonal transforms. However, existing techniques are either data-oblivious or use the query statistics without deriving the transform from a distortion criterion. Moreover, they rely on transforms built on top of random or Hadamard rotations, which equalize variances across entries rather than compacting energy, and fixed-width scalar quantizers, which are suboptimal at low rates. In this paper, we formulate KV cache quantization as a transform coding problem in which distortion is the error in the attention products. We derive closed-form optimal transforms for keys and values from calibration statistics, under a high-resolution model. We show that the optimal key transform is not orthogonal and satisfies a generalized Parseval relation: the attention-aware distortion becomes mean-squared error (MSE) in the transform domain. Thus, we can use MSE-optimal vector quantizers applied directly to the transformed key coefficients. To meet the fixed-width layout requirement, we show that grouping coefficients into equal-volume partitions makes equal-size codebooks attain the variable-rate optimum under the same high-resolution model. At two bits per element, our method, termed NOVA-KV, recovers most of the long-context retrieval accuracy lost by scalar quantization methods at comparable throughput.

Looped transformers have emerged as a parameter-efficient alternative to scaling depth for strong reasoning. By reusing one stack of layers across $T$ iterations, they attain the effective depth and reasoning capabilities of larger models at a fixed parameter count. Yet existing approaches suffer from latent overthinking and undifferentiated computation, largely because intermediate representations receive no guidance across loops. Multi-token prediction (MTP) supplies exactly the dense, forward-looking supervision the loop is missing. We propose \textsc{LoopMTP}, which links the two through a structural correspondence in latent space: a model that loops $T$ times can anticipate $T$ future tokens. \textsc{LoopMTP} realizes this by softly aligning the hidden state of loop $t$ with the embedding of the token $t$ steps ahead, while a lightweight gate preserves useful information across iterations. \textsc{LoopMTP} improves average accuracy by up to 8.1% (relative) over the non-looped baseline, with training remaining stable for up to 15 loops.

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

We introduce the Infinite SLAM Transformer (SLAMFormer-$\infty$), the first geometric transformer capable of supporting both long-range frontend and backend processing without an explicit distance bound. Instead of relying on a first-frame-anchored formulation, SLAMFormer-$\infty$ employs memory conditions to define flexible coordinate systems and scales for input frames, enabling more expressive structural conditioning. Built upon this formulation, the frontend preserves efficient local computation, while the backend jointly optimizes long-range trajectories and scene geometry in a globally consistent manner. Experimental results demonstrate that SLAMFormer-$\infty$ achieves superior or highly competitive performance in both trajectory estimation and scene reconstruction across large-scale datasets. Notably, SLAMFormer-$\infty$ generalizes to extremely long trajectories, successfully operating on sequences exceeding $17\mathrm{km}$.

Transformer-based architectures have dominated sequence modeling, largely due to the expressive power of attention mechanisms. However, for a class of deterministic state tracking tasks---such as parity checking, modular counting, and parenthesis matching---attention may be overkill. In this paper, we show that \textbf{state propagation alone is sufficient}. We propose the \textbf{Complex State Propagator (CSP)}, a minimalistic recurrent architecture that \textbf{only propagates hidden states} across layers without output projections at intermediate steps. The state is represented as a complex-valued vector, updated via input-dependent rotations in the complex domain. To enable deep propagation without gradient vanishing or degradation, we introduce a \textbf{block-level skip connection} alongside element-wise complex normalization and SiLU activation at sequence boundaries. Applied with Focal Loss, CSP achieves \textbf{100% accuracy} with perfect F1 scores across canonical tasks.

Local feature matching is a fundamental component of photogrammetry, enabling accurate image correspondence critical for tasks such as 3D reconstruction, stereo mapping, and visual localization. While recent detector-free matching methods, like LoFTR, have advanced the field, the global features obtained by leveraging the global-range modeling capacity of the unconstrained attention mechanism compromise the model's attention to the salient structures in certain scenarios. This limitation leads to a phenomenon we define as attention divergence, wherein a portion of high-confidence matches are distributed outside the valid matching region (overlapping region), especially in scenes with large viewpoint variations. This occurs because similar features in irrelevant regions may receive equal weighting and consideration within the standard Transformer, limiting matching reliability in challenging photogrammetric environments. To address this issue in feature matching, we propose SGFormer (Structure-Guided Transformer), a novel structure-aware matching network that adaptively updates attention on features near salient structure in overlapping regions. SGFormer employs a semi-dense coarse-to-fine pipeline and incorporates the proposed Triple-Structure-Attention (TSA) module into the backbone net for extracting distinctive features. The TSA module utilizes shallow local features from early network layers to enhance the representation around salient structure, guiding subsequent transformer stages to intensify the model's focus on regions with salient structure across the global scope. SGFormer, thereby reinforcing attention to visually consistent areas while mitigating the influence of non-overlapping regions. Extensive experiments show that SGFormer significantly mitigates attention divergence and improves matching accuracy.

Video diffusion transformers (vDiTs) generate high quality but pay quadratic self-attention cost, making inference prohibitive at video-token scales. The challenge is input-adaptive sparsity: selecting critical Q/K/V tokens with negligible overhead and executing them for end-to-end gains. We present SPADE, a training-free sparse-attention engine of three parts: (i) vDiT-SSR, a specification defining 3D blocking candidates and formalizing dynamic masks via Summarizer/Estimator expressions; (ii) runtime scheme generation using SICS and a head-wise policy; and (iii) an executor with low-overhead index search, flash block-sparse attention, and kernel grouping. Across Hunyuan-Video and Wan 2.1/2.2 for text-to-video and image-to-video generation, SPADE raises sparsity and speed while preserving quality, accelerating attention by 2.26x-3.40x and end-to-end inference by 1.49x-1.80x. Our code is open-sourced at https://github.com/6somehow/DAC-SPADE.

We study the problem of learning multi-head softmax attention from black-box input-output access. The learner may query arbitrary real-valued token sequences and observe only the scalar output at the final token. Recent work gives an algorithm using $O(d^2)$ value queries to recover the single-head parameters $(W,v)$. For multiple heads, the same work establishes identifiability under the assumption that the heads occupy pairwise orthogonal subspaces. Applying the single-head recovery algorithm separately to the heads additionally requires bases for these subspaces to be known. We recover a canonical representation by merging heads with the same $W_h$, summing their corresponding $v_h$, and discarding a merged head when this sum is zero, without these subspace assumptions. By varying the number of copies of a token, our algorithm obtains samples of a rational function whose interpolation separates the canonical heads. Additional queries formed by adding selected token vectors then match the same head across different queries. When the oracle outputs and all subsequent computations are exact, the learner chooses its query vectors at random and recovers the canonical pairs $\{(W_h,v_h):h\in[H]\}$ up to permutation with probability one. When $H$ is known, it uses exactly $4Hd^2-2H+1$ value queries of maximum length $2H+1$. If only a known upper bound $H_0$ is available, the algorithm uses $4H_0d^2-2H_0+1$ value queries of maximum length $2H_0+1$. For approximate oracle outputs, we give conditions under which the parameter error is at most a model- and query-dependent constant multiple of the output error. Finally, we extend our result to a one-layer Transformer with multi-head attention followed by a bias-free ReLU feed-forward network. Under additional conditions, we recover a functionally equivalent Transformer without relying on a separate algorithm for learning the feed-forward network.

Existing low rank KV cache methods preserve either model weights or key variance, neither of which directly reflects the attention scores used during inference. We derive the expected attention score distortion caused by rank r key compression and show that it yields a covariance weighted low rank objective. Under a margin condition, controlling this distortion also improves top k recall. The optimal rank r solution has a closed form asymmetric factorization obtained from the SVD of the covariance weighted query key operator. This motivates SAKI, a training free KV cache index that directly preserves attention scores rather than key reconstruction quality. Across LLaMA 3.1 8B, Qwen 2.5 7B, Mistral 7B v0.1, and Llama 3.2 3B, SAKI outperforms key PCA at every tested rank. At rank 32, it removes 13 to 30 percent of PCA's remaining top 64 recall error, including improvements from 0.748 to 0.799 on LLaMA 3.1 8B and from 0.786 to 0.850 on Qwen 2.5 7B. It improves 68 to 89 percent of attention heads per model, with the largest gains in deeper layers. Predicted score MSE reductions closely match empirical measurements, with a Pearson correlation of 0.997, while ablation studies confirm that the gains arise from optimizing the attention score objective rather than covariance weighting alone. Analysis of the scoring operator further explains why weight only, invariant subspace, and key reconstruction methods can be suboptimal. SAKI uses random-matrix theory to separate genuine covariance signal from autocorrelated sampling noise, matching PCA with only 512 calibration tokens and adding value exactly where PCA sees no reliable signal.

Laser line-scanning microscopy enables fast volumetric imaging but produces anisotropic lateral resolution. Orthogonal line scans provide complementary directional information that can recover near-isotropic resolution, yet existing deep-learning methods require a separate model for each optical configuration. We present a unified, resolution-conditioned fusion framework based on Rank Enhanced Linear Attention (RELA). Feature-wise Linear Modulation (FiLM) conditions the network continuously on the resolving-power ratio, enabling one model to adapt across slit widths. We further introduce Adaptive RELA, which replaces fixed-kernel rank enhancement with ratio-conditioned multi-scale depthwise convolutions and uses a learnable attention temperature to adjust selectivity with degradation severity. Training data spanning multiple slit configurations are generated using a physics-grounded separable point-spread-function model verified against measured optical data at 48.3 dB accuracy. The resulting model achieves 34-40 dB PSNR across configurations, whereas unconditioned multi-slit training collapses to 24.3 dB and per-slit specialists lose 4-9 dB outside their training setting. It also generalizes smoothly to unseen intermediate configurations without interpolation artifacts. Ablations show that FiLM resolves configuration ambiguity, global linear attention captures long-range directional correspondences, and adaptive temperature yields an additional 2 dB in the challenging near-isotropic regime, where complementary signals are weak.

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

The attention score with rotary position embeddings (RoPE) decomposes exactly into a sum over its 2D-rotation frequency pairs, and each pair's wavelength limits how far it can discriminate position. Aligned with this structure, we propose the per-RoPE-wavelength distance window: it prunes the query--key inner-product terms beyond a wavelength-proportional distance. Unlike a sliding window, every key remains reachable, at least through the low-frequency pairs. The reduction rate is input-independent, with a closed form logarithmic in the sequence length $N$, in contrast to dynamic-sparse methods like MInference. Such token-level selection is orthogonal to our frequency-level pruning. The window can therefore be applied on top of those methods. On Qwen2.5-0.5B and Llama-3.2-3B, the window prunes 37--48% of the query--key inner-product terms within each model's native context length. Relative to full attention, the top-1 match rate stays at 96--98% and the mean output-distribution KL at the $10^{-3}$-nat level on LongBench-v2 contexts. We examine absolute scores on long-context benchmarks such as RULER, OpenAI-MRCR, LongCodeQA, and $\infty$Bench: they are broadly preserved. We implement the window as a slice of the query--key contraction axis, leaving the online-softmax recurrences untouched, and port it with minimal diffs into the released FlashAttention-4 prefill and FlashInfer decode. On RTX PRO 6000 with Llama, both ports outpace stock with gains growing with context length, up to $1.29\times$ at 128K. End to end on Qwen2.5-7B-1M, with 57% of the inner-product terms pruned, the speedup reaches $1.31\times$ at a 1M-token context.

Model families are typically trained size by size, each from scratch. Can apretrained large model instead be converted into a smaller sibling? Wecharacterize the 1.4B->410M conversion in the Pythia family end to end.Representations align strongly across sizes (ridge R^2=0.84) while parametersalign weakly. Dense weight projection is functionally destructive, and abit-exact reconstruction control shows this is not an assembly artifact: basismixing breaks rotary, per-head, GELU, and LayerNorm structure. After the best-fitlinear operator, weight residuals are statistically indistinguishable from noiseunder shuffle controls. Conversion value therefore lives in initialization. Inmatched-budget continued pre-training we decompose conversion into twoindependent levers: least-squares compensation (a function lever, best zero-shot)and variance-preserving rescale (a dynamics lever, best endpoints). Compensationis a token-efficient, low-budget win rather than a universal one. At 30M tokens itbeats the strongest subcloning variant on both a width-reduced pair (84.0 +/- 1.8vs. 89.7 +/- 3.7, 3/3 seeds) and a held-out depth-reduced pair (109.3 vs. 117.9,3/3 seeds), reaching a given quality with fewer tokens. At a 33x larger budget thetwo converge to parity (40.0 vs. 40.0), both far ahead of from-scratch, whichtransfer initialization always beats: by up to 18x at low budget, with the marginnarrowing at convergence and at the largest scale. We also map the method'sboundary. At about 5x the donor scale (6.9B->1.4B) stacking both leversover-corrects, consistent with ill-conditioning of the compensation solve at largewidth, which points to dimension-aware regularization as a fix. At matched budgetour initialization also beats structured pruning with distillation, the standardpipeline for this task, and improves further when combined with it. Code,checkpoints, and the frozen evaluation corpus are released.

Video Diffusion Transformers (VDiTs) enable high-fidelity generation but incur quadratic cost from dense 3D self-attention. Existing head- and block-level sparse methods share computation budgets across queries, overlooking token-specific attention demand. We observe that retained density varies across queries yet correlates log-linearly with attention entropy, while dominant interactions form query-centered neighborhoods with token-dependent radii. Based on these findings, we propose Token Radius Attention (TRA), a training-free framework that maps query entropy to an analytic token budget and converts it into a temporally decayed radius without explicit key ranking. Fused entropy extraction, warm-up reuse, and block-sparse mask construction further reduce overhead. Across seven Wan2.1, Wan2.2, and HunyuanVideo T2V/I2V configurations, TRA retains only 9-19% of attention interactions and achieves 1.56x-2.05x speedup with competitive generation quality. Code is available at https://github.com/IF-LAB-PKU/Token-Radius-Attention.

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

Automated Sign Language Recognition for under-represented languages remains a largely unsolved problem. Central African Sign Language (CASL) exemplifies this gap: the only available bench-mark, CASL-W60, has a best reported accuracy of 69.93%, and we show that the common heuristic of fine-tuning high-resource models fails to close it. This failure stems from two compounding factors: the limited scale of available CASL data and the significant lexical and visual domain gap between CASL and large-scale corpora such as WLASL, which renders pre-trained representations largely uninformative. To address this, we propose TransSLR, a lightweight Temporal Transformer Encoder trained from scratch on 64-frame normalized pose sequences, with average pooling and a classification head. By operating on geometric keypoint representations rather than raw RGB, TransSLR achieves signer-independent generalization without relying on visual appearance. On the CASL-W60 benchmark, TransSLR establishes a new state-of-the-art accuracy of 80.39%, surpassing the prior best by +10.46%. Beyond accuracy, our encoder-only design significantly reduces computational overhead, making deployment feasible in resource-constrained environments. We conduct extensive experiments on the CASL-W60 benchmark, comparing against RGB-based and multimodal baselines, and demonstrate that TransSLR achieves state-of-the-art performance.

Transformer models are most often understood through what they do: their benchmark performance, generation quality, or behavior on downstream tasks. Yet frozen transformer input-embedding spaces may also be examined through their responses to a controlled deterministic probe before contextual computation or task-specific adaptation. Guided by this response-based view, we introduce \emph{ChaosProbe}, a deterministic neurochaos-inspired method for constructing response-based fingerprints of frozen transformer input-embedding spaces. For each prompt-level embedding matrix, ChaosProbe applies a chaotic trajectory-based transformation and summarizes its Firing Rate and Entropy channel responses with complementary representation-level measures, producing a fixed-length signature for each model. In a bounded proof-of-concept study of $80$ neutral prompts and four pretrained models---GPT-2, DistilGPT2, BERT-base-uncased, and RoBERTa-base---Pearson correlation, Spearman correlation, and cosine similarity each recover all four same-family nearest-neighbor assignments and both expected mutual family pairs. Euclidean distance recovers three of the four assignments and one of the two mutual family pairs. Paired bootstrap resampling supports the stability of the Pearson and Spearman pairings over the observed prompt set, and signature-validity checks show that constant or collapsed responses do not dominate the reported fingerprints. These results provide a cohort-dependent proof of concept that deterministic neurochaotic response signatures can expose broad structure among frozen transformer input-embedding spaces.

The key-value (KV) cache has become a major memory and bandwidth bottleneck in long-context large language model inference, making ultra-low-bit quantization increasingly important. However, existing rotation-based INT2 methods optimize cache statistics or proxy errors before the complete attention readout, even though the model is ultimately affected by the error propagated through attention and the output projection $W_O$. To address this mismatch, we propose \textit{OptR}, an output-aware rotation method that minimizes post-$W_O$ attention-output error. OptR decomposes the post-$W_O$ attention-output error into key- and value-induced terms and learns per-head orthogonal corrections through the full INT2 quantization and attention path. OptR further applies an attention-equivalent key reparameterization to reduce large channel-wise offsets without changing the softmax distribution. Across three models and five reasoning and coding benchmarks, OptR consistently improves both QuaRot and OSCAR and strengthens long-context retrieval, while preserving the paged KV-cache format with negligible inference overhead.

Personalized neoantigen prediction is challenging due to the scarcity of positive samples, the noise of the experimental data, the severe class imbalance trait and the complex of immunogenicity features. Prior arts, such as linear regression and XGBoost fail to model long-range dependencies and contextual relationships within peptide features, therefore the performance of neoantigen positive recall rate is limited. In this paper, we present a novel deep learning framework based on Transformer, coined as TransNRank. By leveraging the self-attention mechanism, our model captures both local and global feature contexts, enabling more accurate recognition of immunogenic neoantigens. A positive-aware training objective is utilized to handle the class imbalance problem, assigning more weights to those few positive samples. Extensive experiments are performed on NCI, TESLA and HiTIDE datasets. Notably, our TransNRank can push the upper bound top 20 recall rate of neoantigen prediction from 46.9% (45 from 96) to 53.1% (51 from 96), while reducing the training epochs from 200 epochs to 20 epochs. Furthermore, we analyze the features contribution based on TransNRank and find that the mutation at anchor and TCGA expression level play an unexpected important role in neoantigen prediction, and removing insignificant features to reduce the input dimensionality of peptides does not drastically impair the overall performance of the model. Our paradigm not only streamlines the prediction pipeline but also sets a new state-of-the-art for neoantigen discovery, with broad implications for accurate immuno-oncology.

We convert 21 of 28 full-attention layers of Qwen3-0.6B-Base into KDA (Kimi Delta Attention) linear-attention layers on a single consumer-grade GPU budget, and ask a simple question: what exactly does the conversion break? After surgery, hidden-state alignment and end-to-end KL distillation drive the student close to its teacher in perplexity, yet multiple-choice accuracy stays near random chance (25-29% vs. the teacher's 50.6% on C-Eval). Using a four-permutation diagnostic that rotates answer options while holding content fixed, we show the model sticks to option labels (predicting "A" 81% of the time; 106/161 questions keep the same label under all four rotations) rather than following answer content -- an interface injury that standard distillation metrics cannot see. A 1,000-step format-targeted completion-only KL stage repairs the interface (+12.48 points on C-Eval, label-stickiness roughly halved), after which persona SFT and one round of on-policy DPO preserve benchmark scores within noise. We release code, weights, recipes, and the full audit trail, and distill the engineering lessons -- including an FP32-master failure mode in which bf16 optimizer updates are silently swallowed -- that made convergence possible at this budget.

In this work we investigate how decoder-only transformers resolve lexical ambiguity through layer-by-layer analysis of three models spanning three parameter sizes (GPT-2-Small-117M, Llama-3.2-3B, Qwen2.5-32B). For both homonyms and polysemes, we find that representations become maximally distinct in middle layers, then partially reconverge in late layers, while the KL divergence between their next-token predictions reaches its maximum in the final layers. The activation patching experiment provides causal evidence that late-layer representational differences directly determine outputs despite apparent increased similarity in embedding space. Our single-layer ablation experiment indicates that models achieve equivalent disambiguation despite qualitatively different layer-wise vulnerabilities. These findings offer a mechanism for recent observations where models' internal embedding similarities show low correlation with their behavioural outputs despite strong performance. The semantic distinctions therefore remain present but become increasingly invisible to similarity measures over the embeddings, with implications for embedding-based methods such as semantic search, retrieval, and clustering that rely on late-layer cosine similarity.

Sparse attention is widely deployed in long-context serving stacks, yet no framework audits how discarding blocks changes the influence of specific content on model output. We first establish that the phenomenon is real and causal: Block Sparse Flash Attention (BSFA) route replay across four architectures changes output decisions in 13 of 16 cells, with zero identity-replay label flips. We then introduce a dense-calibrated counterfactual audit using matched probe cards---Gold (carrying the correct answer label), Poison (carrying a target wrong label), and Benign (filler only)---under six-layout position symmetry, isolating the sparsification-specific effect. Two patterns compete. Signal concentration: the selector preserves Gold and Poison blocks far above filler-matched Benign blocks (G$\approx$P$\gg$B across all model--task pairs). Integration loss: discarding blocks severs cross-block attention---confirmed by an ablation where isolating the probe block collapses its influence from 4.48 logits to zero. Compression ratio governs the balance: a full sweep from mild ($c=0.25$) to aggressive ($c=0.75$) compression across four model--task pairs reveals that three of four cells move toward stronger sparse amplification at higher compression, with two exhibiting sign reversals. Three independent arms---BSFA route replay, controlled block-top-$k$, and KV-cache eviction---converge: sparsification changes content influence in ways aggregate accuracy cannot detect. We provide an open measurement framework deployable on any model exposing block identities.

DeepSeek Sparse Attention (DSA) enables efficient long-context modeling through its Lightning Indexer. However, practical deployment remains constrained by the indexer's expensive $O(L^2)$ scoring overhead and the hardware-inefficient, discontinuous memory-access patterns induced by its outputs. To address these system-level bottlenecks, we introduce LongCat Sparse Attention (LSA), a hardware-algorithm co-designed framework comprising three complementary and orthogonal strategies: (1) Streaming-Aware Indexing, which selectively converts scattered KV entries into hardware-aligned contiguous layouts to enable coalesced HBM access; (2) Cross-Layer Indexing, which amortizes indexing overhead by reusing the results produced by a single layer across consecutive layers, supported by cross-layer distillation; and (3) Hierarchical Indexing, which adopts a coarse-to-fine scoring scheme to progressively narrow the candidate set for each query, thereby substantially reducing indexing computation. Extensive scaling experiments, ranging from 69B-A3B to 560B-A27B models, demonstrate that LSA consistently achieves performance on par with full attention across both general-purpose and long-context benchmarks. Moreover, LSA supports native training with context lengths of up to one million tokens and underpins the development of LongCat-2.0 (1.6T-A48B). To facilitate further research, we also introduce and open-source LongCat-Flash-Lite-Sparse (69B-A3B), which integrates LSA into LongCat-Flash-Lite and incorporates an updated long-context training corpus.

Handwritten Text Recognition (HTR) is computationally imbalanced in two ways: most image pixels are background, and many width-axis sequence positions are blank-dominated. This creates a mismatch for Spiking Neural Networks (SNNs): handwriting is observed as a static image, whereas spiking computation unfolds over timesteps. We propose Spike-HTR, a hybrid spiking recognizer that controls both the number of spiking steps and the number of width positions processed by the deep sequence mixer. To make a static image suitable for short-horizon spiking inference, InkCoder converts it into a coarse-to-fine input stream, where early steps cover broad stroke regions and later steps emphasize sharper stroke details. To reduce sequence computation, a CTC-guided length reducer keeps likely character or uncertain positions and compresses long blank-dominated stretches before deep mixing. With $T{=}2$, Spike-HTR trains only on target data, decodes without language models or lexicons, and reaches validation/test CERs of 3.5/5.4, 2.3/2.5, and 4.2/3.9 on IAM, LAM, and READ2016. Codes are available at https://github.com/QomolangmaH/SpikeHTR.

Vision-Language Models (VLMs) face a critical computational bottleneck when processing high-resolution imagery due to the $O(N^2)$ memory complexity of Softmax Multi-Head Attention (MHA). While substituting MHA with independent Multi-Layer Perceptrons (MLPs) achieves $O(N)$ scaling, it strips the architecture of spatial sequence routing, severely degrading global scene understanding and object permanence. In this paper, we propose the Linear Multi-Timescale Retention (LIA-MTR) module, a memory-efficient cross-modal bridge. By integrating an ELU-based positive feature mapping with adaptive write-gating and log-linearly distributed recurrent decays, LIA-MTR mathematically compresses continuous visual sequences into bounded memory states. Theoretical analysis proves the architecture operates with strict $O(N)$ sequence-interaction complexity. Empirically, synthetic retrieval evaluations demonstrate that LIA-MTR flawlessly routes context across 16,000 tokens, eliminating the "Lost in the Middle" degradation typical of naive linear attention. Hardware benchmarking reveals infinite-context scaling capabilities, natively processing 262,144 visual patches within an 11.2 GB VRAM footprint, whereas standard MHA suffers out-of-memory failure at 16,384 patches. Furthermore, following instruction tuning on 665K conversational samples, LIA-MTR significantly outperforms an industry-standard MLP baseline on the MME benchmark (71.00% vs. 68.11%), driven by a 10% absolute improvement in object permanence and superior global semantic extraction. This work establishes a mathematically rigorous, computationally flat foundation for infinite-context Vision-Language integration.

Detection transformer models, including DETR and its extensions, learn to output a set of object-level embeddings that can be simultaneously decoded into 2D bounding boxes and class distributions. In this paper, we investigate what pre-trained 2D detection transformers understand about the 3D properties of objects. Specifically, we investigate the extent to which properties including the depth of objects from the camera and the 3D location of objects relative to the camera can be recovered from object-level embeddings using linear and non-linear probes. Across a range of detection transformer models, our results show a surprisingly strong and previously unknown ability of 2D DETR models to represent useful information about the 3D properties of objects, despite the complete lack of 3D supervision during model pre-training.

The emergence of transformer-based deep learning models has brought unprecedented performance across various domains, particularly in natural language processing and computer vision. However, deploying these models, especially on resource-constrained devices, poses significant challenges due to their high computational complexity and large memory size and bandwidth requirements. This complexity has led researchers to use low-bit model weights to reduce memory usage and improve efficiency. In addition to reducing processing and memory demands, quantization introduces another useful property: value locality, where the extremely large number of parameters are restricted to a limited range of values. To fully take advantage of this locality, this paper presents DeVIT, an acceleration method for vision transformers that leverages differential computation to enable multiplier-less matrix multiplication.

Diffusion Transformers (DiTs) have emerged as a core architecture in generative modeling due to their scalability and adaptability to multimodal tasks. DiTs comprise isotropic transformer blocks, and learn representations progressively across depth, where the denoising objective drives later layers to focus on fine-detail reconstruction. This results in degraded representation quality and an imbalanced encoder-decoder behavior. Prior approaches such as representation alignment (REPA) mitigate this by encouraging stronger early representations via training regularization. Alternatively, U-Net-style DiT architectures introduce explicit multi-scale encoder-decoder structures for improved convergence. But they build on standard U-Net wisdom via learnable operators for spatial downsampling, which are not well-suited to transformer architectures, introducing inefficiencies and compatibility issues with components such as cross-attention and representation regularization. In this work, we propose UDT, a U-Net diffusion transformer that combines the representation power of DiTs with the encoding-decoding benefits of U-Nets, through data-adaptive token merging for downsampling and upsampling, while preserving the DiT token dimension. Our baseline UDT architecture outperforms existing U-Net DiTs and achieves performance comparable to REPA across all model sizes. Furthermore, using architectural optimization and REPA, UDT outperforms SiT's 7.9 FID at 1400 epochs (w/o CFG) within 40 epochs (~ 40x faster convergence) for XL model size on 256x256 ImageNet. Finally, it achieves strong image generation performance with CFG, reaching FID of 1.38 (320 epochs) with SD-VAE and 1.35 (500 epochs) with VA-VAE, providing a new backbone for DiTs with strong empirical benefits.

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

Depth-routing residual architectures allow Transformer layers to retrieve earlier representations instead of inheriting only the immediately preceding state. Existing Block Attention Residuals, however, use a single content-dependent depth mixture to construct the inputs to queries, keys, and values. This design couples two functionally different decisions: queries and keys determine where attention matches, whereas values determine what content is retrieved. We therefore ask whether matching and content retrieval should be forced to read from the same depth. We introduce Role-Decoupled Attention Residuals (RD-AttnRes), a minimal extension that shares one depth route between queries and keys while learning an independent value route over the same residual sources. Tying the two routing queries exactly recovers the parent architecture, while decoupling them adds only one model-width vector per layer and introduces no additional token-to-token attention operation. We evaluate RD-AttnRes using a frozen, paired pretraining protocol on FineWeb-Edu with five matched seeds for both 120M- and 343M-parameter models and a 2.0B-token training budget. RD-AttnRes improves validation negative log-likelihood in all 10 matched comparisons. The mean reductions are 0.0301 and 0.0247, corresponding to perplexity reductions of 2.97 percent and 2.43 percent at 120M and 343M parameters, respectively. Early-budget controls indicate that neither the additional parameter count, duplicated routing execution, nor a fixed value route reproduces the improvement. Routing diagnostics further reveal persistent divergence between the query-key and value depth distributions. These results suggest that, within the evaluated training regime, attention matching and content retrieval benefit from distinct reads over the residual hierarchy.

Transformers do not merely lack data on some Boolean extrapolation tasks; they generalize in a systematically wrong way. Recent work on generalization on the unseen has shown that, despite fitting the observed domain, Transformers often extrapolate according to a simpler minimum-degree interpolator rather than the true target function. These Boolean tasks are not practical applications, but controlled stress tests for understanding Transformer inductive bias. We ask whether this failure mode can be corrected by injecting explicit structural priors into attention. Existing structured-initialization methods alter Transformer inductive bias indirectly, by choosing query and key projections whose similarity scores approximate a desired attention pattern. However, we find that when applied to Boolean extrapolation, these QK-based priors can be rapidly overwritten during training and fail to change the learned extrapolation rule. We propose a simpler alternative: initialize the additive attention mask directly. Unlike standard hard masks used for causality or locality attention, our mask is a finite, learnable attention-logit bias initialized from task-level interaction structure. This separates the structural prior from content-dependent attention scores, allowing it to persist throughout optimization. On Boolean reasoning tasks, mask-based initialization achieves near-perfect extrapolation where vanilla and QK-initialized Transformers remain trapped by the default inductive bias. The same mechanism also improves low-data arithmetic performance and remains competitive on vision and language benchmarks. These results show that attention masks can serve not only as architectural constraints, but as a simple substrate for encoding persistent inductive bias in Transformers.

KV cache compression is essential for efficient long-context inference. Existing eviction methods permanently discard unselected tokens and consequently remove their aggregate contribution to attention. Merging-based alternatives preserve more information but can perturb retained keys and values that should remain exact. We observe that the information omitted by cache eviction can be formulated as residual statistics in both the numerator and denominator of softmax attention. Based on this observation, we propose ResKV, which divides a fixed KV budget into an exact main cache and a compact residual cache that reconstructs the contribution of omitted tokens. ResKV lets main-cache tokens and residual entries participate in the same softmax normalization, so residual entries restore both attention numerator and denominator mass rather than acting as a post-hoc correction. A construction-time validation proxy determines residual allocation for each layer and KV head, while a decode-time dynamic gate adjusts residual contributions for individual queries. Comprehensive evaluations on LongBench and RULER, covering query-aware and query-agnostic settings, multiple backbones, cache budgets, and representative compression baselines, demonstrate broad improvements under the same retained KV budget while preserving the practical efficiency of compressed decoding, including peak memory usage and long-context decode throughput.

A dense, pretrained language model can be retrofitted with recurrent depth and learn an iterative latent transition that persists after outcome-only annealing. Qwen2.5-0.5B-Instruct is split into a Prelude, a weight-tied Recurrent Block, and a Coda, with an identity-preserving one-loop path and a re-entry bridge on later loops. At loop 1 the retrofit remains non-inferior to its base on a preregistered ARC battery. Three findings. First, the mechanism is a reusable procedure rather than terminal-answer lookup, and installs at two budgets: 6M trained parameters over frozen base weights and 180M full-block. With intermediate-step supervision, the model computes one task step per loop and persists when only final answers are graded. The adapter matched the full block overall (83.8% versus 84.0%), led through depth 11, and trailed beyond. Verbal fine-tuning reached 79-86% on controlled verbal renderings (zero-shot transfer was minimal), and adapter verbal training begun from the installed mechanism outpaced matched fresh training by 18.6 points, including on a held-out test set. Second, the operation extrapolates to roughly 1.5 times its supervised depth, holding 70% accuracy through depth 18. Third, a same-size scratchpad-trained model matched the recurrent model within its learned horizon but collapsed beyond it. The recurrent model won overall, 84% versus 72%, retained 53% versus 2.5% beyond depth 10, and answered 7.6 times faster. An iterative transformer can therefore perform deeper reasoning in latent space faster than comparable or larger models fine-tuned on the same task, in a system-level comparison. A second task, running the rule in reverse, exposed the limits: the inverse was learnable in isolation, but no continuation acquired it while preserving the installed mechanism and general capability, a catastrophic-interference boundary. Learned depth selection remains open.

LLM serving is increasingly accelerated by position-independent caching (PIC). Existing PIC methods, however, are built for full-attention models, where a token-indexed KV cache underlies its core operations: matching reusable token chunks, concatenating their KV entries, and selectively recomputing a few tokens to restore cross-chunk context. Hybrid LLMs break these primitives---they replace most attention layers with linear recurrences that expose only a fixed-size state, leaving no token-indexed KV to concatenate or to locally repair. This raises a natural question: can PIC benefit hybrid models, and what would it take? We present LinearKV, a training-free hybrid-PIC framework. Its key insight is a \emph{decoupled initialization}: each linear layer maps its $K$ matched local states to a single initial state, while full-attention layers concatenate their KV as before. LinearKV is therefore compatible with existing PIC methods, reusing their token selection and recomputation as-is. Under this framework, we find that a \emph{single cached state} suffices as the linear layer's initializer. The algebraically principled alternative---composing all $K$ cached states into the exact full-prefix state, as concurrent work HYPIC does---is unnecessary and, on some architectures, even harmful. We compare the two across three hybrid models and three PIC selectors. On the two GDN models the two tie, both recovering most of full quality (up to $92\%$); on the Mamba-2 model, exact composition instead collapses under every selector---under EPIC, for instance, it recovers only $46.6\%$ of full quality, versus $86.8\%$ for a single cached block initializer. A single state initializer is also cheaper, cutting time-to-first-token to $0.46\times$ full prefill versus a further $5$--$17\%$ overhead for exact composition; results hold across LongBench QA and RULER at 8K--32K.

Visual generation increasingly requires high-resolution images, long videos, and multimodal context, making the quadratic cost of full attention prohibitive. We introduce Chimera, a hybrid visual diffusion backbone with a principled scaling recipe. Chimera processes text, image, and video tokens in one raster-ordered stream without positional embeddings. It combines Kimi Delta Attention (KDA) for long-context state tracking with O(N) complexity, interleaved Multi-head Latent Attention (MLA) for direct global interaction, and modality-aware short convolutions for local spatiotemporal context. Sparse Mixture-of-Experts (MoE) layers expand capacity while controlling activated compute. To scale this heterogeneous architecture, we introduce HeteroP, a module-wise scheme that transfers hyperparameters across width and depth according to each tensor's functional fan-in and model depth. HeteroP yields a consistently tuned family used to fit Chinchilla-style compute-optimal laws for activated model size, training-token count, and image-video data ratio. Guided by these laws, we train an 11B-parameter Chimera with 2B activated parameters. Experiments show three results. First, measured by pretraining diffusion loss, the dense backbone is 1.7x as compute-efficient as a matched full-attention Wan-2.1 2B baseline, while the complete system reaches 7.3x. Second, without length-specific fine-tuning, Chimera extrapolates zero-shot from 5-second training clips to 30-second videos, with only 6.5% FID degradation in the last five seconds. Third, the fitted laws show that compute-optimal image pretraining divides compute nearly evenly between activated model size and training-token count, whereas video pretraining modestly favors model size at higher budgets. These results establish a foundation for designing and scaling efficient long-context diffusion architectures.

Causal discovery in multivariate time series data is challenging due to complex interactions, high dimensionality, and nonlinear dependencies among variables. Existing methods often struggle to capture these complexities, resulting in inaccurate causal structures. To address this issue, we propose a novel framework that leverages self-attention mechanisms within the transformer architecture for causal discovery. Our approach introduces a novel inverted causal self-attention mechanism (CSAM) that emphasizes latent and indirect causal relationships by inverting tokens and inducing sparsity in attention scores, focusing on significant causal interactions and reducing spurious correlations. Additionally, we develop a global causal algorithm to identify global causal links, providing a holistic metric for causal influence, along with a causal verification module to ensure robustness in the identified causal relationships, enhancing the reliability of our framework. Experiments on both linear and nonlinear datasets, along with ablation studies and sensitivity analyses, show that our framework outperforms existing methods, demonstrating its potential for causal discovery in complex multivariate time series.

Long-context retrieval and agentic workloads repeatedly reuse the same documents under changing instructions, histories, and document orders. Prefix caching cannot exploit this reuse, while position-independent caching (PIC) remains unreliable because independently compiled KV states lack the future context in which they will be consumed. Our diagnostics show that a learned boundary-conditioned baseline sharply reduces attention deviation near reusable-block boundaries but leaves interior and task-level residuals, motivating adaptation of the document representation itself. We present \emph{SemPIC}, which trains a LoRA-enabled Writer to compile native per-layer document KVs through behavioral distillation while retaining the pretrained decoder as an unchanged Reader. Adaptation is confined to offline cache construction, preserving the standard KV interface and cache-hit decoding path. We further introduce KV Gradient Checkpointing, which reduces peak training memory without severing gradients through cached KVs. Across three models and four tasks, SemPIC raises mean micro-F1 over KV Packet from 0.53 to 0.60, approaching Full Recompute at 0.62. Code: https://github.com/jn12-29/SemPIC

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

Standard masked-language-model fine-tuning applies a uniform masking probability across every token position, assuming reconstruction difficulty is position-agnostic. When the degradation process is characterised and concentrated at predictable positions, this assumption fails: at peak damage sites the model can underperform a frequency-matched random predictor. We introduce VESTIGE, a parameter-free, drop-in replacement for the standard MLM collator that aligns the masking distribution with an empirically measured per-position corruption profile. We apply it to ancient DNA (aDNA) reconstruction, where cytosine deamination produces a position-dependent C-to-T / G-to-A gradient quantified per-position by mapDamage2. Rescaling so the mean C/G masking rate equals 15% - identical to standard MLM - isolates spatial redistribution as the sole variable, with model, data, seed, and hyperparameters held fixed across both DNABERT-2 runs on a mammoth CDS corpus (two specimens, seven genes). Across six terminal-zone widths and 626 paired windows, VESTIGE leads standard MLM at every width (Delta = +4.18 to +10.35 pp, all p < 10^-8), cuts validation cross-entropy by 13% (3.274 vs. 3.757), and yields ESMFold reconstructions with TM-score > 0.95 across all six reconstructions (three genes) even under damage amplified 10-30x beyond authentic PMD rates. A 1D CNN biosecurity classifier returns AUC = 0.935 and clears 98.2% of reconstructed windows, the 1.76% remainder attributable to reference-genome features, not reconstruction artefacts. The principle is domain-agnostic: any measurable position- or context-specific corruption profile - FFPE, bisulfite, metagenomic, or nanopore - substitutes directly for the PMD array, making VESTIGE a knowledge-guided training routine for intelligent systems operating on degraded or noisy sequence inputs.

Looped Transformers create a useful train- and test-time compute axis by reusing the same Transformer block over recurrent depth, increasing effective depth at a fixed parameter count. However, that shared block must then govern an entire trajectory of varying hidden states over trained and extrapolated depths. Furthermore, in additive-injection looped Transformers, an input-conditioned signal is reintroduced at every recurrent step, so applying the shared transition at an input-conditioned reference can still move the hidden state. In this paper, we propose Source-Centered State Evolution (SCSE), which is designed to reconcile input conditioning with reference-preserving shared recurrence. Specifically, SCSE retains input dependence through its learned anchor and initial deviation, allows nonzero deviations to drive recurrent computation while mapping zero deviation to zero, and guarantees exact anchor invariance through its zero-deviation mask. The designated anchor is thereby a one-step fixed point by construction. The zero-deviation forcing bias is the next deviation produced from the anchor itself and vanishes in SCSE, while nonzero deviations remain active and support state-dependent recurrent computation. Our theory shows that the zero-deviation forcing bias is a design degree of freedom whose task effect can be harmful, neutral, or beneficial; SCSE resolves this choice in favor of exact anchor invariance by setting the bias to zero. Across WikiText-2, WikiText-103, direct web-corpus pretraining, held-out web-text transfer, and LAMBADA completion, SCSE improves the controlled recurrent quality frontier. Ablation studies identify the learned anchor and the anchor-coordinate deviation recurrence as the primary contributors to the gain, and a trained-model case study grounds the anchor-response diagnostic in observed recurrent motion.

Wearable sensors continuously capture fine-grained multivariate time-series data, providing opportunities to model behavioural patterns associated with health outcomes. However, existing deep learning methods prioritise predictive accuracy over interpretability, limiting their application in health research. In this study, we present HealthCAT, a flexible framework that integrates an Encoder-only Transformer with an Attentive Class Activation Token (AttentiveCAT) to generate class-specific, time-step-level interpretations. These interpretations can be mapped back onto behavioural cycles that are relevant to the domain (e.g., time-of-day), supporting individual-level analysis of wearable sensor data. We evaluated HealthCAT using two real-world wearable sensor datasets (306 participants in total). HealthCAT outperformed deep learning baselines by up to 17% in F1-score and 12% in accuracy on both datasets ($p<0.05$). In masking experiments, the time steps identified by HealthCAT carried significantly more predictive value than random selection across all masking conditions ($p<0.05$), indicating that the identified time steps are predictively informative. By coupling predictive performance with validated time-step-level interpretability, HealthCAT moves wearable sensor analysis beyond aggregated metrics towards temporal patterns that support health monitoring, behavioural pattern analysis, and intervention design in health research. The significance of this work is that it enables accurate prediction of health indicators from wearable sensor data while providing insights into when and how physical activity patterns occur, rather than relying solely on aggregated summary measures.

Emergency Departments (EDs) are critical access points in healthcare systems, yet they face persistent pressure from unpredictable patient demand, seasonal surges, and non-urgent visits. Effective ED planning requires forecasts at multiple decision-making levels: hospitals need local demand estimates for staffing and bed management, regions require forecasts to coordinate healthcare units, and national authorities need system-wide projections for capacity planning. However, most existing approaches forecast ED demand independently at a single level, ignoring the hierarchy linking hospitals, regions, and national systems. This can produce incoherent predictions, where hospital-level forecasts do not aggregate consistently to regional or national demand. We propose HierSTT, a hierarchical Transformer-based framework for coherent multi-level ED forecasting. HierSTT jointly predicts hospital, regional, and national level demand in a single end-to-end model. A Temporal Fusion Transformer captures national dynamics, while spatio-temporal Transformer encoder-decoder modules model regional and hospital demand conditioned on higher-level forecasts. A coherence-aware loss penalizes cross-level inconsistencies during training. We further introduce a nationwide Portuguese ED dataset covering 81 hospitals across 5 regional health administrations, with heterogeneous covariates at each level. Experiments show that HierSTT reduces average WAPE by 32% relative to the best non-hierarchical deep learning baseline and outperforms all classical hierarchical reconciliation methods, while producing near-coherent predictions across levels. Additional resources associated with this work are available at https://github.com/FilipaLino/HierSTT.

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

Multi-head latent attention (MLA) is increasingly important for long-context LLM inference because compact latent states replace the growing key-value (KV) cache and reduce decoding memory traffic. Yet most capable open checkpoints use multi-head or grouped-query attention (MHA/GQA), so conversion is needed to obtain MLA's cache efficiency without retraining from scratch. Speculative decoding offers complementary acceleration, but its speedup depends on agreement between draft proposals and target verification. We find that direct MHA/GQA-to-MLA conversion can sharply reduce this agreement: low-rank factorization and RoPE handling introduce attention-function errors that may be tolerable for standalone generation but substantially lower draft-token acceptance. We therefore formulate MLA draft construction as functional reconstruction rather than cache compression. Our end-to-end (E2E) method optimizes each converted MLA attention module to reproduce the post-output-projection response of its original MHA/GQA counterpart on calibration hidden states. This converter-agnostic post-conversion procedure preserves the converted cache and inference graph and requires neither verifier logits nor verifier supervision. We evaluate 192 model-converter-backend-method-task configurations spanning four Llama/Qwen draft-target pairs, TransMLA and MHA2MLA, HF and vLLM, and four 200-prompt tasks. With a 0.5-percentage-point reporting tolerance, Functional Reconstruction materially improves acceptance in 37 of 64 matched task cells, leaves 26 practically unchanged, and materially decreases one. Code and evaluation artifacts are available at https://github.com/swyhahaha/FunctionalMLA.

Plant biosynthetic gene clusters (BGCs) encode specialized-metabolite pathways, yet curated plant BGC labels remain scarce, hindering supervised discovery at genome scale. Existing plant BGC mining tools are largely signature- and rule-driven and do not fully leverage recent advances in contextual representation learning for modeling long-range domain context and controlling false positives under strong domain shift. We seek an AI-assisted workflow that narrows experimental search space by transferring supervision from well-annotated microbial BGCs to plant genomes. We present PlantBGC, representing genomes as ordered Pfam-domain sequences and learning BGC-likeness with an encoder-only Transformer trained on MIBiG microbial BGCs and adapted to plants via label-free masked language modeling. On microbial benchmarks, PlantBGC achieves token-level AUC = 0.988 (10-fold CV) and 0.979 (leave-class-out). On plants, adaptation improves known-BGC recovery on n = 34 curated loci under strict 100% coverage, increasing recovery from 29.4% to 67.6% and indicating more complete boundaries. GO/KEGG-derived weak supervision reduces proxy primary-like ratio by 48.40% (GO) and 45.20% (KEGG), with consistent per-species reductions (paired Wilcoxon p = 1.53e-5). Compared to plantiSMASH, PlantBGC yields more compact loci on matched regions (median length ratio = 0.278; 93.8% of pairs are shorter).

Recently, photonic transformer accelerators (PTAs) have successfully achieved significant speedup and energy efficiency improvements over electronic accelerators for expediting Transformer inference. However, state-of-the-art rely on expensive multi-wavelength light generation and large dot-product units due to active phase-shifter components, thus making their approach inefficient and impractical. To address this, we propose MDTransformer, a novel hardware-software co-design of PTA based on mode-division optical dataflow and operations. Specifically, MDTransformer performs complex matrix operations using spatial-mode interference, that leverages the inverse-designed multi-mode couplers, crossings, and Mach-Zehnder IQ modulators into a compact mode-division photonic tensor core (MPTC), capable of executing matrix multiplications in the optical domain. Its each guided mode (i.e., TE0-TE3) acts as an independent computational lane, enabling four-fold parallelism-per-waveguide without spectral filtering or free-spectral-range limitations. Moreover, its coherent detection and IQ modulation jointly encode amplitude and phase, realizing complex-valued arithmetic for full-range operations in transformers. MDTransformer offers analog multiplication with sub-4-bit effective precision and inter-modal crosstalk below -30 dB. Its inverse-designed approach also offers scalable and full compatibility with single-laser continuous-wave operation at 1550 nm. Experimental results show that MDTransformer achieves 40.4% area reduction, 63.6% power saving, 40.6% energy saving, and comparable latency over the state-of-the-art PTA across different workloads (i.e., DeiT-Tiny/Small/Base and BERT-Base/Large). These results show that MDTransformer offers a practical solution for high-performance and energy-efficient transformer-based systems.

Complex structured reasoning tasks often require additional computation, yet current language models obtain it mainly by increasing parameter scale or by serializing intermediate steps as chain-of-thought (CoT) tokens. The former raises training and deployment costs, while the latter ties reasoning computation to autoregressive output length. We introduce Penelope, an efficient latent-reasoning framework for pretrained decoder-only Transformers that localizes recurrent computation to a selected decoder interval. The lower decoder prefix is evaluated once to construct a problem-conditioned boundary memory, which is then iteratively refined through time-modulated GRU dynamics and recurrent readout states before answer generation. A progressive CoT-to-latent curriculum transfers visible reasoning into this internal recurrent path, allowing additional computation to be allocated in latent space without repeatedly executing the complete decoder or generating a long intermediate trace. Experiments on open-source structured-reasoning benchmarks show that, at validation-selected latent budgets, Penelope attains competitive accuracy relative to established latent-reasoning models while reducing measured inference latency. These results show that latent refinement can be localized to a narrow decoder interval, reducing repeated full-decoder execution without generating a long visible reasoning trace and providing a practical accuracy-efficiency tradeoff for decoder-only Transformer models.

An often overlooked factor of robot manipulation performance is the embodiment of the robot itself. Motivated by this problem, we study motion-conditioned robot co-design, where the goal is to generate complete robot designs that track target end-effector trajectories (from human demonstrations) while optimizing user-defined rewards. We introduce Transformer Transformer, a diffusion transformer trained on RoboTokens, a unified tokenization of robot embodiments, states, and actions. The same architecture can be used across embodiment spaces (e.g., wheeled bimanual, quadrupeds, humanoids) and use cases (embodiment generation, cross embodiment controller). Rather than overfitting to one reward function, Transformer Transformer is a dynamics model, whose reward-agnostic state and action predictions can be converted into reward-specific value predictions. These value predictions are used to steer embodiment diffusion towards high value robot designs, through a procedure we call Dynamics Self-Guidance. Experiments across multiple design spaces show zero-shot optimization of unseen rewards and trajectories, improving performance and runtime over the evolutionary baseline. Finally, we fabricated an optimized ALOHA design, which reduced tracking error by over 70% compared to the original design.

Transformer-based surrogate models are increasingly used to replace expensive first-principles simulation in engineering design. But conventional transformer architectures are often over parameterized for the small, low-dimensional datasets typical of engineering design spaces, where large simulation data is expensive to generate. Under these conditions, excess parameter capacity leads to overfitting rather than improved accuracy, while also incurring unnecessary memory and compute overhead. This motivates a shift towards architectures that focus on additional compute rather than additional learnable parameters. This paper presents a hardware-aware evaluation of three recursive transformer paradigms for surrogate thermo-mechanical analysis of advanced packages: a)Tiny Recursive Model, b) our proposed Depth Recursive transformer, c) and a simple recursive transformer. We systematically compare their predictive performance (Recall, Mean Reciprocal Rank), parameter count, computational complexity (FLOPs), providing practical design guidelines for selecting recursive transformer architectures under resource-constrained scenarios. We validate this principle on two low-dimensional engineering prediction tasks: 1) thermo-mechanical reliability analysis of advanced semiconductor packages, where stress and warpage from thermal cycling must be evaluated repeatedly across a design-of-experiments sweep under costly finite element analysis (FEA). 2) Laplace PDE iterative numerical solver for capacitance field. Overall, recursive weight-sharing transformers provide an effective and generalizable trade-off between prediction accuracy, parameter efficiency, and computational cost for small data engineering surrogate modeling.