Louis Chen, Torbjörn E. M. Nordlingcs.CV cs.AI eess.IV
Background. Remote photoplethysmography estimates the cardiovascular pulse from facial video, and its explanations have rested on inspecting heatmaps rather than on quantitative evidence about where a model reads it. We quantified the explanations and asked whether such explanations transfer between datasets and track model performance. Method. We trained eight condition-specific RhythmFormer models on NCKU-rPPG, recorded under three illumination levels, speaking, rotation, and cycling, estimated one heart rate per 5.12-second clip, and set them beside a UBFC-rPPG reproduction. Raw attention, rollout, attention flow, and Beyond Intuition were assessed by skin coverage and the Salience-guided Faithfulness Coefficient (SaCo). Results. Beyond Intuition ranked highest on both datasets, at median coverage 0.789 and SaCo 0.837 on Static level 3 against 0.826 and 0.917 on UBFC-rPPG; lower ranks differed. Within one participant of one condition, neither measure was related to a clip's heart-rate error, waveform correlation, or signal-to-noise ratio on either dataset: 186 of the 252 coefficients fell below $|ρ|=0.10$ and 28 reached $p<0.05$ against the 13 expected by chance. Across the eight scenarios only Beyond Intuition's coverage followed the three performance measures, at $ρ=-0.43$, $+0.57$, and $+0.43$, while the attention-only methods' SaCo ran opposite to each. It failed at 40 lux alone, its median coverage falling to 0.180 and its median SaCo to $-0.178$, whereas motion degraded the estimates far more without such a drop. Conclusions. Skin coverage and SaCo carry information complementary to the performance measures rather than a proxy for them: attributing to the skin does not guarantee an accurate estimate. What an attribution reveals about a condition is where the model looks rather than how faithfully its map is ordered.
Test-time scaling uses extra test-time compute to improve performance, such as letting language models reason longer when solving a problem. As models keep the entire reasoning trace in memory via full attention, hard tasks that need long thinking can be prohibitively expensive. However, we find most intermediate reasoning tokens lose importance as the model continues reasoning. This calls into question whether retaining them is worth the cost. Based on this insight, we propose Prefix Sliding, which discards tokens during reasoning that are not part of the prefix or the window of the last few thousand tokens. The prefix has key instructions and tools available to the model, while the most recent tokens are the current reasoning the model is working on. This caps the total memory requirement regardless of how long the model reasons, allowing for efficient long-horizon test-time scaling. Without training, Prefix Sliding can make existing models 3x faster while maintaining performance. Training with Prefix Sliding using reinforcement learning can achieve better performance by enabling scaling to reasoning traces beyond a hundred thousand tokens. Ablations show Prefix Sliding outperforms summarizing intermediate tokens or vanilla sliding window. Our code is at https://github.com/Muennighoff/prefix-sliding
Choosing the rank of a low-rank adaptation (LoRA) update is usually an empirical task. In this paper, we provide a task-dependent theory of the approximation error achievable at each LoRA rank for Transformer attention. We fix a pretrained attention head, a target attention function, and a distribution over inputs from the downstream task, and bound the smallest expected Kullback--Leibler (KL) error achievable by a rank-$r$ query LoRA update. When target attention probabilities are bounded away from zero, we prove a lower bound of the error proportional to $ψ(\|d\|_2)$, where $d$ is the difference between candidate and target attention scores and $ψ(t)=\min\{t^2,t\}$. We also prove an unconditional upper bound $\min\{\|d\|_2^2/4,\sqrt2\|d\|_2\}$. Under explicit realizability, geometry, and moment conditions, we then bound the best rank-$r$ error between an explicit multiple of $ψ(\sqrt{T_r})$ and $\min\{T_r/4,\sqrt{2T_r}\}$, where $T_r$ is the downstream-weighted tail energy of the target update. We also provide target-Fisher bounds when candidate scores remain within a fixed range of the target scores, and an unrestricted lower bound when a subset of tokens carries most of the probability mass. These spectral bounds describe finite-score approximation. We then construct explicit families in which softmax saturation makes the rank required to match the attention function strictly smaller than the rank required to match the finite logits. Finally, we extend the analysis to fused multi-head LoRA and joint query/key updates, exposing the effects of rank sharing and query/key factorization constraints.
Taebong Kim, Youngsik Hong, Minsik Kim +3cs.LG cs.AI
We formalize prefix invariance: representations at position t must not depend on future inputs. We give a lightweight audit, two forward passes, no training or gradients, that localizes exactly where causality breaks. Attention-mask inspection is incomplete: leaks can occur via scans or normalization despite correct masks. Across 192 injected-fault trials on eight checkpoints, mask inspection found none, while our audit localized all 192/192, also finding a defect in Zamba2 and Nemotron-H.
Large language models generate tokens sequentially, but can they execute multiple tasks concurrently while forming each token? Broader attention allocation may provide a mechanism for such task concurrency. Existing approaches to scaling inference primarily rely on longer generations, more samples, or additional verification stages, while attention dispersion is often treated as a signal of interference or error. Task concurrency within serial generation therefore remains underexplored. We propose the Model Hyper-Threading Hypothesis and evaluate its predictions using multiple coordinated tasks that share state within the same problem. We design three conditions (Baseline, Serial Functional Scheduling, and Concurrent Functional Loading) and evaluate their benefits and costs using accuracy, output-token distributions, and attention metrics. On an AIME 2025 development set, Concurrent Functional Loading achieves the highest accuracy. Relative to Serial Functional Scheduling, its typical output length is similar and it is shorter on most problems, while exhibiting greater attention dispersion and higher task-relevant coverage, albeit with a heavier output-length tail. Within-step concurrency and its causal mechanism still require direct tests. Our results show that more dispersed attention can coexist with higher accuracy, providing preliminary behavioral and correlational evidence for the hyper-threading hypothesis. These findings motivate a shift in perspective on inference scaling from "generating more tokens" toward "having each generation step carry more tasks," pointing to a new avenue for improving reasoning performance.
KV-cache compression is often justified by attention maps with a few large weights. This is incomplete: large weights may not contain most of the mass, omitted values can cancel, and preserving the attention output may not preserve the task. We separate these questions. Global score gaps -- not threshold counts -- determine how many tokens are needed to retain a target mass. For a realized row, the weighted sum of omitted values is the exact missing statistic. A controlled retrieval--aggregation model explains when truncation helps and when it hurts. These results motivate CertKV, a training-free compressor that reserves one tail-summary slot per head and allocates the rest by value dispersion. Under matched budgets, CertKV is top-two in seven of nine LongBench-v2 settings, remains in the leading compressed tier on 128K RULER, and realizes a ten-fold cache budget in a packed Llama prototype. Compressibility depends on the mass, values, future queries, and task -- not on a sparse-looking map alone.
Long-context prefill in large language models (LLMs) incurs substantial computation and memory traffic because dense self-attention computes quadratic query-key scores. Existing methods either use a uniform low-precision path or select token interactions, leaving spatial precision routing over hardware-aligned score tiles outside fused dense attention. We introduce TileMix, a tile-centric precision-routing kernel that makes numerical precision an executable spatial decision over score-tile groups within fused dense attention. TileMix partitions the attention matrix into hardware-aligned score tiles, packs routing decisions into compact bitmasks, and dispatches each tile group through FP16 or INT8 score computation while both paths update a shared online-softmax state. Scalable precision grouping lets each routing bit govern multiple adjacent key tiles, preserving hardware-aligned compute tiles and compact metadata at long contexts. By routing all legal tile groups, TileMix preserves dense token connectivity, requires no training, and supports grouped-query attention, variable-length batches, and INT8 key/value caches. Across LongEval, LV-Eval, and A100 prefill benchmarks on LLaMA, Qwen, and Vicuna, TileMix recovers long-context quality lost under uniform INT8 and improves prefill throughput over FP16, yielding a controllable accuracy-efficiency frontier across model families. The implementation is available at https://github.com/HanzhiZhang-Ulrica/TileMix.
Efficient LLM serving is often bottlenecked by the need to pad sequences to a fixed maximum length, and this wastes compute and degrades throughput. Predicting output lengths in advance makes it possible to adopt length-aware scheduling, and this reduces the overhead. This advantage is especially pronounced in long-context reasoning and reinforcement learning applications. Existing approaches, such as entropy-guided token pooling, use token-wise entropy as their primary signal, but they tend to ignore differences in semantic content across tokens. So, important tokens are often underweighted, and tokens carrying little information receive disproportionate emphasis. This hurts the reliability of length prediction. We introduce ESTP (Entropy-and-Semantic Token Pooling), a lightweight framework that addresses this issue by combining entropy with attention-based importance scores. These scores are derived directly from the self-attention weights computed during the LLM prefill phase, and this allows ESTP to capture both uncertainty and semantic importance with minimal additional computation. Since the framework reuses prefill activations, it adds almost no extra memory overhead and introduces only minimal latency. On the ForeLen benchmark, ESTP outperforms baseline methods, achieves better prediction accuracy and lower error rates in most scenarios. When integrated with a length-aware scheduler in end-to-end system tests, it further helps improve overall throughput and reduce the padding ratio. Our results offer a practical and effective building block for length-aware LLM serving systems.
Language models hold latent quantities in a form they can report on, and more of a quantity is present in that form when the task requires reusing it flexibly. What causes a representation to enter that form is open, and the word workspace invites an admission story: a gate that decides what gets in. Testing it on open-weight models with Jacobian lenses, over a benchmark whose five arms share an identical context, we find no gate where it predicts one. Demand raises a concept's lens visibility beyond what applying an operator to a supplied value produces: +0.050 [+0.045, +0.057] in percentile rank on our primary checkpoint, positive on all four we measure, though that arm answers at ceiling and the accuracymatched contrast is stronger under that readout. At the same time one shared linear map decodes the variable from every arm, the control included, at 6.4-9.0x its selection-corrected floor. What produces the later readable form at the queried position is attention-mediated gathering inside a mid-depth window: separating patch depth from readout depth puts transport there at least 17x above anywhere shallower under non-saturating readouts, with no tested MLP output contributing positively inside it. Under the saturating percentile rank the same grid does not localise the window, which is a fact about that measure. An arm that needs the variable for nothing concentrates sevenfold less, so the window is demand-specific. That window has two measured edges, a survival failure below and destruction above, and it falls at the same fractional depth in a 64-layer hybrid and a 62-layer dense model from another family. We localise where the variable is installed and read, not the route from the passage, which transports nothing. But the readout is not a calibrated measure of use: three components move it to within 12% of one another and differ 7.4x in what they do to the answer.
Amanda Bertsch, Luca Soldaini, Matthew R. Gormley +4cs.CL
One might imagine that architectural variations within the dense transformer paradigm have a limited effect on accuracy. However, we demonstrate that this is not the case in the long context setting. Specifically, we show that a set of four minor architectural decisions --- all made by at least one of the Olmo, Llama, and Qwen dense model families --- have a compoundingly negative effect on long context extensibility. Any one of these choices alone has a minor impact on long context performance, but combining three or more can drop the performance downstream by up to 47%. Furthermore, these differences are not detectable from short-context loss or validation datasets. We show that much of the variation in long context ability across model families is driven by these architectural features and detectable from applying context extension early in pretraining. We demonstrate this with controlled ablations that hold data, tokenizer, and extension recipe fixed while varying normalization, GQA, pretraining context length, and sliding window attention. After over 170,000 GPU hours of training, we release the resulting set of models as OlmPool, a set of 26 comparable 7B models with checkpoints before and after long-context extension. This pool includes several architectures that outperform the Llama 3 architecture on long context extensibility. In an analysis of our ablation models, we identify patterns in attention sink behavior and attention distributions across context that are attributable to specific architectural differences.
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.
Multimodal large language models (MLLMs) encode images as long visual token sequences, making prefilling and KV-cache storage expensive. Existing training-free pruning methods select tokens by importance, diversity, or spatial coverage, but treat retained tokens as interchangeable and do not explicitly track which object-related regions are already covered. We present RoRA, a training-free framework that casts visual token pruning as role-oriented regional evidence allocation. Given a fixed budget, RoRA partitions tokens into a protected semantic core, complementary context, and fine-grained detail. It first calibrates text-conditioned attention with a positional prior and a prompt-calibrated object prior, then builds Attention-Anchored Regions (AARs) from high-confidence anchors as lightweight proxies for covered object support. Context is explored mainly outside AARs, while a small AAR-guided budget restores local detail; pairwise similarity is used only for context-stage redundancy filtering. Under matched budgets, RoRA consistently outperforms strong training-free baselines across LLaVA and Qwen-VL families, retaining most of the unpruned accuracy even at aggressive pruning ratios, e.g., 96.5% of full performance at 88.9% pruning on LLaVA-1.5, and improving over D2Pruner by about 5% on Qwen3-VL at 75-90% pruning. At a 66.7% pruning ratio, RoRA requires only 0.7 ms for token selection and reduces end-to-end inference time by 24.6%, corresponding to a 1.33x speedup over unpruned inference on an NVIDIA H800.
Key-value (KV) cache management through compression and eviction strategies has emerged as an important research direction in recent years. Computational demands of large language models (LLMs) and their multi-modal variants during output generation can be partially alleviated by caching previous key and value calculations needed by subsequent scaled dot-product attention operations. However, this leads to another problem: the size of the resulting KV cache grows linearly with context length and quickly consumes all available GPU memory when either the prompt or the generated output are long. KV cache management periodically prunes entries from the cache thereby reducing its memory footprint while attempting to retain sufficient information for accurate generation. A by-product is faster inference speed. We propose a simple yet effective KV eviction scheme motivated by the insight that past tokens which can be well-predicted from more recent tokens are redundant and their associated keys and values can be removed from the cache. To score entries for eviction we run the model on the tokens in their original order, reusing the key and value representations already stored in the KV cache, and applying a counter-causal attention mask so that each position attends only to its future context. This is in-distribution, tied directly to the actual cache contents, and requires no additional training. To further reduce cost, we additionally propose a fast single-layer approximation that restricts the counter-causal pass to the last transformer layer, achieving a significant speedup per refresh cycle at marginal accuracy cost. We evaluate our strategy on various open-source LLMs and benchmark datasets showing competitive or improved performance over other state-of-the-art methods. Reference code is available at https://github.com/metacognitionai/counter_causal.
A. Contreras, D. Porres, R. Abad +4cs.CV cs.AI cs.SE
The development of autonomous vehicles (AVs) usually relies heavily on data-driven artificial intelligence (AI) models that require large volumes of sensor data with ground-truth annotations. While modular architectures are widely used, end-to-end driving paradigms offer a promising alternative by directly mapping sensor inputs to control actions. However, their adoption is limited by challenges in interpretability and explainability. To address this, we present LAIA (Labelled Attention for Intelligent Automobiles), a novel synthetic dataset designed to enrich end-to-end driving research with human attention data. Collected using the CARLA simulator in closed-loop environments, LAIA comprises over 15 hours of driving from 44 participants across carefully crafted scenarios designed to evoke natural responses. Each sequence includes RGB images under six weather conditions, semantic and instance segmentation, depth, optical flow, CAN bus signals, and synchronized eye-tracking data. LAIA enables applications including training attention-aware end-to-end AI drivers, predicting driver behavior, developing methods to detect anomalous driver-attention patterns, and improving model explainability. In this work, we use LAIA to compare human attention with the perceptual attention emerging in our end-to-end driving models, thereby providing insight into their behavior.
A language model with a bounded working memory must repeatedly decide which stored items to keep. Every deployed method decides the moment an item arrives, from the past (StreamingLLM, H2O) or from a guess about the future (SnapKV). We recast the choice as an estimation problem on a hidden signal, whether an item will be reused, placing existing methods on one axis, the commit lag $H$: online filters and learned predictors commit at $H=0$, while Belady's offline optimum sits where the whole future is known. The missing regime in between, fixed-lag smoothing, waits a bounded number of steps, observes which items a correct near-future prediction attended to, and only then commits. This measurement, demonstrated utility, turns Belady's unobservable future request into something we read off the model itself. We instantiate it as a training-free policy, RMM, a strict generalization of H2O that reduces to it exactly when the measurement is uniform. In controlled settings where reuse is endogenous and separated in time, demonstrated utility identifies used memory far better than accumulated attention, and a small bounded memory behaves like a much larger one. But on independent third-party benchmarks, run inside NVIDIA's KVPress harness against its own SnapKV, H2O, and StreamingLLM implementations, the advantage mostly disappears: RMM is on par with H2O for single-turn question answering and loses to both H2O and SnapKV in a streaming multi-turn setting. The cause is simple: on natural text the model is correct about most tokens, so weighting attention by correctness barely changes it, and demonstrated utility collapses onto accumulated attention unless reuse is sharp and endogenous, which standard benchmarks do not exercise. Our contribution is the framework and an honest map of when measuring beats accumulating, not a new state of the art.
Serving large language models at long context is bottlenecked by the key-value (KV) cache, which is read in full at every decode step. Attention keys are locally low-rank though globally high-rank: shared low-rank bases discard page-specific directions that a page's own compact basis retains. LOCKS gives every page its own spectral summary (resident, about a tenth the cache's size), reconstructs within-page logits, estimates each page's attention mass by log-sum-exp, and attends only the top pages; selection itself reads no candidate keys or values. Selecting on this summary alone stays within about a point of the full cache on long-document QA (LongBench-v1), tracks the read-every-key oracle on retrieval-dense RULER down to the smallest budgets, and shows its largest margins on long-form reasoning (AIME26, MATH-500), where baseline selectors collapse. At its shipped $2048$-token budget LOCKS matches FullKV aggregate quality at $100$K$+$ context while attending about $2\%$ of the tokens, and halves per-token decode latency ($2.0\times$ at $1$M tokens) against dense attention. LOCKS ships as a drop-in plugin for unmodified vLLM, with batched decode running in full CUDA graphs.
Jianlin Yu, Jing Lin, Linghui Kong +13cs.LG cs.AI cs.CV
The quadratic cost of attention is a major bottleneck in diffusion-based video generation models. MXFP4 attention provides a promising path toward efficient inference, but direct MXFP4 quantization often degrades generation quality due to two numerical issues: the clipping-underflow trade-off from power-of-two scaling and the row-wise normalization error introduced in the softmax loop. We propose MXAttention, a data-free post-training quantization framework for MXFP4 attention. MXAttention introduces two components: Universal Optimal Scaling (UOS), which exploits the periodic structure of power-of-two microscaling to derive a distribution-independent optimal scaling boundary Qmax=7.25 without calibration or search, and Pre-Normalization Quantization (PNQ), which quantizes unnormalized softmax exponentials before row-wise summation to preserve normalization by construction. Experiments on Wan2.2 and HunyuanVideo show that MXAttention closes at least 95% of the VBench Imaging Quality gap between OCP MXFP4 and FP16, substantially improves frame-level similarity, and preserves FP16-level generation quality with less than 0.01 absolute degradation on all reported VBench metrics. MXAttention also achieves performance competitive with strong NVFP4-based baselines with negligible overhead when fused into the attention pipeline. The implementation is publicly available in MindIE-SD.
Masoud Badiei Khuzani, Sharath Honnaiah, Atiq Islam +2cs.LG cs.AI
Randomized features provide a scalable approximation to kernel machines, but their performance depends strongly on the choice of feature distribution. We propose a particle-based method that learns this distribution by optimizing kernel-target alignment while regularizing particles with a Riesz/Coulomb repulsive potential. The resulting Hamiltonian yields diverse, task-adaptive random features and admits a mean-field description through a McKean--Vlasov equation. We instantiate the method in linearized Transformer attention by learning positive random-feature maps in a first alignment phase, then freezing the kernel and training the remaining network parameters with cross-entropy. Experiments on synthetic classification and sentence-level benchmarks show that learned kernelized attention can improve accuracy, calibration, and robustness for several feature maps while preserving linear-attention inference complexity.
Neural scaling laws describe how loss decreases as models, data, and compute grow, but they do not answer a prior question: for a fixed task, what is the minimum model capacity required to solve it? We study this through the Entropic Bound, a spectral notion of task-intrinsic capacity for Transformers. We first prove that, in a linear attention surrogate, the intrinsic rank $r^*$ of the token-mixing operator is a tight lower bound: any rank-deficient model incurs unavoidable excess risk, and the bound is achievable at $r^*$. We further show that gradient descent recovers this rank under standard low-rank implicit-bias assumptions, confirm all three properties empirically, and show $r^*$ is recoverable from data before training. We then ask whether this transfers to real attention. A naive transfer fails, and a controlled interpolation ladder localizes the cause precisely: it is not softmax and not a rank constraint, but the input-conditioned nature of attention's mixing operator, which a static weight kernel cannot summarize. Motivated by this, we introduce an attention-native intrinsic rank -- the minimum query-key kernel rank realizing the task within the attention class -- and show that under this definition the full Entropic Bound structure (deficiency, achievability, recovery) is restored for both linear and softmax attention, with the energy effective rank as the estimator robust to softmax distortion. Finally, we map the boundary of data-only predictability: $r^*$ is exactly recoverable for linear QK attention, even without the value map at scale, while softmax attention admits only partial pre-training recovery due to nonlinear inversion and kernel-value identifiability effects. Our results reframe the Entropic Bound from a post-hoc descriptor into an attention-native capacity measure with a precisely characterized predictability frontier.
Deterministic KV-cache eviction keeps the top-$k$ tokens under an importance score and deletes the rest. We prove that this design cannot know what it destroyed: evicted values can be altered so that everything the serving system retains is unchanged while the true attention-output error grows arbitrarily, so no serving-time estimator of that error is consistent. Randomized eviction restores identifiability. With a Poisson-sampled tail at known inclusion probabilities, one logit offset performs the Hájek correction inside the softmax, and a survey-sampling variance estimator over the retained set becomes a per-step error certificate with 0.97 empirical coverage at no accuracy cost. On real workloads we pre-registered seven claims and lost three: question-aware eviction at 25--50\% budgets is nearly free; output log-probability predicts failure better than the certificate; certificate-gated budget escalation adds nothing. What survives is attribution: the certificate separates cache-induced from inherent failures (AUC 0.73--0.75, against 0.47--0.54 for output confidence) and schedules recomputation better than random or confidence gating. Randomization buys attribution, not prediction.
Streaming video diffusion models have made substantial progress toward interactive and dynamic world simulation, but the nested autoregressive and denoising loops of conventional next-frame generation hinder real-time deployment. Recent rolling-window methods pipeline denoising across multiple consecutive frames at different noise levels, improving throughput and long-horizon stability. However, they tokenize every state at the same fine spatial granularity, leaving substantial noise-dependent redundancy in the joint denoising window. We propose Ms.Forcing, an efficient streaming video generation paradigm that adapts spatial granularity to each state's noise level. Its Multi-Scale Patchification (MSP) assigns coarser patches to noisier states, reducing the active-window token count by 45%, while Multi-Scale Self-Attention (MSSA) matches the density of visible non-sink keys and values to each query scale to further reduce attention cost. Because both schedules are fixed by window position, Ms.Forcing retains a static, hardware-friendly computation graph. We further introduce Homogeneous-Noise-Level DMD (H-DMD), which assembles each fake video from clean predictions sharing the same source noise level, thereby reducing the mismatch between DMD training sequences and inference-time rollouts. The multi-scale design helps offset the additional training cost of backpropagating through overlapping windows. We include both quantitative and qualitative experiments to show that Ms.Forcing reaches 22.84 FPS on a single H200 GPU, 39.6% faster than Rolling Forcing, while significantly improving VBench scores in both short video and long video generation setting.
We derive four memory-optimal inference artifacts for transformer attention using the Mathematics of Arrays (MoA), each following directly from the forward-pass Denotational Normal Form (DNF) of with the query-row index fixed to the current decode step. The artifacts are: (1)~a single-query decode DNF in which the $ψ$-reduction eliminates the $K^\top$ buffer algebraically, achieving $(d_k + nd_k+ nd_v+ d_v)\times4\,{B}$ Dynamic Random Access Memory (DRAM) traffic result numerically verified to $\|{err}\|_\leq2\times10^{-7}$; (2)~a C/OpenACC Graphics Processing Unit (GPU) kernel with Operational Normal Form (ONF) stride arithmetic and hardware-coalesced memory access, verified to $\|\mathrm{err}\|_\infty=0$ (exact IEEE-754 floating-point arithmetic); (3)~a multi-step KV-cache with $O(d_k+d_v)$ per-step append via MoA concatenation $\#$; and (4)~Grouped-Query Attention (GQA) and Multi-Query Attention (MQA) derived via $ψ$-selection, achieving a proven $\frac {h_q} { h_{kv} }$ reduction in KV traffic. All programs are verified against PyTorch scaled_dot_product_attention.
Transformers with relative positional encodings often extrapolate to sequences longer than those seen during training, whereas transformers with learned absolute encodings typically do not. This is a robust empirical regularity, and the explanations offered for it so far are chiefly about expressivity, that is, about whether a length-generalizing solution exists. We give an optimization explanation. On a minimal fixed-offset retrieval task that isolates positional selection, the gap is governed by the implicit bias of the trained attention head: among the many solutions that fit short sequences, which one gradient descent actually selects. We prove that rotary encodings make the attention logit a function of relative offset alone, an exact equivariance, so whatever selection rule is learned at training lengths is reproduced verbatim at every longer length. Learned absolute encodings instead leave out-of-range positions unconstrained, and the trained head pins to a fixed absolute position inside the training range. We characterize the learned rotary rule as a low-rank ``carrier'' kernel aligned with the target offset, and we derive the resulting graceful accuracy decay as an attention-dilution law; both predictions are confirmed across seeds and offsets. A linear-attention control shows the mechanism is specific to softmax: without normalization, training selects a min-norm interpolant that does not extrapolate. The phenomenon, the equivariance, and the carrier all transfer to a multi-layer, multi-head transformer trained on a full-sequence length-generalization task. The account connects the implicit bias of attention, implicit bias for extrapolation in recurrent models, and the learning side of the RASP-L conjecture.
Understanding long videos with multimodal large language models (MLLMs) requires selecting a compact set of frames from thousands of candidates, yet identifying the right frames seemingly requires understanding the video first. We resolve this circular dependency with a simple observation: cross-modal attention at validation-selected extraction layers in MLLMs already provides query-relevant frame evidence without requiring autoregressive generation. We exploit this property to build DAFS (Dynamic Attention-based Budget-aware Frame Selection), a training-free frame selector. A lightweight MLLM selector, even with only 2B parameters, can extract frame-level evidence by converting selected-layer attention into relevance scores through query-conditioned aggregation. This enables cross-frame comparison without autoregressive decoding. To handle the selector's own context constraint, we formulate the joint allocation of candidate pool size and per-frame token budget as a discrete optimization problem solved by dynamic programming. Under a 32-frame budget, our selector improves over uniform sampling by up to 6.4 points on Video-MME and outperforms prior training-based selectors under matched frame budgets, while generalizing across selector and answerer backbones, and across tasks, without retraining.
Attention-based KV cache eviction (H2O and its descendants) compresses the memory-constrained state of a long-context model by ranking tokens on accumulated attention mass, treated here as signal energy, and keeping the heaviest. On schema-dense input streams such as nested JSON, this score acts as a non-stationary filter that disproportionately retains noise: a non-content sink role (delimiters or whitespace) carries an order of magnitude more energy than any content role, and structural KEY tokens are over-retained at roughly 1.8x the rate of the answer-carrying VALUE tokens, collapsing exact-match accuracy from 88% to 0% at a 5% budget as the signal-to-noise ratio of the retained state degrades. A counterfactual experiment establishes that suppressing KEY tokens is the best deployable filter. Our retraining-free, role-conditional allocation over SnapKV's windowed score, governed by a single tuned hyperparameter, closes 63-98% of the H2O gap at sub-20% budgets and, at higher budgets, modestly matches or exceeds full-cache accuracy -- a small, seed-sensitive denoising effect (borderline significant at B=0.50; not distinguishable from zero at B=0.30 over four seeds). A 15 MB linear role probe supplies these labels at negligible inference cost, though matching parser-level downstream accuracy remains open.
Wenhui Chen, Jianlin Chen, Ziyao Lin +1cs.AI cs.IT
The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality. We propose its sequel and boundary, the Capability Convergence Hypothesis (CCH): under a fixed per-token inference budget, representational convergence does not entail capability convergence. Capability instead converges toward a class, the access-complete hybrid: any architecture holding both a compressive O(1)-state channel and a scalable verbatim-index channel. We anchor it on a witness task, the Newton's-apple problem in an infinite stream, and name three resource walls: a Shannon wall barring any o(Nb)-state architecture, a horizon wall barring any fixed window, and a circuit wall barring fixed-depth attention-only composition (conditional on TC0 != NC1). Under an explicit separability assumption a hybrid crosses all three by paying each wall's price, so capability is strictly super-additive under composition. We separate what we prove from what we conjecture: the access-completeness principle rests on information-theoretic lower bounds and pre-registered experiments, while the field-level convergence trend is an economics-motivated conjecture. We report the first pre-registered small-scale tests under criteria frozen before the data: the predicted scissors gap is measured (exact-retrieval error 0.994 vs. 0.000 once a 64-scalar state gains one global-attention layer), the state-tracking bifurcation lands at the registered boundary, and a conjunction witness shows an irreducibly two-channel solution; one prediction failed with its direction reversed and is reported as such. Representational convergence is given freely by scale; capability convergence must be purchased by access structure.
Fixed-state sequence models compress an unbounded past into a bounded state, which caps their associative recall at roughly the state dimension; attention escapes the cap by keeping a key-value entry for every token, at quadratic compute and a cache that grows with the sequence. We study the middle ground: a sparse cache that allocates a slot only when an input is novel, so its size tracks the number of distinct items rather than the number of tokens. The allocation rule is the DP-means clustering rule, the small-variance limit of a Dirichlet-process mixture, used not as latent-variable inference but as the key-value memory operator for a deep recurrent backbone. We develop it in two forms, a static cache with a fixed concentration and a surprise-adaptive variant whose concentration follows the recent novelty rate. On a controlled associative-recall benchmark with redundancy we show that the cache matches full-attention recall while storing only the distinct items, that it dominates a fixed-budget eviction cache on the recall-versus-size frontier, and that on a state-space backbone it answers both a recall query and a long-range aggregate at the lowest memory of any model tested. The allocation is learnable end to end: a two-parameter novelty-threshold gate trained on the task loss alone recovers the rule exactly, whereas an over-parameterized gate fails, so the operative ingredient is the inductive bias rather than capacity. The evidence is a family of controlled mechanism studies at modest scale, with the distinct-items property confirmed on four real streams (recommendation, systems logs, clinical events, and insurance claims); a real-backbone, real-corpus language validation is pursued in a companion study.
Scaling Large Language Models (LLMs) has been driven mainly by enlarging the Transformer backbone, but for an already-strong model this requires another round of costly pretraining. We study whether an existing backbone can keep improving by allocating more computation to each token while leaving the Transformer backbone fixed. Depth-recurrent (looped) Transformers pursue this goal but are hard to scale, because looped computation does not fit naturally with the pipeline parallelism used to train the largest models. We add computation along the sequence-length dimension, where the extra computation is simply a longer input and stays compatible with standard large-model training. We propose Hidden Decoding, a sequence-length scaling method applied during continued pretraining (CPT). It expands each token into n streams with independent embedding tables and keeps the intermediate streams' key-value cache as context, so each token performs more internal computation without adding or widening Transformer layers. To keep this affordable at scale, we introduce Stream-Factorized Attention, in which most layers attend only within each stream and only a few layers mix across streams, reducing the attention cost from quadratic to roughly linear in n. Experiments support two scaling results. At frontier scale, we train WeLM-HD4-80B and WeLM-HD4-617B at n=4 and improve their matched non-HD baselines, making Hidden Decoding the first demonstrated sequence-length scaling method at the 100B+ MoE scale. Across expansion factors, the gains grow as n increases, showing that sequence-length expansion is a practical fixed-backbone scaling path for frontier-scale LLMs.
Modern LLMs are increasingly deployed in long-context applications such as retrieval-augmented generation, repository-level coding, and agentic workflows whose accumulated reasoning and tool traces routinely push the input an order of magnitude past the pretraining window, making zero-shot context extension the dominant deployment path for open-weight checkpoints. The dominant zero-shot methods (YaRN, Self-Extend, DCA) fix a single rescaling factor up front, so an aggressive factor sacrifices short-context fidelity while a conservative one breaks down at long contexts; recent length-aware variants adapt the mapping, but with a fitted or distance-dependent schedule. We propose Jet-Long, a tuning-free zero-shot method that pairs a local RoPE-faithful window with a long-range window whose rescaling factor adapts dynamically to the current sequence length via a parameter-free analytic schedule, recovering the base model exactly at short inputs while extrapolating cleanly at long ones. An inclusion-exclusion attention merge and an on-the-fly RoPE correction rotation make the bifocal construction essentially free at inference; fused into a single CuTe kernel, long-context prefill reaches up to $1.39\times$ FA2 throughput on H100 (approaching the Hopper-only FA4), and single-batch generation incurs $\le 4\%$ overhead at every length. On Qwen3-1.7B/4B/8B up to 128K context, Jet-Long leads RULER by $+4.79$/$+2.18$/$+2.03$ pp over the strongest baseline at 1.7B/4B/8B, achieves the best overall accuracy on HELMET-RAG (a benchmark identified by HELMET as the most efficient predictor of downstream long-context performance) and attains the lowest PG-19 perplexity. Jet-Long also generalizes to hybrid attention architectures such as Jet-Nemotron for further long-context improvement without retraining, and remains hyperparameter-resilient for ease of deployment.
In this report, we present Pelican-VLA 0.5, a unified VLA model that integrates vision-language understanding, future-frame generation, and action prediction within a single architecture. Pelican-VLA 0.5 achieves attention-level generalization: without object annotations, segmentation masks, attention supervision, or task-specific fine-tuning, its action pathway already focuses on the manipulation-relevant object and contact region. This behavior persists across unseen scenes and unseen robot embodiments, and is substantially stronger than in other open-source VLA baselines. We verify that this ability originates from the learnable Bottleneck Token inserted between perception and action: by routing task-relevant visual information through a compact bottleneck, the tokens interface induces manipulation-centric attention during pre-training and remains effective across different policy structures, including a MoT-style architecture.