Papers

We revisit the claimed converse theorem for mismatched decoding over binary-input discrete memoryless channels (Balakirsky, 1995) and the subsequent work refuting this converse via a numerical counter-example (Scarlett, Somekh-Baruch, Martinez, and Guillén i Fàbregas, 2015). A notable gap in the existing understanding is that no concrete flaw was identified in Balakirsky's analysis. In this paper, Balakirsky's proof is "diagnosed", and it is demonstrated that (i) his permutation lemma is flawed regardless of the correctness of his combinatorial approximation lemma; (ii) there are at least two specific incorrect steps regarding restricted codes and selector sequences, and these appear to be unlikely to admit a local repair; and (iii) the proposition in which these incorrect steps are used is false in general.

While hypergraph-based Retrieval-Augmented Generation (RAG) effectively captures higher-order multi-entity correlations, existing paradigms treat extracted hyperedges as isolated factual assertions. This structural fragmentation engenders rigid "knowledge islands" that bottleneck multi-hop causal inference, temporal tracking, and narrative synthesis. To systematically address these challenges, we introduce Dual-Hypergraph Indexing (DHI), a hierarchical representation framework that elevates discrete facts into structured analytical insights. DHI couples a foundational entity-relation factual hypergraph ($H_K$) with an elevated deep-insight hypergraph ($H_D$) via a dual-pathway aggregation algorithm. Specifically, DHI employs: (1) importance-driven hub aggregation via 5-metric topological profiling and adaptive thresholding to capture spatial semantic clusters; and (2) temporal chunk-chain progressive aggregation via sliding-window greedy exploration to track chronological evolutions. Across five benchmarks, DHI achieves state-of-the-art performance, boosting logical coherence by +1.53 on the multidisciplinary Mix benchmark and scoring 85.78% on complex medical pathology reasoning tasks. DHI provides a robust architecture for next-generation multi-hop RAG.

Advances in generative modeling have recently been extensively employed in robotics for policy learning. In particular, Conditional Flow Matching (CFM) trained with expert demonstrations has been shown to outperform existing methods on robot manipulation benchmarks. While prior work has mainly focused on single-task settings, we study the problem from a multi-task perspective, as training independent models for each task is computationally expensive. Multi-Task policy learning comes with its own set of challenges, as naively training on a concatenated dataset of demonstrations would either require increased model capacity to accommodate the added complexity or result in drops in performance. We propose to distill knowledge from single-task CFM experts into a shared multi-task policy by transferring their learned velocity fields. We combine this distillation signal with the original CFM objective to retain fidelity to the demonstrations. Experiments on RLBench show that our approach improves multi-task policy performance over naive training while maintaining a fixed model size.

Multi-center clinical studies and biomedical research collaborations increasingly seek to utilize data across centers to build models that generalize beyond any single center. This creates two distinct challenges: data protection regulations may restrict the sharing of raw patient data across institutions, while centers may collect only partially overlapping sets of features under different protocols. Federated learning enables collaborative model training without centralizing raw data. However, existing federated imputation methods rarely evaluate feature-level missingness, in which entire features are unobserved at some centers. To address this setting, we adapt the ReMasker masked autoencoder to federated learning (Fed-ReMasker), enabling centers to impute features never observed locally by leveraging knowledge learned across collaborating centers. We evaluate Fed-ReMasker in a benchmark spanning synthetic datasets with linear and nonlinear relationships and real-world tabular datasets, including clinical data. The benchmark varies the number of centers, the missingness ratios, and client heterogeneity. Fed-ReMasker achieves the lowest imputation error in 93.2% of value-level and 96.7% of feature-level scenarios in the homogeneous benchmark. It also remains robust to client heterogeneity using simple federated averaging, outperforming all baselines in all 36 value-level scenarios and each baseline in at least 35 of 36 feature-level scenarios, and comes within 3.0% on average of a centralized model trained on the pooled data.

A graph is biplanar if it is the union of two planar graphs on the same vertex set. The largest chromatic number of a biplanar graph is known to lie between 9 and 12. The lower bound comes from Sulanke's graph, which has independence number 2, and a biplanar graph on 19 vertices with independence number 2 would have chromatic number at least 10. Gethner and Sulanke asked in 2009 whether such a graph exists. We show that it does not, and more generally that every biplanar graph with independence number at most 2 is 9-colorable. The proof embeds a hypothetical counterexample in the union of two sphere triangulations, enumerates with SAT modulo symmetries the 3271 graphs that pass a necessary filter for the complement of such a union, and shows with a SAT solver that none of them is such a complement; a matching argument reduces the general statement to this computation and one further case on 18 vertices. The computational part of the proof, including the completeness of the enumeration and every refutation, is checked in Lean 4, assuming three classical facts about planar graphs. The Lean development, the SAT instances, and the enumeration certificates are available on Zenodo.

Deep vision systems remain vulnerable to corruption, occlusion, and distribution shift despite strong benchmark performance. Existing reliability methods typically evaluate uncertainty at individual time steps and do not explicitly model how a system progresses toward failure. We introduce Visual Tripwires, a predictive reliability framework that uses temporal instability in model behaviour to anticipate impending failure. Our central hypothesis is that predictive degradation develops progressively through measurable changes in latent representations, prediction trajectories, and attention structure. Visual Tripwires captures these changes using representation drift, prediction oscillation, trajectory curvature, and attention entropy. A lightweight tripwire predictor aggregates these signals over a temporal window to estimate the probability of failure within a future prediction horizon. Experiments across multiple datasets, architectures, and progressive perturbation settings show that the proposed instability signals emerge before predictive degradation and provide earlier and more accurate failure warnings than conventional uncertainty estimation methods. These results demonstrate that temporal instability contains useful information about future model reliability and provides a practical basis for early warning in deep vision systems.

Recent advances in text-to-video generation have enabled high-fidelity visual synthesis, yet realistic motion remains challenging. Generated videos may exhibit temporal discontinuities, inconsistent action progression, and structural distortions during complex movements. Even when individual frames appear realistic, the underlying motion may evolve in inconsistent or implausible ways. Standard generative objectives provide limited motion-specific supervision, leaving motion evolution insufficiently constrained. In this paper, we propose MotionSpec, a motion supervision framework centered on Spectral Trajectory Consistency (STC). STC constructs dense anchor-relative motion trajectories and transforms them into motion spectral volumes via a temporal Fourier transform. By aligning the spectral amplitude and phase of predicted and target trajectories, STC constrains both motion strength across temporal frequencies and the temporal organization of motion. To complement this trajectory-level supervision, we introduce Local Flow Consistency (LFC), which aligns consecutive-frame optical flow between predicted and target videos to stabilize local motion transitions. Experiments demonstrate that MotionSpec consistently improves motion consistency, temporal coherence, and plausibility while preserving visual fidelity.

Backtest auditing is a calibration problem: high flaw recall is not useful when the model falsely flags matched clean strategies. We build a 96-item paired benchmark in which every flawed backtest has a clean control that holds strategy, dates, code style, labels, and reporting scaffold fixed while changing one methodology detail. A deterministic scorer separates flaw recall, clean-control false positives, evidence localization, and fix relevance. Over 1440 cached audits from four text endpoints, the primary DeepSeek auditor reaches 100.0% closed and clean-aware code recall, but open prompts over-flag 93.8% of clean code controls, and clean-aware all-three specificity is 87.5% even where recall saturates. A clean-aware warning drops DeepSeek code false positives from 20.8% (95% CI 11.7–34.3) to 0.0% (0.0–7.4) at unchanged recall, while the budget anchor still flags 38/48 clean controls under the same prompt. Reporting recall alone would rank three of these four models identically; reporting the clean-control rate separates them by 79 points.

The integration of model-based and data-driven paradigms provides a powerful framework for fault diagnosis by combining the interpretability of analytical redundancy relations, i.e., input-output relations that are used as diagnosis indicators in model-based diagnosis, with the adaptability of learning techniques. DT4X is a recent diagnosis algorithm that uses symbolic regression to generate multivariate relations leveraging some properties of analytical redundancy relations and uses them as split functions in a decision tree. However, its symbolic regression procedure optimizes only the separation between two selected classes at each node, often fragmenting the remaining classes and degrading both interpretability and diagnosis performance. This paper introduces DT4X+, an enhanced version of DT4X that modifies the construction of training sets and the symbolic-regression loss so that expressions separate the target classes while preserving the coherence of non-target classes. The resulting relations become fully consistent with ARR properties and lead to more informative splits, improved robustness, and better performance on dynamic-system datasets. Experiments conducted on several benchmark systems demonstrate the benefits of this enhanced formulation.

We propose LAYERSCOPE, a label-free, layerwise framework that aims to characterize a model's learned representations in video and multimodal settings. Evaluating downstream performance using representations from final or intermediate layers typically requires large amounts of labeled data, repeated task-specific evaluations, and substantial computation. To address these limitations, LAYERSCOPE uses local, global, distributional, and correspondence-based geometric metrics to compare layerwise representation structure within and across models without requiring task-specific labels. We evaluate seven architecturally diverse models across video and multimodal classification, clustering, and text-to-video retrieval tasks from MVEB/MVEB+. We find that intermediate-layer representations can outperform final-layer and model-default outputs. We also find that no single geometric metric consistently predicts downstream performance, but note that distinct layerwise geometric signatures emerge across model families. LID shows task-dependent relationships with performance, while RankMe provides the strongest measure for classification and clustering, but is not a universal layer selector. We also find that pairing-aware metrics explain retrieval better than distributional distances alone. LAYERSCOPE therefore offers a framework for comparing representations across models and layers, enabling a more systematic evaluation in video and multimodal settings.

The job shop scheduling problem is a challenging combinatorial optimization problem, and recent reinforcement learning approaches using graph neural networks have shown promise for learning scheduling policies directly from problem instances. However, training on large instances remains computationally expensive, and generalization across instance sizes remains challenging. This paper studies curriculum learning for graph neural network-based reinforcement learning in the job shop scheduling problem by comparing it with single-size training across three target sizes: 20 x 20, 25 x 25, and 30 x 30. In the curriculum setting, the policy is first trained on smaller instances and then progressively adapted to larger target sizes, allowing scheduling behavior learned in earlier stages to support learning on larger instances. Models are evaluated on unseen instances from 8 x 8 to 30 x 30 using the optimality gap, considering both generalization across all evaluation sizes and specialization on the target size. Results show that curriculum learning consistently reduces wall-clock training time, with larger benefits as the target size increases. The strongest advantage is observed at 30 x 30, where curriculum learning reduces the mean optimality gap across all evaluation sizes by approximately 8.1 percentage points, reduces the target-size mean optimality gap by approximately 8.6 percentage points, and saves approximately 50 hours of training time.

Digital zoom transitions between dual cameras often exhibit conspicuous discontinuities in geometric structure and chromatic consistency, degrading the user experience. While recent dual-camera smooth zoom (DCSZ) methods attempt to mitigate this by fine-tuning frame interpolation (FI) models on DCSZ data, they struggle with the large cross-view disparities and complex geometric transformations. Considering that the generative prior of diffusion models is suitable for addressing this problem, we explore their application to DCSZ. However, naively applying existing diffusion-based FI models still yields low-fidelity transitions due to insufficient conditional guidance, high-frequency information loss during VAE encoding, as well as inadequate temporal consistency. To address this, we propose ZoomDiff, a high-fidelity diffusion model that leverages dual-camera inputs in both latent and pixel spaces for photo-realistic transitions. Specifically, we first strengthen dual-image conditional guidance during the multi-step denoising process to improve geometric consistency. Then we inject flow-aligned multi-scale features from the VAE encoder into the VAE decoder to recover high-frequency details, where flow-guided temporal consistency supervision are introduced to produce more smooth transitions. Extensive experiments on both synthetic and real-world datasets demonstrate that ZoomDiff outperforms state-of-the-art methods quantitatively and qualitatively. Project page: https://jiayi-hit.github.io/ZoomDiff.github.io/.

We study the distributed average consensus problem under persistent link-level disturbances modeled as a martingale difference sequence with uniformly bounded conditional second moments. Under such disturbances, the standard stochastic-approximation-based linear iteration with diminishing stepsizes drives the network to consensus on an unbiased random variable with non-vanishing variance instead of the exact initial average. To understand and resolve this limitation, we develop an anchoring-based mechanism derived from a decentralized gradient descent formulation and study the effect of incorporating a decaying anchoring term that continuously pulls each agent state toward its initial value. This perspective provides an intuitive interpretation of how state anchoring counteracts disturbance accumulation. Under standard summability conditions, we prove that the resulting algorithm achieves exact average consensus almost surely. Furthermore, this decentralized gradient perspective offers a unifying framework for several related methods and an interpretable design principle for exact average consensus under persistent disturbances.

Conventional image registration algorithms are robust to domain shifts and achieve low errors, but they are slow and computationally expensive. Deep-learning methods are efficient at inference-time, but face challenges in out-of-domain samples. We propose Recursive Uncertainty-Gated Image Registration (RUGI), an algorithm for iteratively refining deformation fields predicted by learning-based registration models. At each iteration, the registration model predicts an incremental deformation, and a gating map modulates the update. Refinements are hence concentrated in regions that remain difficult to register. We explore two gating strategies: a learned uncertainty-based approach and an image residual error approach. We evaluate RUGI on cardiac MRI and echocardiography datasets and show consistent improvements over single-step inference. Ablation experiments demonstrate that iterative refinement alone improves registration, but informative spatial gating provides a significant additional benefit. The error-gated variant of RUGI can also be applied directly to existing pretrained models; applied to VoxelMorph, TransMorph, and CycleMorph, it yields MSE reductions of 27-37% with no modification to the original training procedure. The improvements in registration performance are reflected in decreased errors in ejection fraction estimation relative to ground truths. These results demonstrate that spatially selective iterative refinement provides an effective strategy to improve registration accuracy at inference-time.

Evaluating open-ended text generation involves understanding how different properties of a continuation relate to its perceived quality. We present a reference-based framework for examining coherence and diversity through three perspectives: aligning their evolution with human trajectories, comparing their summaries with a human continuation of the same prompt, and estimating their likelihood under a human reference distribution. Experiments with human quality ratings suggest that diversity-based alignment and mean-based comparisons capture quality-related variation, although the comparisons do not establish a predictive advantage for temporal alignment over simpler baselines. Reference likelihood also shows positive associations with ratings, with results varying across reference configurations and scoring horizons. Together, these analyses provide a structured way to examine how measured coherence and diversity relate to human judgments, while distinguishing similarity to human references from quality itself. Code and analysis resources are available at https://github.com/EstebanGarces/likely_human.

Segmentation-based multi-object tracking (MOT) with foundation video models such as SAM2 offers strong localization quality, yet remains fragile in crowded, real-world scenes. In detector-prompted SAM2 pipelines, failures typically arise at three stages of the object lifecycle: (i) erroneous or duplicate track initiation, (ii) memory drift during close interactions, and (iii) unreliable re-identification after long occlusions or re-entry. These errors corrupt object memory and accumulate over time, making long-horizon tracking unstable. In this paper, we reframe MOT as a lifecycle memory integrity problem. We present LiAM-SAM, a Lifecycle-Aware Memory (LiAM) framework with targeted mechanisms for each of the three failure modes. At track birth, to prevent faulty or duplicate initiations, we apply contrastive track initiation, which conditions each prompt on existing nearby tracked instances. To preserve memory integrity during strong interactions, we introduce motion- and geometry-grounded memory correction that resolves interaction confusions and suppresses drift. For reliable re-identification after disappearance, we maintain an adaptive context memory that promotes diverse and trustworthy references as long-term identity anchors. Finally, similarity aware spatial pruning optionally selects the memory tokens to retain at cross-attention time, improving efficiency with minimal accuracy loss. LiAM-SAM represents a modular, detector-agnostic, SAM2-based MOT system that achieves state-of-the-art HOTA and IDF1 on the evaluated benchmarks. In association-challenging environments, our ablations show that LiAM improves a detector+SAM2 baseline by +10.5 HOTA, +17.4 AssA, and reduces identity switches by 96%.

Steel surface defect detection is critical for automated industrial quality control but remains challenging due to subtle inter-class texture differences and pronounced class imbalance. We introduce TEEP-RCNN (Texture-Enhanced Edge-aware Perception Region-based CNN), a two-stage detector built on Faster R-CNN with a Feature Pyramid Network backbone and an improved Convolutional Block Attention Module (CBAM). Our CBAM adds dropout regularization in the channel attention MLP and batch normalization on the spatial attention branch, reducing co-adaptation and stabilizing gating logits. Training uses a differential learning rate protocol with cosine annealing warm-up, separating update rates for the pre-trained ResNet-101 backbone and the detection head. At inference, predictions are refined via Test-Time Augmentation fused with Weighted Box Fusion (WBF), improving localization stability on elongated and boundary-adjacent defects. On the NEU-DET benchmark across six defect categories, TEEP-RCNN achieves 73.3% mAP@50 and 37.9% mAP@50-95 in only 10 training epochs on a single GPU, competitive with YOLOv11m (76.2% mAP@50, 100 epochs) while outperforming it on the rolled-in-scale category under the COCO metric. Per-class analysis shows the spatial attention branch is most effective on elongated texture defects such as patches and scratches, while crazing remains an open challenge across both paradigms due to its distributed non-local texture structure.

Driving world-action models improve planning by coupling multimodal reasoning with future prediction, but their growing inference cost increasingly conflicts with the real-time latency requirements of vehicle control. Existing acceleration methods reduce tokens, layers, or sampling steps with policies selected prior to deployment, yet leave residual runtime variation largely unexploited after offline profiling and static scheduling on shared onboard compute. We observe that the largest admissible compute budget varies systematically with the residual runtime state, while recent realized latency provides a direct signal of the available compute slack. Motivated by this observation, we propose SlackDrive, a pre-inference compute allocator that reuses realized latency to select the compute budget of each control step before model execution. SlackDrive profiles the latency and planning utility of a small discrete budget set once, estimates online compute state from completed forwards, and selects the highest-utility budget predicted to remain within the admissible latency envelope, complementing existing profiling and resource scheduling while preserving the driving backbone and its compute actuator. On NAVSIM v2 with DriveDreamer-Policy, SlackDrive improves latency-constrained EPDMS by $21.7\%$ over the strongest baseline under a stringent latency regime, while the full-budget model and preconfigured token-pruning baselines exceed the admissible latency envelope under runtime contention.

Automated LOD3 building modeling typically relies on purpose-built geometric or learning-based pipelines, limiting flexibility across heterogeneous buildings and input evidence conditions. This study investigates whether Astra, a general-purpose multimodal foundation model, can address these limitations through zero-shot reconstruction of LOD3 building models within an agentic framework under bounded autonomy. AstraLOD3 combines multi-view images, calibrated cameras, and a filtered sparse SfM point cloud with a natural-language reconstruction specification, while the Astra agent dynamically selects and executes computational procedures using Python and Blender. Across 35 runs, including 24 benchmark buildings, AstraLOD3 achieved a mean FRDS of 0.9647 and geometric agreement comparable to that of previous purpose-built methods. Controlled ablations further revealed the effects of reconstruction guidance, evidence modalities, model configuration, and run-to-run variability. The results demonstrate that structured LOD3 reconstruction can be formulated as a constrained agentic process rather than as a fixed pipeline. Future work will investigate adaptive refinement, user-guided correction, task-specific specialization, and damage-aware reconstruction.

Self-supervised speech models encode rich phonetic information, but it remains unclear how to transform this information into interpretable metrics for second-language (L2) pronunciation assessment in spontaneous speech. We propose a native-reference coordinate geometry in which phone-class averages from native speech define a low-dimensional reference subspace, and L2 speech is evaluated by its distance to matching native phone-class coordinates. Unlike prior distance-based approaches, our method does not require parallel recordings with matched linguistic content or dedicated pronunciation labels. Across different self-supervised encoders and modeling choices, the resulting native-reference distances show negative Spearman correlations up to -0.5 with speaking proficiency, indicating that higher-proficiency speakers tend to have smaller distances to the corresponding native phone-class coordinates.

Mixture-of-Experts (MoE) training requires global load balance to prevent expert under-utilization and local balance for efficient expert-parallel execution. Existing distributed Quantile Balancing (QB) uses shard-dependent or approximate global quantiles, while token-independent expert biases cannot ensure microbatch-level balance. We introduce Exact Quantile Balancing (EQB), which computes exact global-batch BF16 quantiles with negligible communication, and Load-Error Injection (LEI), which injects local load errors directly into router-score gradients. On 7.5B-parameter MoEs trained for up to 500B tokens, EQB improves global balance and downstream performance over naive QB, while LEI improves local balance and outperforms the GShard loss at comparable quality.

Video understanding is usually benchmarked on curated, single-actor, or professionally filmed clips, and a strong score there is routinely read as evidence a model is robust enough for deployment. Amateur team sport is a useful, largely untested place to check that assumption: over eight million students played a school sport in the United States in 2024-25 alone, almost none of it filmed by more than a single fixed camera, with several candidate actors crowded into frame and no operator or second angle to fall back on. Using volleyball as a test case, we ask whether strong performance on general video and world-model benchmarks translates into reliable, per-player attribution once footage is this chaotic, turning footage into statistics through a chain of tasks from finding play boundaries to naming who did what. We evaluate four approaches (prompting and agentic reasoning over frontier vision-language models, classical computer vision with small trained specialists, self-supervised video world models, and manual annotation) at every stage, on 66 amateur matches with 46,648 human-labelled contacts, filmed under conditions no published benchmark uses. No single paradigm wins every stage, and static, single-frame computer vision is not competitive at any stage involving motion or identity. A prompted model segments matches well, yet a far smaller trained model beats it at spotting contacts for a fraction of the cost, and the sport's own rules recover rally outcomes the pixels cannot. Identity is where every automated approach struggles: a jersey number is a static fact temporal reasoning cannot recover if never visible, unlike sporting action, a repeated motor pattern a temporal model can exploit, which is why holistic reasoning improves event detection while identity stays unchanged. We close with where each approach earns its cost, and what transfers beyond volleyball to amateur sport.

Modern information retrieval (IR) systems rarely represent time, yet many information needs depend on it: in clinical, journalistic, and legal search, when an event occurred can decide whether a document is relevant. Dense retrievers and Retrieval-Augmented Generation (RAG) pipelines match queries to documents well on topic but poorly on time, so they surface content that is on-topic yet temporally wrong. We introduce Temporal Textual Similarity (TTS), a task that measures how well two anchored texts align in time, independent of their topical similarity. We then present TEMPS (Temporal Embedding Model for Precise Search), a modular temporal branch that attaches to a frozen semantic retriever and trains on that signal. It resolves anchored temporal expressions to intervals and moment-matches each one to a Gaussian; the resulting ordering supervises an anchor-date-conditioned encoder, whose score we fuse with the semantic score at inference. Grounding supplies the supervision, so training uses no hand-labeled temporal data. The temporal score itself is the Gaussian-KL inclusion measure from distributional embeddings; what TEMPS adds is the grounding and the moment-matched supervision. On three temporal benchmarks, TEMPS improves MRR for every semantic backbone tested and, on TS- Retriever, lifts R@1 from 19.92 to 25.39 over the prior temporal state of the art.

Conference policies distinguish using Large Language Models (LLMs) to polish one's own review from delegating the critique, but current Artificial Text Detection (ATD) methods largely measure surface form rather than the origin of its content. We instead measure the external information carried by a review: information not explained by the reviewed paper and a generic reviewing instruction. We propose Self-Conditioning, an unsupervised information-theoretic estimator that compares the likelihood of a review under its production context with its likelihood when that context is augmented with hints extracted from the review itself. On the IntelLabs peer-review benchmark, Self-Conditioning separates fully-delegated from machine-polished reviews with AUC up to $1.0$ while remaining largely insensitive to surface rewriting. Moreover, as generators receive increasing amounts of externally-provided information, their scores move monotonically towards the human regime, unlike standard ATD baselines. High-temperature sampling can evade the estimator, but at the cost of output quality.

This paper characterises substantive agency and identifies the additional bridges under which it has a standard complexity-theoretic consequence: conditionally, P __ = N P . The constitutive core separates coherent plurality, causal openness, anticipatory non-pointing, act-level singularisation, and endogenous sourcehood. Its temporal claim yields a two-sided modal result: exact passive pre-act selection is incompatible with jointly retaining singularising priority and invariance under causally inert informational extension. If every standard polynomial procedure is deployable in that passive form, the actualisation map $\alpha$ has no polynomial-time selector. On an effective presentation, $\alpha$ is therefore either computable outside FP or noncomputable. A separate certifiedactualisation protocol supplies polynomially bounded, polynomially verifiable traces with extensional unique projection. This is the constructive interface that turns historical actualisation into a total standard search relation; combined with the modal result, it places that relation in TFNP search \ FP search , from which a self-contained search argument yields P __ = N P . The result is a domain-relative conditional transfer theorem: it neither assumes polynomial non-anticipability in the definition of agency nor proves that human decision-making satisfies the bridge and certification premises.

The key-value (KV) cache of autoregressive transformers can be viewed as a fourth-order tensor spanning attention heads, tokens, features, and grouped layers. We measure the singular-value spectra of all four mode unfoldings on Mistral-7B-v0.3 and LLaMA-2-13B and compare four standard tensor decompositions: Tucker, CP, tensor train, and t-SVD, at matched storage. The spectra partition the four axes into two classes. The token and feature modes carry low-rank structure, particularly for keys. The head and layer modes are nearly full-rank and resist compression at any practical error level. Among the four decompositions, Tucker achieves the lowest reconstruction error at every compression ratio from $2\times$ to $5\times$, because it can leave the full-rank modes untouched. Comparisons with two-dimensional unfolding baselines show that the preferred representation differs between keys and values: 2D methods achieve lower key error, while four-way Tucker achieves lower value error at matched storage. A mode-pinning theorem certifies the full-rank preservation from the measured spectra alone. Two further spectral properties affect the compressible modes without touching the full-rank ones: values reach a higher error floor than keys at every ratio, and post-RoPE keys lose $41\%$ - $64\%$ of their pre-RoPE compressibility on both models.

For every fixed integers $r \ge 4$ and $2 \le k \le r-2$, we construct $r$-dimensional cubical sheaf complexes whose degree-$k$ CSS codes have positive constant rate, linear distance, and constant soundness, with bounded row and column weights. Taking $r=4$ and $k=2$ gives a family of asymptotically good binary qLTCs. At the core of our construction is a uniform product-expansion theorem for explicit Reed-Solomon codes on norm-one evaluation sets. The key point is that the expansion constant stays bounded away from zero as the local code lengths grow. We place these codes on arithmetic cubical complexes, obtaining constant local expansion for both the resulting sheaf and its dual. Together with the local-to-global framework of Dinur, Lin, and Vidick (FOCS 2024) and sheaf duality, this gives linear distance and constant soundness, while an asymmetric choice of local code dimensions gives positive rate. The resulting codes are explicit and polynomial-time computable.

Providing personalized exoskeleton assistance across varying walking speeds remains challenging. Existing online optimization methods are sample-inefficient, requiring extensive human-in-the-loop (HIL) evaluations to optimize the entire assistive torque profile. Sim-to-real reinforcement learning (RL) offers a promising alternative but cannot directly account for individual user preferences. We propose a framework integrating sim-to-real RL with online preference learning for personalized exoskeleton assistance. Specifically, assistance timing is learned in simulation by training RL policies with human musculoskeletal models across varying walking speeds. The learned policies are then distilled and deployed on a physical hip exoskeleton using onboard sensory observations. Gaussian-process-based preference learning further personalizes the assistance magnitude through pairwise user comparisons. By decoupling assistance timing learning in simulation from magnitude optimization in real-world experiments, our framework substantially reduces the online optimization space. Human-subject experiments demonstrate efficient identification of personalized assistive torque profiles across varying walking speeds with fewer real-world evaluations.

We investigate whether state-of-the-art large language models (LLMs) generate feedback that reflects the pedagogical practices of expert teachers in terms of feedback focus and adaptivity. Previous evaluation efforts have examined feedback characteristics, its impact on learning, and its target, yet the focus of feedback and its adaptivity remains largely overlooked. To bridge this gap, we adopt and refine Narciss's taxonomy into seven feedback focus types to annotate teacher and LLM-generated feedback across three university writing courses. We release FeedType, a benchmark containing annotated teacher and LLM feedback from six LLMs under three prompting strategies. We assess the coverage and distribution of feedback focus types, and examine whether LLMs adapt their feedback across draft stages and student performance levels as an expert instructor does. Our findings show that while most LLMs cover most feedback focus types, they fail to reflect teacher feedback distributions and show varying levels of adaptivity, with none matching the teachers' adaptive behavior. We believe FeedType will support future research on pedagogical alignment in LLM feedback generation.

The lettericity of a graph $G$ is the smallest size of a set $\Sigma$ such that there exist $w_1, \ldots, w_{|V(G)|} \in \Sigma$ and a so-called decoder $D \subseteq \Sigma^2$ for which $G$ is isomorphic to the letter graph $(\{1, \ldots, |V(G)|\}, \{ij : 1 \le i < j \le |V(G)|, w_iw_j \in D\})$. It took around two decades of the study of lettericity for, in the simpler case of paths, a closed-form expression for its lettericity to be derived; this suggests that the question of whether the lettericity of an arbitrary graph can be computed in polynomial time is nontrivial. Indeed, this question has been raised repeatedly as an open problem in recent literature. We solve this problem by showing that the lettericity problem on arbitrary graphs is NP-complete. We also show that each of the natural ways in which a single part of a structure $(\Sigma, w_1, \ldots, w_{|V(G)|}, D)$ witnessing the lettericity could be constrained corresponds to an NP-complete problem, which resolves an additional three open problems from the literature; in particular, we show that the coloring extension, word extension, and decoder extension problems are NP-complete. Additionally, we use the reduction in the NP-completeness proof to give a lower bound on algorithms for lettericity under the Exponential Time Hypothesis (ETH): unless the ETH is false, there cannot exist a deterministic algorithm to decide whether the lettericity of an $n$-vertex graph is at most $k$ in time $2^{o(n)}$, even when $n = 6k$. Finally, we complement the known result that Lettericity is fixed-parameter tractable when parameterized by the standard parameter $k$ by providing a fixed-parameter algorithm with respect to the dual parameterization by $n-k$ running in $2^{\mathcal{O}((n-k)^2)} + \mathcal{O}(n)$ time.