Science & Mathematics

The Key-Value (KV) cache is the main memory bottleneck of long-context LLM inference. Token eviction methods such as SnapKV, H2O, AdaKV and L2Norm shrink it, but they give every transformer layer the same budget, although layers differ in which tokens they need. We present MOSAIC, a multi-objective neural architecture search that learns per-layer KV-cache budgets for any eviction method. One search maps the trade-off between average budget and task score; its best allocation transfers to every target budget without further search, and an optional budget-constrained search refines it. Across four eviction methods on Llama-3-8B-Instruct and Mistral-7B-Instruct-v0.2, MOSAIC beats uniform allocation in 146 of 154 (task, method, budget) settings, by up to +48 points on RULER and +11.9 on LongBench (LCC). On both models, it reaches the score of uniform allocation with up to 4x less KV cache (75% smaller). Against EvolKV, MOSAIC explores a ~10^40 x larger search space with 4x fewer evaluations and 18% fewer GPU-hours per budget, and scores higher in 5 of 6 settings. The learned allocations consistently favour a small set of middle layers.

Graphs, which are made up of points connected by lines, are used to represent relationships between objects. They are useful for solving problems in computer science, logistics, biology, and other fields, including social networks and the internet. Neutrosophic graphs are graphs whose points and lines are characterized by membership, indeterminacy, and non-membership degrees. In the simplest case, only lines are characterized by these degrees. The process by which we transform one graph to another is called graph rewriting. It has been shown that graph rewriting can be described mathematically by pushouts, which are category-theoretic structures. It has also been shown that fuzzy graphs have this property, and here we prove that neutrosophic graph rewriting can be described by pushouts in a certain category. By providing a fuzzy version of category theory, it is possible to define fuzzy categorical structures and thus to define neutrosophic graph rewriting in a more suitable manner. Since graph rewriting is actually a model of computation, neutrosophic graphs are a neutrosophic model of computation. A hypergraph is a generalization of a conventional graph. It allows a single "hyperline" to connect many points, which is different from regular graph lines that only connect two points. Neutrosophic hypergraphs can be used to reformulate Wolfram's models, which are supposed to be a mathematical model of reality.

Verifiable rewards have advanced reinforcement learning in mathematics and code. However, many valuable open-ended tasks share three properties: no automatic verifier of overall quality, multiple requirements to satisfy jointly, and multiple valid responses to each query. Training therefore needs feedback on requirement satisfaction across different valid responses. Rubric-based reinforcement learning provides this feedback by aggregating scores from explicit criteria. As learning progresses unevenly, some criteria become fully satisfied and lose discrimination while others remain informative. Dynamic methods revise shared rubrics or select evolving criteria to restore discrimination, but may also change useful criteria. To address this, we propose Reinforcement Learning with Adaptive Rubric Evolution (RARE). The core idea is to use current policy feedback to guide both which criteria change and what their replacements assess. Sample-level updates replace criteria fully satisfied across current outputs with checks of remaining quality differences, retaining all other criteria and scores. Within this rule, we compare rewarding desirable qualities with penalizing observed flaws. Video script generation exemplifies these properties and supports content production. Its demands for coherent, executable narratives under constraints make it a challenging testbed. Targeting flaws performs best across three video types with a mean gain of 3.82 points over matched static rubrics. Model and human preferences support these gains. Improvements also extend to writing and general generation benchmarks.

Shared autonomy is a control paradigm that combines human cognitive abilities with robot precision to enable effective remote manipulation in complex environments. A key challenge is how to adapt the level of autonomy using information extracted from the human, task, and/or environment. In this paper, we propose a novel arbitration strategy that dynamically adjusts the level of autonomy in the system using the entropy of a belief distribution derived from a multimodal intent inference. Human intent is modeled with a Dynamic Bayesian Network (DBN), which updates beliefs over goals given real-time operator gaze data and robot arm motion during teleoperation. We then formulate the blending of human input and autonomous control as a Model Predictive Control (MPC) problem, where the system's autonomous behavior is guided by the belief distribution. This approach enables continuous, gradual transitions across the full spectrum of autonomy levels, from direct teleoperation to full autonomy. To validate our approach, we conducted experiments to compare the performance of our proposed algorithm against two MPC-based shared autonomy methods. Compared to the baselines, our approach achieved reductions of at least 61% in object retrieval time, 44% in trajectory length, and 60% in human control input. Participants reported high perceived control, predictability, intent recognition, and responsiveness, along with low workload.

This work explores monocular motion capture for dragon-type characters, which currently relies on manual keyframing due to the lack of high-quality datasets and parametric models. The primary obstacle lies in the extreme topological diversity across dragon rigs, where varying joint counts and naming conventions render traditional fixed-template regressors inapplicable. To address this, we introduce DragonMoCap, a novel framework that treats the target rig as a dynamic input rather than a fixed prior. By deliberately scoping the framework to the most prevalent production topologies, we ensure high-fidelity results across diverse morphologies. The core of our approach is the design of language-grounded joint query tokens, which establish a dual-property representation: ensuring intra-rig discriminability while maintaining cross-rig similarity. We further propose a non-parametric query-token retrieval mechanism to enable zero-shot adaptation to unseen rigs without retraining. Extensive evaluations demonstrate that DragonMoCap consistently outperforms HMR-style baselines across diverse dragon topologies. The practical utility of our framework is further evidenced by its integration into professional animation workflows, highlighting its potential for real-time industrial applications.

Photo Response Non-Uniformity (PRNU) is widely regarded as the most reliable marker for source camera identification. Recent studies, however, report high correlations between images and fingerprints from different modern smartphones, which calls into question the discriminative power of PRNU on these devices. Using 30 recent smartphones under controlled acquisition conditions (e.g., no digital zoom), we investigate whether the fingerprint itself is at fault or the way it is compared. We find that a component shared by all fingerprints of the same model inflates the standard signed peak-to-correlation energy (sPCE). To counter this, we propose $Δ$sPCE: the sPCE between a query image and a candidate camera's fingerprint, minus the mean sPCE between that image and the fingerprints of the remaining candidates, in the spirit of T-norm score normalization. $Δ$sPCE improves attribution accuracy, suggesting that the device-specific PRNU signal is still present. Although the limited dataset size and the dependence of $Δ$sPCE on the candidate camera set currently restrict operational applicability, these results suggest that PRNU-based attribution of modern smartphones remains feasible when fingerprints are compared appropriately.

Building and expanding access to digital archives supports language reclamation and creates lasting resources for community revitalization. Designing effective tools to support these efforts requires taking into account the community-, language-, and document-specific context. We investigate how small ($\leq$3B) vision-language models (VLMs) can be adapted as optical character recognition (OCR) tools for Lakota, a North American Indigenous language. In addition to benchmarking modeling approaches, we inspect four practical facets of low-resource archival OCR that arise in previous work and conversations with community members: constrained training budgets, segmentation noise, scan degradation, and orthographic variance. We demonstrate that fine-tuning VLMs for OCR post-correction on 35 pages of transcribed data decreases character error rate (CER) from 17.1 to 3.9\% on a bilingual corpus, and find that training only with nine pages increases CER by only 1.1\% over this. However, evaluating under realistic automatic segmentation nearly doubles the CER of the best-performing models, stressing the importance of taking realistic use cases into account. We hope this work encourages future research on developing language technologies grounded in the workflows and constraints of ongoing revitalization efforts.

Verifying the reasoning of large language models is increasingly important as they are applied to complex mathematical and scientific problems. Existing work focuses on large decoder models and reports mixed results for generative and discriminative verifiers, leaving unclear which paradigm is more effective and whether large models are necessary. In this work, we cast stepwise verification as a natural language inference task: the problem and partial solution prefix form the premise, while the next reasoning step serves as the hypothesis to be classified as entailed or non-entailed. This formulation enables error localisation at individual reasoning steps and direct comparison of encoder classification, decoder classification, and decoder verdict generation across model scales and annotation budgets. Across five reasoning datasets, a 0.15B encoder classifier outperforms most generative verifiers with up to 4B parameters. On identical decoder backbones, classification outperforms generation from 0.5B to 4B parameters and matches it on the strongest 7B backbone---reaching comparable performance with roughly one tenth as many annotated problems. Our findings establish classification as a parameter- and data-efficient approach to stepwise verification and show that strong verification does not require large generative decoders.

Masked diffusion language models (MDLMs) generate text by iteratively unmasking tokens with bidirectional context. As these models reach real-world deployment, machine unlearning becomes essential. This process aims to remove the influence of a designated "forget set" without retraining from scratch, so that sensitive, copyrighted, or restricted content can no longer be elicited while preserving retained capabilities. Masked Diffusion Unlearning (MDU) is the first publicly available unlearning method customized for these models: it tunes the model $p_θ$ to match a frozen prompt-masked anchor $p_{\mathrm{anchor}}$ on the forget set by minimizing the anchor-last divergence $\mathrm{KL}(p_θ\Vert p_{\mathrm{anchor}})$. We identify two failure modes of MDU. First, random answer masking can leave key forget tokens visible to the anchor even when the question is fully masked. Second, at a memorized (near-one-hot) prediction, the anchor-last logit gradient vanishes while the anchor-first divergence $\mathrm{KL}(p_{\mathrm{anchor}} \Vert p_θ)$ logit gradient does not. As a result, MDU training stalls on the tokens we most need to forget. Backed by theoretical and empirical analyses, we propose Enhanced Masked Diffusion Unlearning (EMDU): anchor-first KL divergence toward a frozen anchor whose entire answer span is masked. On TOFU and RWKU benchmarks using LLaDA-8B and Dream-7B, our EMDU matches or exceeds the forgetting of MDU and adapted AR baselines, while better preserving retain utility.

Multimodal perception improves autonomous-driving performance by combining complementary sensor information. However, stronger multimodal predictions do not necessarily imply stronger representations in each modality-specific branch. Such branch-level weaknesses can remain hidden in conventional output-level evaluation. We introduce UBD-Bench, a systematic benchmark for studying unimodal branch degradation (UBD) in multimodal perception. UBD-Bench uses a Paired Frozen-Branch Probe to compare the task-relevant representation quality of the same modality after independent unimodal training and multimodal joint training under matched decoding conditions. Across four autonomous-driving perception tasks and 10 models, we find that Camera branches consistently degrade after multimodal joint training, whereas LiDAR branches exhibit weaker and more model-dependent changes, revealing a pronounced modality asymmetry. Hierarchical probing further shows that Camera-branch degradation extends from the visual backbone through the Camera-to-BEV pathway and is most severe at the pre-fusion Camera BEV representation. Guided by this diagnosis, we introduce unimodal-to-multimodal distillation at the degraded representation. This intervention consistently improves both Camera-branch Probe performance and full-model performance across all four tasks. These results show that multimodal gains can coexist with degraded unimodal representations, highlighting branch-level representation quality as an important dimension for evaluating and improving multimodal perception.

We propose to model singular data clouds by subanalytic sets, and develop an approach to semi-supervised learning in this setting. It relies on a Morrey-type embedding for Sobolev spaces relative to globally subanalytic measures with possibly singular support. As an illustration, we present a greedy method based on a Monte Carlo approximation of the Sobolev norm of the candidate solutions. We report numerical experiments on point clouds sampled from real algebraic varieties, as well as a test on a classification problem based on MNIST images downsampled into $7\times7$.

Classical robot control, Finite State Machines and Behavior Trees (BTs), is deterministic and inspectable but fixed at design time: it fails on situations its designers did not anticipate. Foundation models can synthesize new control logic at runtime, at a cost in latency and non-determinism hard to accept in safety-critical aerial systems. Existing LLM-driven approaches keep the model in the loop permanently and discard what it produces. We propose Self-Crystallizing Behavior Trees (SCBT), in which the foundation model is a compiler rather than a runtime. When a BT node fails, an LLM proposes a minimal, mission-agnostic subtree patch; CMA-ES tunes its parameters in simulation; a contextual bandit decides whether a stored patch or a new LLM call is worth its cost; and a three-stage admission pipeline (static check, invariant-monitored replays, an empirical margin over the unpatched tree) admits only patches that demonstrably recover. Admitted patches are stored in a fleet library and, once the LLM call rate decays, crystallized into a deterministic BT that no human wrote. We implement SCBT on Microsoft Project AirSim with a schema-constrained LLM pipeline (Gemini 3.1 Pro) and a lockstep simulator. Over three seeds of a 20-episode learning phase with wind-gust and battery failures, SCBT used $11\pm1.4$ LLM calls against 26 for whole-tree regeneration and 22 without a library, with 0.33 calls per episode in the second half. The crystallized trees, 28 and 33 nodes with two patches each, reached $97\pm2\%$ mission success with no learning running, against 12\% for the unpatched tree and 98\% for a hand-coded expert tree, and reproduce decision traces exactly when re-ticked offline. Two negative results: replay admission rejected useful wind recoveries by attributing wind-induced geofence excursions to the patch, and a static-only ablation generalized better to held-out failures.

Decision models return probabilities over supplied options, but a deployed agent may also need to reply in words. The present study introduces System X, a large language model (LLM) decision model that adds a text-reply option to the LLM-as-Jev readout. When this option wins, or confidence is low, the same model continues from the decision's key-value (KV) cache, avoiding a repeated prompt prefill. Qwen3-0.6B has been fine-tuned with LoRA on Reason-9k and Bitext reply rows. JevBench accuracy shows no statistically significant change (55.4% to 54.5%, p=0.87), while expected calibration error falls from 0.292 to 0.169. Held-out Bitext routing accuracy reaches 98.3%. Cache reuse saves 15-37% of latency on an Apple M4 Pro, with token-identical replies in the FP32 demonstration cases. Scoring options on copies of the prompt cache matches full-sequence scoring to within 1.4e-6 in probability. Adding dialogue, industry and complaint data (System X+) improves support-task results but lowers IFEval accuracy from 55.5% to 45.0%. System X v4 uses Qwen3-1.7B, rebalanced data and teacher-rewritten reply targets. Against its base LLM, JevBench accuracy rises from 55.0% to 61.0% (p=0.04), with no statistically significant IFEval change (p=0.71). A matched latency test on unadapted Qwen3-1.7B saves 17-39%. One LLM judge prefers v4 replies to an unadapted 1.7B second call (31 to 11 pairs, p=0.003); the other's preference is not significant. These reply comparisons also differ in prompts and generation limits. State conflicts and unsupported reply details remain failure modes. Further studies with several seeds, human raters and real support data are recommended.

Small language models have improved to the point where a phone can plausibly screen its own calls, answering on an absent owner's behalf without sending call content off the device, a privacy-respecting alternative to cloud call handling. Realizing that promise takes a model that can do two things well: reply within the owner's authority during the call, and afterward tell the owner what happened and what needs attention. Released small models do neither reliably - they raise unwarranted alarms about ordinary callers and write summaries that drop material conditions or report a caller's claims as fact - and real calls supply no reference replies or summaries to learn from. We construct supervision for both tasks from synthetic calls under an information-boundary constraint: a caller writer works from a private scenario brief, a reply writer sees only the conversation up to the current turn, and a summary writer sees the completed transcript. Separate model-based reviews of the full dialogue and the summary decide which calls enter training, yielding a corpus of 3,395 calls with 15,102 targets (11,707 reply, 3,395 summary). Training a single shared LoRA adapter on both tasks, we evaluate six models (0.6-4B parameters) before and after adaptation on 192 held-out calls. Reply qualification rises from 21-54% to 94-97% and summary qualification from 0-6% to 43-72%; all twelve paired gains (six models x two tasks) have bootstrap intervals above zero, and the summary gains hold in every source family. Because one model both screened the training data and scored the outputs, these rates measure agreement with that evaluator's standard rather than human acceptance, which a planned human study will test. After adaptation, coherence and naturalness failures nearly vanish, leaving grounding and usefulness - faithfully tracking who said what, under which conditions - as the remaining challenge.

Bimanual manipulation with dexterous hands has attracted growing attention in research on robotic action models. However, few studies have developed benchmarks specifically tailored for dexterous manipulation, leaving the dexterous manipulation capabilities of existing models insufficiently characterized. In this paper, we present BiDex-100, a simulation benchmark for bimanual dexterous manipulation that combines broad task coverage, multi-dimensional evaluation, and high-DoF hand embodiments. Concretely, the benchmark comprises 106 tasks organized along five capability axes: generalization, instruction following, limited demonstrations, long horizon, and memory. Each task is paired with an out-of-domain variant featuring controlled visual and spatial changes, allowing systematic assessment of robustness. In addition, the benchmark supports two embodiments and provides 8,080 success-validated teleoperated demonstrations, totaling 6.25 million frames. We evaluate seven recent Vision-Language-Action models under a unified protocol, establishing baselines for capability-specific performance, robustness, and data efficiency. The website is available at https://robbyant-research.github.io/BiDex-100/.