Papers

We prove that the nonvanishing conjecture implies the abundance conjecture.

Working with tools from infinite-dimensional topology and using measure-theoretic ideas we analyze numerous well-known fami\-lies of copu\-las and quasi-copulas from a topological perspective, prove that most of them are homeomorphic to the Hilbert cube $\mathcal{H}$ and hence have the Fixed Point as well as the Disjoint Cells property. Working with so-called $Z$-sets, we then study how large one set is within another. Doing so, in order to show that a set $A$ is small/topologically negligible within a compact metric space $(\Omega,m)$, we construct a homeomorphism $h: [0,1] \times \mathcal{H} \to \Omega$ mapping $\{0\} \times \mathcal{H}$ to $A$. The obtained results are to a certain extent surprising since various supposedly small families are topologically large.

We prove a homological obstruction to smoothing projective Calabi-Yau threefolds with nodes and anticanonical cones over smooth del Pezzo surfaces of degrees six and seven. On a crepant resolution that is small over the nodes and blows up the cone vertices, any smoothing forces a relation among link classes bounding in the local Milnor fibers. The relation is nonzero at every node and degree-seven point, and at each degree-six point smoothed through the one-dimensional component. The proof uses vanishing periods and applies to smoothing arcs of arbitrary contact order, extending the necessity direction of Friedman's criterion. We apply the obstruction to a Batyrev hypersurface whose thirty singularities are individually smoothable but which admits no smoothing, even formally. On its mirror partner, two nodes cannot be smoothed by any analytic deformation, independently of a locally nonsmoothable cone point.

Restriction site-associated DNA sequencing (RADseq) is a family of reduced-representation sequencing methods. It uses restriction enzymes to sample subsets of the genome, therefore allowing multiple individuals to be sequenced and genotyped together at low cost. RADseq is widely used for population genomics, evolutionary biology, marker discovery, and the development of SNP panels, but complete analysis still requires expert coordination across multiple tools and processing stages. Traditional RADseq analysis requires expert coordination of heterogeneous bioinformatics tools, intermediate artifacts, quality-control checks, and parameter-dependent decisions across multiple stages. Although individual steps can be scripted, executing the complete workflow still requires human oversight for state tracking, result validation, and failure handling. To automate this expert-driven coordination, we present RADAgent, which introduces a modular agentic method for reliable RADseq workflow execution with an open-weight LLM. RADAgent maps the natural boundaries of the RADseq workflow into 16 independently executable and verifiable agent modules and uses a model-independent runtime for bounded tool execution, on-disk verification, and failure recovery. We evaluate RADAgent on a real population-genomics dataset containing 476 samples from 19 populations. The results demonstrate that RADAgent reliably automates the complete RADseq workflow with an open-weight LLM while keeping genomic data and model execution within the local computing environment. The code is publicly available at https://github.com/wenlu-lab/RADAgent.

Diffusion large language models (dLLMs) enable flexible generation through iterative masked denoising, but incur substantial inference cost because token representations are repeatedly recomputed across denoising steps. Existing cache-based methods reduce this cost by reusing intermediate results across denoising steps and recomputing only a subset of positions at each step, chosen either on a fixed schedule or by heuristic signals of change. Our trajectory experiments instead point to decoding trajectory as the more relevant quantity. Cached generation remains accurate when it stays close to the full-denoising trajectory, with errors concentrated around unmask-order deviations and reduced as longer reference prefixes are recovered. This suggests a more direct principle: limiting representation error helps, but keeping generation on the full-denoising trajectory is a more direct route to accurate decoding. We therefore formulate efficient dLLM inference as trajectory-guided querying. Rather than broadly repairing representation error, we use full-denoising trajectories to supervise which unresolved positions should receive limited fresh computation. Based on this formulation, we introduce TRACEQUERY, a lightweight sparse decoding framework that predicts a small set of near-future trajectory-relevant positions, queries only those candidates, and lets the backbone select which one to commit from their fresh predictions. TRACEQUERY delivers the strongest quality-computation trade-off among cache-based approaches, sustaining high accuracy with substantially fewer fresh token computations, and generalizes across tasks, model variants, and families. Code: https://github.com/fish1928/tracequery.git

Natural-language service intents in integrated terrestrial and non-terrestrial (TN/NTN) 6G networks can be incomplete, ambiguous, or inconsistent, making unconstrained LLM generation challenging for reliable network-facing orchestration. This paper proposes a knowledge-guided LLM framework that combines grammar-constrained semantic parsing with a knowledge-graph (KG)-driven clarification loop to produce validated, orchestration-ready service profiles across four representative service classes. On a 200-sample intent dataset, the framework achieves 89% classification accuracy and 95% policy validity with an average of 0.66 clarification turns per request. Compared with a Pure-LLM baseline, the proposed framework improves policy validity and contradiction detection while requiring fewer clarification turns, demonstrating the value of explicit knowledge-guided reasoning for robust intent processing in integrated TN/NTN 6G orchestration.

Transformer-based large language models (LLMs) impose substantial computation and memory costs as context sizes increase, motivating methods that compress a context into a shorter representation before inference. Existing soft-prompt compression methods typically use the same Transformer backbone as used in the target model, where producing the compressed representation leads to significant latency overheads. This restricts them to the offline setting where context is compressed once and then reused across many queries. We propose the Boa Compressor, a plug-and-play online context compressor built on a Mamba state-space model (SSM) that encodes arbitrary-length context in a single linear-time pass, producing a representation on which we condition a frozen target LLM. The SSM is trained by distillation, matching the next-token logit distribution from the LLM ingesting the full context (as teacher) to the same LLM ingesting the compressed representation (as the student). At equal compression ratios, Boa matches or surpasses the performance of existing state-of-the-art offline compression baselines, while being an order of magnitude faster than Transformer-based implementations, thereby reducing end-to-end latency rather than adding compression time overhead. We demonstrate that Boa also scales well to longer contexts and to compression ratios as aggressive as 16x. By enabling effective compression that is cheap enough to run on every query at inference time, Boa becomes a practical and general tool for efficient long-context inference.

Energy-based models have shown promising properties for domain-specific tasks but remain challenging in modeling general-purpose scenarios. To bridge this gap, we design energy-steered models (ESMs) for foundational language modeling. ESMs integrate energy steering and token generation within a single architecture to leverage the energy-guided search to refine token generation. Specifically, ESMs first optimize a latent state over the energy landscape, then leverages the refined latent state for token generation. By performing such energy-guided pre-training on large-scale corpora, ESMs learn generally effective energy landscape where favorable tokens correspond to lower energy values. To explore the scaling behavior of ESMs, we pre-train ESMs on three large-scale corpora, then evaluate across 26 downstream tasks spanning a broad range of domains. Our results demonstrate that ESMs have promising scaling behaviors with increasing model size and training data, and outperform GPTs on most downstream tasks. These findings highlight ESMs as a promising architecture for large-scale pre-training and general purpose problem solving. We fully release the model weights and training infrastructure to enable the community to completely reproduce and extend our results. GitHub: https://github.com/datamllab/openesm HuggingFace: https://huggingface.co/collections/guan-wang/openesm

Optical Character Recognition (OCR) is essential for digitizing historical archives, yet standard evaluation metrics such as Character Error Rate (CER) do not necessarily reflect whether meaningful information, such as names, dates, and identifiers, is preserved. In this work, we investigate entitylevel analysis of OCR errors as a complementary perspective for evaluating OCR quality in historical documents. Using a publicly available benchmark of 175 documents from the Berrutti Archive, augmented with 5,209 manually annotated entity mentions that will be released upon acceptance, we compare sequence-recognition OCR systems, OCR-specialized vision-language models, and general-purpose vision-language models. Beyond global transcription accuracy, we analyze entity preservation and recoverability under varying character-level edit tolerances. Our experiments show that OCR rankings depend on the evaluation criterion: while Qwen 3.6 achieves the highest entity coverage across all tested tolerances, several systems with lower exact-match coverage recover substantially when small errors are tolerated, suggesting that many of their errors correspond to localized character-level deviations rather than fundamentally incorrect entity transcriptions. Conversely, some systems remain unable to recover many entities even under relaxed matching. These findings show that OCR quality cannot be fully characterized by aggregate transcription metrics alone and highlight the importance of evaluating how OCR errors affect the preservation and recoverability of meaningful information.

One of interest of the author lies in the canonical projections of the unit spheres and generalizations. He is interested in the canonical projections of embedded manifolds in the higher dimensional Euclidean spaces, including height functions, especially, their construction and representations by explicit equations. This is a kind of fundamental studies on construction or global theory on singularity theory of differentiable maps, closely related to differential geometry, differential topology, and algebraic geometry. Rather than knowing existence, construction has been difficult in certain senses. We construct smooth maps onto regions in Euclidean spaces locally modeled by height functions and show new examples. This is related to a pioneering study of the author, certain generalizations of the canonical projections of the unit spheres (, so-called special generic maps), and construction of them as projections of connected components of the zero sets of some smooth maps to some Euclidean spaces.

In a previous paper we derived an uncertainty relation for nonlocal fields by showing that the physical localization width in nonlocal quantum field theory is broadened by the response kernel generated from the entire-function regulator. In this follow up we will reinterpret that result as just the position-sector limit of a more symmetric statement as we did not take into account the inherent nonlocality of momentum. We find and we prove under normalized, centered response kernels for both position and momentum the variance laws and derive the corresponding nonlocal phase-space uncertainty relation. The result still preserves the conclusions of the original paper all while strengthening the interpretation as nonlocal quantum field theory implies not merely a minimal measurable length, but a finite phase-space cell. We also explore experimental routes to test the theory.

Many molecular biology data sets contain thousands of features, such as genes in single-cell experiments or other omics data. Standard predictive models often perform poorly in such settings, as they tend to retain a large number of features and fail to adequately handle correlations among them. Combinatorial approaches, such as feature selection based on the Independent Dominating Set (IDS) model, have shown promising results, but appear to have been largely overlooked, possibly due to their high computational complexity. In this paper, we propose an improvement to IDS-based feature selection that (i) favors features exhibiting greater diversity and (ii) generalizes the notion of independent dominating set to a node packing model. The resulting formulation is used as an intermediate step within the feature selection process. We evaluate our approach on five genetic data sets and compare the results with those obtained using existing methods. Our experimental results demonstrate notable improvements in predictive accuracy over traditional models, as well as increased stability of the selected feature sets.

Acoustic models for cough detection achieve high accuracy on curated benchmarks but fail silently in deployment, where speech, environmental noise, and audio unlike the training data induce confident misclassifications. In health monitoring, a confidently wrong prediction is worse than no answer at all. We present SECURE-AI (Self-aware Estimation of Cough Uncertainty for Reliable Evaluation of AI), a multi-signal uncertainty quantification framework that wraps a frozen MobileNetV3 cough classifier and estimates when its predictions should not be trusted, combining Monte Carlo Dropout, Temperature Scaling, and Mahalanobis distance in the embedding space. On a held-out split of 12,161 Coswara recordings, the probability-space methods are individually insufficient: Monte Carlo Dropout assigns lower uncertainty to incorrect than to correct predictions, and temperature scaling improves calibration but not discrimination. The strongest signal is embedding-space distance: Mahalanobis distance separates true positives from false positives (means 44.7 versus 63.4; Cohen's $d = 0.94$; AUROC 0.86) and, among predicted non-coughs, false negatives from true negatives (AUROC 0.82), so the same signal can flag both false alarms and missed coughs. At a descriptive operating point selected from labeled test data, retaining 90 percent of true-positive detections removes about two-thirds of false positives and raises precision from 59.9 to roughly 80 percent. A rejection threshold tuned on one split does not transfer to another (validation F1 of 82 percent falls to 34 percent on test), so we report threshold-independent AUROC as the main measure. An error taxonomy shows that failures are systematic, with most false positives related to speech. The pipeline runs on Raspberry Pi hardware costing 30 to 90 US dollars. Probabilistic calibration alone is thus inadequate for reliable cough detection.

In-context learning (ICL) enables language models to make accurate predictions from demonstrations, but prediction success alone does not reveal the extent to which the underlying concept has been recovered. Existing evaluations typically assess recovery at the level of the whole concept, making it difficult to identify which components are recovered and to separate model limitations from ambiguity in the demonstrations. We introduce a component-level framework for concept recovery that decomposes concepts into their defining components and uses controlled structural interventions to evaluate both component-level and whole-concept recovery under identifiable demonstrations. Across four instruction-tuned LLMs and three composition forms, we find that models often achieve high prediction accuracy despite poor whole-concept recovery, with systematic over-specification of relevant attributes and level constraints. Individual structural components are generally insufficient for whole-concept recovery, whereas jointly specifying complementary components, particularly relevant attributes and their level constraints, substantially improves recovery. However, this improvement is fragile: a single plausible but unnecessary level constraint can substantially disrupt recovery. Finally, joint supervision of recovery and implicit prediction substantially improves recovery while preserving prediction performance, with the learned capability transferring across composition forms. Overall, our component-level analysis provides a more diagnostic view of what models recover from demonstrations than the existing holistic view.

Speculative decoding accelerates large language model inference through parallel verification of tokens proposed by a drafter. Diffusion drafters further parallelize proposal generation, but greater proposal capacity or higher mean accepted tokens (MAT) need not yield higher throughput. Because verification accepts only a consecutive prefix, early rejections can render later correct predictions ineffective, limiting MAT gains, while even higher MAT may not improve throughput if per-round latency increases. We introduce DScout, which uses two complementary factorizations to guide diffusion drafter training and inference for higher throughput. For training, DScout factorizes position-wise loss into inclusion, weighting, and prediction loss. This guides the design and combination of mixed-horizon training, intra-block unmasking, and acceptance-weighted loss to align supervision with prefix acceptance and improve MAT. For inference, DScout factorizes throughput as the ratio of MAT to per-round latency, guiding target-conditioning depth, drafter depth, and inference block size selection to identify a high-throughput configuration for each workload. Across six benchmarks, DScout achieves $3.84\times$ and $4.14\times$ mean speedups over autoregressive decoding on Qwen3-4B and Qwen3-8B, respectively, improving mean speedup over the state-of-the-art baseline by 9.1% and 7.1%. Across models and concurrency settings, our inference configuration policy provides up to 9.75% additional mean speedup over DScout's fixed configuration.

When using a large language model (LLM) to simulate a user population, how should we combine individual behavioral histories to predict the fraction of users who take a particular action? We study this question in e-commerce, predicting observed product-level conversion rates from browsing sessions without task-specific model training. We vary two design choices, each involving a bias-variance tradeoff. Summarizing a product's sessions before inference reduces cost but can discard predictive detail, adding bias, whereas predicting outcomes for individual sessions and averaging afterward preserves that detail but requires many calls to reduce variance. Evaluating products together in one prompt can help the model infer what is typical in the setting, reducing bias, but also makes each prediction depend on which other products appear alongside it, adding noise. We evaluate both choices across five LLMs and two datasets. Our main finding is that predictions from individual sessions outperform predictions from summaries when products are evaluated separately, but summaries lead when products are evaluated together. Comparative summaries achieve the highest Spearman correlation with observed rates in 12 of 15 settings, with no alternative significantly better. Comparison thus helps summaries far more than session predictions, overcoming the advantage of behavioral detail. We interpret this difference through a Bayesian model of the second tradeoff, which suggests that comparison helps more when the inputs in a prompt reveal more about differences across products, consistent with our results for four types of comparative context. Comparative summaries also incur a small fraction of the inference cost of the session methods. With the best model for each outcome, they attain 66-89% of the correlation of the best supervised benchmark trained on thousands of labeled products.

Enterprises run schema-guided structured field extraction on documents with frontier multimodal models, and accuracy keeps improving as new models and systems arrive. Two things have not kept pace: the evidence for each extracted value, meaning the location of the document it was read from, and how far to trust the value and that evidence. Neither is a component of most extraction systems today, so we build them as a framework that attaches to an existing extractor and leaves it untouched. We present VERDICT, a plug-in framework that uses a small Vision–Language Model (VLM) to ground/localize the evidence once per document over a fixed external extractor's output, then calibrates value and evidence confidence. Fine-tuning the VLM for evidence localization substantially improves visual evidence quality and, more importantly, expands VERDICT's selective-prediction operating range. At a strict confidence threshold $0.80$, VERDICT with the fine-tuned VLM gives usable precision–coverage trade-offs for both value and evidence confidence across the in-distribution and out of distribution datasets, whereas the frozen setting often collapses to little or no coverage. Running an open-weight VLM for localization rather than a closed API makes its internal states available to the calibrator, and they are worth more than output log-probabilities: in-distribution AUROC rises from $0.730$ to $0.914$ for value confidence and from $0.681$ to $0.906$ for evidence confidence. This advantage does not survive a distribution shift. We show that the signal is displaced rather than destroyed, and that labeling roughly $120$ fields from the target dataset takes evidence confidence from $0.641$ to $0.905$ on one dataset and from $0.675$ to $0.829$ on the other.

Imaging FlowCytobot (IFCB) systems generate large volumes of phytoplankton imagery that exceed the capacity of manual expert analysis. Although machine-learning approaches achieve high image-level classification performance, it remains unclear whether their predictions can provide ecologically meaningful temporal information for monitoring. This study investigates whether AI-derived phytoplankton classifications can reproduce temporal occurrence patterns and elevated-occurrence signals under realistic sampling and independent-domain transfer. A monitoring-oriented framework was developed using MedPlanktonSet and evaluated on an independent IFCB dataset from the Swedish Meteorological and Hydrological Institute (SMHI). Eight biologically comparable taxa were selected as targets, while all remaining observations were retained as background to preserve the full image-stream denominator. Session-aware partitioning prevented temporal leakage, and alternative preprocessing strategies and convolutional neural network architectures were evaluated. Cross-domain experiments showed that preprocessing strongly affected generalisation. EfficientNet-B0 provided the strongest target-versus-background discrimination and was selected for temporal analysis. Despite residual image-level errors, AI-derived target-occurrence rates closely reproduced expert-derived signals after aggregation (mean absolute error = 0.0432, Pearson $r$ = 0.9696, Spearman $\rho$ = 0.9568). Agreement remained strong across multi-session windows, and elevated, strong, and persistent occurrence proxies were recovered in held-out testing. These results show that AI-based phytoplankton classification can support monitoring-relevant temporal indicators beyond image-level identification and support future operational early-warning development.

Vector quantization is widely used for large-scale data compression and approximate nearest neighbor search (ANNS). Multi-codebook quantization (MCQ) is a practical paradigm that represents database vectors with compact codes and supports efficient retrieval through asymmetric distance computation (ADC). However, existing shallow MCQs encode vectors independently within each inverted file (IVF) cluster, without exploiting local references. Therefore, we propose Spatio-Topological Linkage Quantization (STLQ), a topological shallow MCQ method that organizes each IVF cluster as a directed-forest with compact codes and scaling coefficients. Its basic encoding phase first quantizes vectors independently, while the linked encoding phase re-encodes relative residuals with respect to selected reconstructed parents, reusing local reconstruction information to obtain finer representations. The corresponding linked-ADC preserves linear scanning complexity. STLQ further compresses the scaling coefficients and directed-forest structure to control the additional topology overhead. Extensive experiments show that STLQ achieves higher recall than the evaluated shallow MCQs at comparable bit budgets, although at a higher offline construction cost. Meanwhile, it has a competitive recall-QPS tradeoff against deep MCQs. The code is available at https://github.com/ighxiy/STLQ.

Recognizing micro-expressions in real-world conversations is challenging, as these facial movements are brief and faint, and their interpretations are strongly dependent on the contextual circumstances of their occurrence. Most existing methods are de-contextualized, as they analyze isolated video clips while disregarding the semantic and acoustic cues in the surrounding dialogue that help explain the emergence of an expression. Decades of psychological studies have shown that social context exerts influences on facial behavior over two key dimensions: how an expression is interpreted and how strongly it is generated to begin with. However, existing micro-expression research rarely incorporates such contextual factors into its models. As an example, provocative utterances from an interlocutor may elicit suppressed negative affective reactions, which isolated silent clips are unable to account for. We propose TriCoME, a trimodal dataset consisting of visual, audio and text data sourced from real-world conversations. In this dataset, each micro-expression is paired with its concurrent utterance and preceding context. We further annotate the context based on conversational role to denote two categories: external stimuli from an interlocutor's utterance and internal background from the subject's own utterance. On this basis, we propose the Hierarchical Focusing Fusion Network (HFFNet), which aligns acoustic and semantic streams at fine granularity, compresses long dialogue sequences, modulates attention toward conversational roles via a context-type embedding, and routes each sample between visual-only and multimodal decisions based on visual confidence to prevent noisy context from degrading recognition performance.

Vision-Language Models(VLMs)have advanced Visual Document Retrieval (VDR) by enabling OCR-free, multi-vector representations. However, these models generate excessive tokens to preserve dense visual details, which severely limits retrieval scalability. Existing compression methods mitigate this overhead but rely on isolated heuristics that fail to balance token importance, semantic redundancy, and coverage capacity. We propose a visual token compression framework formulated as an Unbalanced Optimal Transport (UOT) problem. Our approach unifies these three objectives into a single alternating optimization process. Furthermore, we theoretically show that minimizing the transport cost upper-bounds the MaxSim retrieval error, ensuring ranking stability. Extensive experiments on the ViDoRe V1 and V3 benchmarks demonstrate that our method preserves fine-grained document semantics and improves the efficiency-effectiveness trade-off over state-of-the-art base-lines. Code is available at https://github.com/shhhhhyy/Unbalanced-Optimal-Transport-for-EVDR.

Native NVFP4 promises to accelerate reinforcement learning (RL) for large language models (LLMs), but achieving stable learning across separate training and sampling engines remains challenging. We show that matching model weights and numerical formats is insufficient to ensure consistent policy evaluation, highlighting the importance of cross-engine numerical execution. We introduce miniTE, a lightweight framework that combines execution diagnostics, cross-engine numerical alignment, and efficient native W4A4 (4-bit weights and activations) GEMM computation for LLM RL. It improves numerical execution consistency without modifying the RL objective, while reducing implementation overhead to realize the benefits of native low-bit computation. Long-horizon RL experiments on Qwen3-30B-A3B demonstrate stable training and benchmark performance close to BF16, outperforming naive Transformer Engine (TE) NVFP4 in evaluation quality. On single NVIDIA B300 GPU node, the optimized learner reaches 33,540 tokens/s, yielding 1.39x and 1.47x the throughput of BF16 and TE NVFP4, respectively, for complete learner updates. We released the framework, kernels, diagnostics, and training configurations to make native low-bit RL easier.

Long chain-of-thought decoding is memory-bound: the KV cache of the generated tokens grows linearly with the test-time compute being spent. Evicting cache entries does not fix this, because a model never trained on a cache with entries removed generates longer, often up to the length limit. We instead train the model to compress its own output. AbridgeKV compresses each completed block of generated text into the KV entries of a few learned pause tokens. These are extra input tokens with trained embeddings that produce no output. Once the pause tokens have encoded the block, AbridgeKV frees the block's original cache; subsequent tokens attend to the pause tokens' KV entries in its place. Three novel choices make this work: the pause tokens' KV entries take positions inside the block they replace, the cache budget is allocated across layers according to the measured value of each layer's entries, and compression operates on relatively large blocks. On 446 competition problems from AIME, HMMT, AMC, BRUMO, CMIMC and SMT with 32K-token generations, keeping a quarter of the generated cache matches an identically trained full-KV model in accuracy and output length; the strongest published evictor at a matched budget writes far longer, and the closest trained compressor, retrained on the same data, loses 10 points. Served in vLLM, the cache is 3.5x smaller per sequence and a saturated H100 finishes a problem 3.2x faster than with full KV.

We develop a theory of ending currents for properly discontinuous isometric actions of hyperbolic groups on Gromov hyperbolic spaces, generalizing Thurston's ending laminations. Several natural generalizations are considered, which agree in the 3-dimensional hyperbolic setting but are otherwise distinct. We illustrate these invariants and their differences by several examples, including closed surface group actions on hyperbolic group extensions arising from Teichmüller theory and a geometrically finite action of a closed surface group on $\mathbb{H}^4$ with a single cusp that corresponds to a non-simple curve on the surface. We also discuss the conditions under which ending currents characterize geometrically finite actions, obtaining several equivalent conditions and some surprises, illustrated by an example of a geometrically infinite action whose ending currents are all supported on a single orbit of peripheral subgroups.

As LLM agents are increasingly deployed in high-stakes enterprise settings, understanding how they handle sensitive information in agentic dialogue has become critical. Privacy leakage in such settings requires reasoning about whether information flows respect the contextual norms under which they originated. We extend CIMemories to CIMEMORIES DIALOGUE, a benchmark of 4,410 two-agent dialogue instances grounded in Contextual Integrity theory. Using this benchmark, we systematically evaluate 7 open-weight models from the Qwen3 and Llama 3.1 families across conversation lengths of 1 and 6 turns under three prompting conditions. We find that task capability and privacy leakage are fundamentally coupled: more capable models are systematically leakier, with no model in our evaluation able to decouple the two. Thinking models consistently leak more than their non-thinking counterparts, a pattern we attribute to the extended reasoning surface created by chain-of-thought. Leakage compounds with conversation length, rising up to 3x from 1 to 6 turns. Our results suggest that the coupling between task capability and privacy leakage is not an artifact of misconfiguration but a structural feature of current agentic systems.

Hybrid quantum neural networks (QNNs) pair a classical feature extractor with a variational quantum circuit, and the effective dimension of the circuit's quantum Fisher information matrix (QFIM) is widely used to assess such models. This scalar is often interpreted as an indicator of trainability or accuracy, although these readings are rarely tested under controlled conditions. We therefore investigate what it actually measures. We define the effective dimension as the participation ratio of the QFIM diagonal, which lies between one and the parameter count, and we evaluate it across two image datasets, four frozen backbones including a random-projection control, four circuit depths on eight qubits, and three seeds. During training, the effective dimension remains well below the parameter count, and its correlation with test accuracy ranges from -0.72 to +0.87, changing sign across seeds in half of the configurations. Increasing depth activates a larger share of the circuit directions, from 0.38 to 0.91 of the parameter count, while the initialization gradient variance remains between 1e-5 and 1e-4, so no barren plateau (BP) appears at eight qubits. At a fixed circuit, the four backbones share an initial effective dimension of 6 to 9, even though CIFAR-10 accuracy ranges from 23.14% to 86.44%. These results show that the effective dimension characterizes circuit geometry rather than model quality. We conclude with a practical protocol that assigns each diagnostic to the question it can answer.

Let $(M^n,g)$, $n\ge2$, be a compact connected Riemannian manifold with smooth nonempty boundary, $\operatorname{Ric}_M\ge(n-1)Kg$ for $K>0$, and nonnegative outward boundary mean curvature. We derive an explicit algebraic lower bound $B_\eta$ for the first Dirichlet eigenvalue from Kasue's mixed inradius model. With $R$ the inradius and $s=4KR^2/\pi^2$, the bound involves one square root and approximates the model eigenvalue with relative error $O_n(s^4)$ as $s\downarrow0$ for fixed $n$. The construction uses the first two moments of a positive representation of the averaged model potential and a sharp pointwise corrector estimate. For the chosen spectral transfer, the first two moments determine an optimal bound. We also show that the model eigenvalue is the geometric infimum at fixed $(n,K,R)$. For $0<s<1$, it is approached by smooth collapsing balls with sectional curvature at least $K$ and totally geodesic boundary. At the maximal inradius, the model value is attained by the round hemisphere. The bound strictly improves the variance refinement throughout $0<s\le1$. We also give a direct algebraic comparison with an optimized power-test benchmark.

We prove that the three-element flat semiring $S_7$ is strongly nonfinitely based within the class of additively idempotent semirings. More generally, let $\mathcal N$ be the subvariety of $\Var(S_7)$ defined by $x^2y\approx x^2$. For every finite ai-semiring $A$, each variety $\mathcal W$ satisfying $\mathcal N\subseteq\mathcal W\subseteq\Var(A)$ has infinite axiomatic rank.

Competitive humanoid table tennis requires two distinct abilities: executing a desired return and deciding where to return the ball. We separate these two problems, with the ball landing target serving as an interface between motor control and strategy. (1) We first train a whole-body motor policy conditioned on the desired landing target, which maps the target to an executable humanoid stroke through a model-based strike planner and a learned controller. (2) We then improve the motor policy through self-play in closed-loop rallies, where the robot learns to handle incoming balls generated by another player rather than only prescribed incoming balls. At this stage, the landing targets are still sampled without considering the opponent, so the policy improves its execution without learning game strategy. (3) Finally, we freeze the entire motor stack and train a stroke-level strategic policy to choose landing targets through competitive self-play. Motor self-play improves both landing accuracy and legal-return rate during rallies. More importantly, with the entire motor stack fixed, changing only the target-selection policy leads to large differences in game outcomes: the learned strategy wins 89%, 82%, and 73% of points against center, random, and away-from-opponent baselines, respectively. The learned strategy also changes where it sends the ball according to the opponent's position and the previous target, showing that self-play learns more than simply aiming at fixed "good" locations. On hardware, the same frozen execution stack and strategic interface support complete 11-point games against a recreational human opponent, including multi-stroke rallies with both forehand and backhand returns.

Bird's-Eye-View (BEV) representations are increasingly used as compact inputs for autonomous driving perception and planning. However, lightweight and interpretable methods for evaluating candidate ego trajectories directly on BEV outputs remain useful for vehicular safety workflows, rapid prototyping, and human-in-the-loop validation. This paper presents a modular trajectory ranking pipeline that consumes BEVFusion object detections and map segmentations derived from nuScenes sensor data and ranks manually specified candidate trajectories according to safety-first criteria. The ranking prioritizes avoiding collisions and walkway violations, then smaller end distance to the target, and finally path efficiency. To study whether these rule-based rankings resemble human judgment, we created seven BEV traffic scenarios and compared the script output with preferences from a survey of 21 participants. Across 146 pairwise votes, 124 matched the trajectory ranked first by the evaluator, corresponding to an overall agreement of 84.9 %. The results indicate that simple BEV-centric safety heuristics can approximate human preferences in constrained trajectory choice tasks while remaining transparent enough for analysis, dataset curation, and autonomous driving studies.