Papers

Conventional reasoning protocols present a fixed, preselected task, so they cannot test whether an agent propagates relevant updates, preserves unaffected work, or reconstructs a historical task binding. We therefore study dynamic task routing, in which an event stream revises task bindings and a system must select the document version valid at each query time before solving it. To study this problem, we repurpose six widely used benchmarks: MMLU, MMLU-Pro, MedMCQA, MATH, GPQA, and HumanEval into 31{,}119 dynamic episodes comprising 373{,}428 temporally categorized queries. This setting exposes a central trade-off: recomputing after every event wastes work, whereas unguarded reuse returns stale conclusions. We introduce the Revision-Aware Independent Agent Graph (RIAG), a bounded multi-agent policy that separates deterministic temporal resolution from task reasoning. RIAG caches solutions by immutable document identity, starts each fresh task with two unexposed attempts, and conditionally invokes audit and repair, using at most four calls per document version. On this collection, homogeneous RIAG achieves 54.24% joint routing-and-answer accuracy at 0.62 calls/query, compared with 32.22% at 18.00 calls/query for the strongest comparison method; heterogeneous RIAG reaches 49.78% at 0.63 calls/query.

We explore the fundamental limits on finite-time driving in quantum critical systems described by boundary conformal field theory. We show that stochastic work fluctuations arising from external driving are a resource for speedy control, and derive an exact, saturable fluctuation-based speed limit in weakly driven boundary conformal field theories at finite temperature. The bound and saturating protocol can be expressed entirely in terms of the universal scaling dimension, and the result interpolates between the Kibble–Zurek regime,where temporal correlations are strongly nonlocal, and an adiabatic regime where linear driving becomes optimal. For small scaling dimension, the enhanced temporal correlations produce pronounced departures from linear protocols and a larger optimization advantage. These results establish a universal work precision–time tradeoff for boundary-critical control, applicable to quantum impurity, fractional quantum Hall, and superconducting-circuit platforms.

In this paper, we consider the quasi-copulas and copulas with a prescribed sub-track section, i.e., with given values along the curve segment connecting the points (x0,0) and (1,1-x0) for 0<x0<1. By employing the technique based on the W-ordinal sum, we provide methods for constructing quasi-copulas and copulas whose sub-track section coincides with a given one. Then, we further investigate construction methods for symmetric quasi-copulas and copulas with a prescribed sub-track section. Furthermore, we determine the best-possible bounds for the class of quasi-copulas sharing a common sub-track section, and verify that the lower bound obtained is also the best-possible lower bound for the class of copulas with a common sub-track section. Finally, we examine several properties of the bound (quasi-)copulas with a prescribed sub-track section, including their comparison with bound (quasi-)copulas with a given track section or a sub-diagonal section, as well as their statistical characteristic and concordance order.

Equality Saturation (EqSat) is a powerful technique for program optimization, systematically exploring the search space of candidate programs to overcome the phase ordering problem. However, the feasibility and performance of EqSat rely heavily on the specific rewrite rules used to derive equivalent programs. These rule sets are typically handcrafted, requiring extensive domain expertise and carrying the risk of missing valuable transformations. In this work, we evaluate Knuth-Bendix Completion (KBC) as a method for automatically generating and augmenting rewrite rules for EqSat. Our experiments show faster optimization as well as reaching better terms with previously missed optimizations.

For a class of nonlinear Fokker-Planck equations for probability densities, we construct distributional solutions by using an approximation scheme with nonlinear Neumann problems in balls. Moreover, we introduce nonlinear functional inequalities to estimate the convergence rates of the distributional solutions to the stationary solution, with respect to the $p$-variance for $p\in [1,2]$ including the relative entropy $(p=1)$ and the variance $(p=2)$. These nonlinear functional inequalities are then established in both non-degenerate and degenerate settings, so that the main results are applied to a number of typical models with various convergence rates.

Multi-agent systems are often judged by whether they reach the correct answer. This can miss a distinct failure: collaboration may leave behind a corrupted information state even when the immediate decision is correct. We call this an off-query failure. To study this failure in collaborative decision support, we introduce OffQuery, which separately evaluates evidence verification (T1), shared-state reconstruction (T2), and task resolution (T3) in two representative high-stakes settings: healthcare and disaster response. Across GPT, Gemini, and Qwen models, standard collaboration shows much stronger task performance than state reliability. Averaged over 21 model–setting combinations, task resolution reaches 64.7%, while evidence verification and state reconstruction reach only 14.3% and 43.1%. We trace this gap to selective information use: current queries often bypass corrupted facts, which become consequential when later tasks require them. We further introduce ReGround, which resolves conflicting evidence, verifies shared facts, reconstructs a trusted state, and reasons over that state. Across seven models from three families, ReGround improves all three capabilities in every evaluated setting, with average relative gains of 309.0%, 82.9%, and 17.6% on T1, T2, and T3. Reliable collaboration therefore requires both a correct decision and a reliable shared state for future reasoning.

Vision-language models (VLMs) increasingly act as judges that pick the best of several generated images, so their choices decide what users see. Such judges are usually validated by score agreement with human ratings, not by the images they return. We audit VLM judges as decision-makers: on 300 culturally situated prompts, we compare the returned image with human ratings the judge never sees and with random choice from the same candidates, and repeat every decision with the candidates reordered. A 4B-parameter judge barely beats random and falls short of a CLIP similarity baseline. It picks the first image shown in 49% of calls (chance: 28%), and reordering changes its choice on 60% of prompts. For this judge, agreement across orders is informative: decisions that survive reordering are much better than random, whereas agreement with a weaker second judge keeps the wrong ones. An 8B judge shows almost no position bias and outperforms CLIP, yet for it the same filter mostly discards good decisions. Agreement helps only when it targets the judge's failure mode, so filters must be re-audited whenever the judge changes. The 4B judge's slight rise in stereotype ratings is no longer detectable after aggregating across orders or with the larger judge.

The generalization ability of Fake Speech Detection (FSD) models is crucial for real-world deployment. Existing multi-dataset co-training methods rely on fixed training sets and cannot adapt to emerging spoofing types. Although con-tinual learning has been explored, many approaches overlook limited data storage at individual devices, thereby restricting practical applicability. To address this, we propose FedCFM, a Federated continual domain generalization framework via Conditional Flow Matching (CFM) for collaboration without sharing raw speech data across distributed clients facing diverse and evolving spoofing attacks. Each client trains a CFM-based generator to model spoof-type-specific embedding distributions, and cross-client generator exchange enables synthesis of unseen spoof-type embeddings for continual classifier updating through generative replay and knowledge distillation. With the same training datasets, FedCFM achieves lower EER than the eval-uated centralized and federated domain generalization baselines, demonstrating strong cross-domain generalization. Code will be released on https://github.com/jspycpp/FedCFM.

Large language models (LLMs) have achieved strong performance across various natural language processing tasks. However, their robustness to typographical errors remains underexplored, particularly in Japanese, where text input involves multiple writing systems and IME-based conversion. In this study, we evaluate the robustness of Japanese LLMs against realistic Japanese-specific typos. We introduce five typo categories: Character Transposition, Character Replacement, Homophone Conversion, Japanese IME Conversion, and Full-Width Conversion. These perturbations are applied to three Japanese benchmark datasets (JMMLU, JCommonsenseQA, and JamC-QA), and eleven Japanese and multilingual LLMs are evaluated. The results show that Character Transposition and Character Replacement typos consistently reduce accuracy across benchmarks, whereas IME Conversion, Full-Width Conversion, and Homophone Conversion have relatively limited impact. These findings reveal that current Japanese LLMs remain vulnerable to realistic Japanese typing errors, particularly those that substantially distort the original input, highlighting the importance of robustness evaluation in practical input environments.

In 1965, D. H. Lehmer conjectured that the permutations of every multiset admit an imperfect Hamiltonian traversal by adjacent swaps: a walk in the neighbor-swap graph that visits every word, with some words visited twice in order to reach a neighbor and return. The question is posed as an unsolved research problem in Knuth's Art of Computer Programming. Verhoeff (2017) chose the stutter words, in which every domino is a double, as the words to be reached this way, and reformulated the conjecture as the Hamiltonicity of the graph $N(S)$ on the non-stutter words, with two exceptional families — binary signatures with an odd multiplicity, and the permutations of $(2k,1,1)$ — that admit a Hamiltonian path but no cycle. This article proves the reformulated conjecture, and with it Lehmer's conjecture. The key structure is a partition of the words into hypercubes: the swaps inside dominoes turn each class of words with the same domino contents into a hypercube, and the stutters are exactly the $0$-dimensional classes. When every multiplicity is even, Hamiltonian cycles of the hypercubes are glued along a spanning tree, with no finite check. The case of exactly one odd multiplicity reduces to the all-even case and to a theorem of Stachowiak (1992), the one inherited Hamiltonicity input, which also settles two or more odd multiplicities. The only finite ingredients are two explicit cycles, of 28 and 84 words. Every construction is implemented in Python and checked against brute-force graphs, and the proof is formalized in Lean 4 over Mathlib.

Convective-reactive events are phases of stellar evolution where turbulent mixing and nuclear burning directly compete, since their timescales become similar within convection zones. During these events the convection zone structure is shaped by a complex and dynamic interaction of convective transport and nuclear burning of individual chemical elements, with plasma streams connecting the entrainment regions with the burning layers. Here we analyse a 3D hydrodynamic simulation of an oxygen–neon shell merger in a massive pre-supernova star. We study the emergent structure using the Reynolds-Averaged Navier-Stokes (RANS) mean-field composition transport equation. We find that the merged convective zone develops a complex, turbulence-driven mixing structure of multiple nested convective-reactive shells, all contained within the single convection zone. Key controlling factors include not only the mean stratification and mixing, but also emergent collective behaviour of involved nuclear reactions for every chemical isotope. Almost all layers show a quasi-steady balance between burning and mixing. We categorise the various layers, and discuss/contrast with 1D stellar evolution code treatments, highlighting some implications.

Unified language models are increasingly expected to combine heterogeneous capabilities, such as mathematics, code, instruction following, and controllable thinking behavior, within a single set of parameters. A common solution is sequential post-training on multiple objectives, but this entangles all objectives along one optimization trajectory and makes the final model highly sensitive to training order, data ratios, schedules, and stopping criteria. Weight-space merging offers a modular alternative, but naive merging of single-objective experts often fails: domain capabilities degrade sharply, or think/non-think modes collapse into one dominant behavior. We attribute both failures to incompatible weight-space geometry: experts trained on single objectives drift to distant regions of parameter space, placing their interpolations outside any shared low-loss basin. We propose Mixture-Trained Merging (MTM), which trains each branch on an objective-biased data mixture rather than a single objective, exposing it to cross-objective interactions and making branches compatible at merge time. MTM uses merged-model evaluations as a low-cost signal for selecting branch mixtures, avoiding expensive data-mixture ablations. The procedure is iterative: each round promotes the base model using globally selected merge coefficients and refines each branch mixture using domain-preferred coefficients under constraints that preserve other objectives. To scale beyond simplex grid search, MTM uses qNEHVI-based multi-objective Bayesian optimization. Across code, mathematics, instruction following, and think/non-think control, MTM outperforms naive merging and preserves behavioral separation where single-objective merging collapses, suggesting that effective unified models require branches trained to be mergeable.

Optimal experimental design (OED) decides which measurements to acquire for downstream estimation. Classically, this is done by optimizing an information criterion derived from a linear-Gaussian model, for which the estimator is available in closed form. Many modern estimators such as Lasso, elastic net, or total-variation-based estimators, however, are nonsmooth and lack a closed-form solution. To extend OED to these scenarios, we recast the problem as what it implicitly is: a bilevel program whose lower level computes the deployed nonsmooth estimator and whose upper level scores its validation prediction risk. Rather than fixing the number of measurements in advance, we charge each continuous acquisition weight a concave sparsity price. As a result, how many and which measurements to keep are both outcomes of the optimization. A measurement survives only if its estimator-aware value exceeds its price, and progressively increasing the price yields a sequence of designs that explores the trade-off between measurement cardinality and estimation accuracy. Using a value-function penalty reformulation, we develop a single-loop proximal-gradient algorithm that avoids differentiating the nonsmooth solution map and establish its convergence to an (approximate) stationary point. Experiments on synthetic sparse recovery and image reconstruction demonstrate the benefits of the proposed method.

Collaboration between a small language model (SLM) and a large language model (LLM) offers an opportunity to combine the efficiency of smaller models with the strong reasoning capabilities of larger ones. Existing approaches primarily frame such collaboration as a computation allocation problem, determining which model should handle each portion of the reasoning process. In black-box API-based settings, however, this paradigm can be inefficient due to coarse-grained delegation or repeated transmission of context across model switches. In this work, we instead formulate SLM-LLM collaboration as an information acquisition problem, under an API budget constraint. The SLM remains the primary reasoner and selectively queries a black-box LLM advisor only when needed, issuing targeted queries rather than delegating the reasoning process itself. To realize this strategy, we develop a three-stage RLVR framework that learns whether to call the advisor, how to formulate useful queries, and how to integrate the collaboration into the reasoning process by jointly refining advisor invocation and information use. Across mathematical reasoning and coding tasks, our approach improves the performance–cost tradeoff over existing collaboration baselines and, in some settings, matches or exceeds oracle problem-level routing. Finally, we show that our strategy can transfer to other advisor model families, without further training.

Language agents rely on external harnesses to track state, organize workflows, and verify answers. Beyond providing tools and information, these harnesses supply control decisions about what to investigate, whether to revise, and when to stop. Training on successful harness-supported trajectories can improve task performance while leaving these decisions dependent on runtime intervention. We ask whether harness-supported experience can also teach the model to make these decisions, allowing the division of control to change as the model learns. We call this objective harness internalization: learning to assume specified control responsibilities while retaining task performance after the corresponding support is withdrawn. We introduce HARNESS ANNEALING TRAINING (HAT), which combines explicit control supervision with a curriculum over teacher trajectories collected under progressively weaker harnesses. Experiments with 9B and 35B models on SWE-QA and SWE-QA-Pro evaluate every checkpoint under four deployment harnesses. Selected annealed checkpoints operating with tools alone achieve scores close to those of their respective starting checkpoints deployed with the full harness. The benefits vary with model scale and deployment configuration, and further annealing does not uniformly improve performance. These findings suggest that harness-supported experience can help reduce the runtime control required by a trained agent.

Automatic SOAP note generation can ease the documentation burden on physicians, but existing reasoning methods often omit clinically important information and generate unsupported content. Progress in Thai is further hindered by the lack of publicly available datasets. We propose ASCRIBE, a physician-inspired reasoning framework that ascribes a clinical-significance level to each extracted atomic fact in the conversation before summarization, making a general-purpose LLM a more reliable scribe. We also release ThaiClinicBench, the first de-identified Thai clinical summarization benchmark of real encounters, together with a synthetic training corpus derived from real clinical notes. As a prompt, ASCRIBE outperforms chain-of-thought prompting on GPT-5.4 and Gemini 3.1 Pro across the physician-aligned LLM-judge metrics and improves on standard prompting by up to 10.3 points on the completeness LLM-judge metric. As a GRPO reward, it enables a Gemma-4-E4B model trained solely on synthetic data to match Gemini 3.1 Pro in factual precision and surpass it in completeness. Code and data can be found at https://github.com/loolootech/ascribe.

Flow matching is central to 3D generation, yet in practice its reinforcement learning (RL) methods are largely adapted from 2D visual generation. Representative DPO-, GRPO-, and NFT-style objectives, when applied to negative trajectories, mainly steer predicted velocities away from the corresponding directions without explicitly specifying a target velocity field toward preferred samples. In 3D generation, constrained by pretrained model capabilities, rollout diversity, and reward-distribution complexity, directly applying these RL methods yields limited gains in geometric quality. We introduce a forward-process RL method Dynamic Homing Optimization (DHO), which reformulates negative-trajectory optimization as positive-sample attraction-guided dynamic homing. Specifically, Minimum-Cost Attractive Matching (MAM) assigns each negative sample a distinct positive target, and Time-Aware Dynamic Correction (TDC) then redirects its trajectory toward the target using a remaining-time-aware corrective velocity. Building on asynchronous online DHO, we develop Flow3D-Pro, an image-to-3D geometry generation framework. Experiments show that DHO outperforms representative DPO-, GRPO-, and NFT-style objectives in 3D generation, while Flow3D-Pro produces higher-quality 3D geometry than existing mesh generation methods.

Learning can improve an individual's behavior, yet a population risks losing that experience whenever individuals die and are replaced. Inheriting learned preferences offers a way to preserve useful behavior across generations, raising a question for artificial populations: when does inheritance improve collective performance, and how can its benefits be measured fairly? The challenge is that inheritance changes not only offspring behavior but also survival, reproduction, and opportunities for further hereditary updates. Random controls with equal update magnitudes may therefore yield misleading comparisons if they alter different states or obey different stability constraints. We investigate this problem in a resource-limited artificial ecology, combining structured random controls with interventions on newborn preferences and the allocation of hereditary updates. Preserving the state structure of random updates substantially narrows the apparent inheritance advantage, while a conditional establishment-speed benefit remains. Preference erasure and faster-learning compensation support a contribution from reduced offspring relearning. Update allocation also changes the comparison: event quotas and common time cutoffs can reverse rankings, although they also change realized update amounts. With update count and cumulative magnitudes matched, staged release improves occupancy but does not achieve the prespecified establishment criterion. These findings provide a framework for distinguishing the value of inherited preferences from the effects of control design and update allocation, clarifying how inherited learning should be evaluated in artificial populations.

Generative artificial intelligence has reduced the cost of producing plausible symbolic artefacts, leading recent organisation scholarship to identify evaluation and discernment as constraints under conditions of production abundance. This perspective examines a further possibility: that machine evaluation itself becomes inexpensive enough to be deployed routinely and at scale. The investigation is prompted by Jev, TypeSafe AI's specialised model for typed probabilistic decisions. TypeSafe explicitly invokes William Stanley Jevons to argue that lower-cost machine intelligence can unlock previously uneconomic uses. Treating this as a technological provocation rather than an established empirical result, the article formulates a conditional Jevons hypothesis for machine evaluation: sufficiently large reductions in the total marginal cost of usable machine evaluation may increase its organisational consumption where latent demand is substantial and complementary costs do not dominate. The article integrates rebound economics with research on cheap prediction, production abundance, machine evaluation, decision allocation, authority, reliance and Executive Judgement to examine this possible scarcity transition. It distinguishes prediction, machine evaluation, organisational judgement and authorisation as functional activities whose costs need not fall together. Evaluations can share evidence, criteria and errors; scale mis-specified rubrics; operate on representations from which consequential qualifications have disappeared; and change practical decision rights through thresholds and exception routing. The resulting research problem is when cheap machine evaluation substitutes for human evaluative work, when it redistributes or creates demands for judgement, and how it affects the grounds available at consequential organisational commitment.

Efficient long-context inference is essential for large language models (LLMs), yet it poses a severe computational bottleneck. Hash-based retrieval offers an efficient alternative by encoding queries and keys into binary codes and using Hamming distance for key selection. However, this leads to a critical mismatch between Hamming distance and attention relevance. Query-Key logits depend jointly on directional similarity and feature magnitudes, whereas hash binarization discards magnitude information, causing both false-positive retrieval of low-logit keys and false-negative omission of high-logit keys. To address these failures, we propose Hierarchical Hash Retrieval (HHR), a coarse-to-fine framework that progressively improves retrieval accuracy through Geometry-Aware Key Routing (GKR) and Learned Hash Projection (LHP). GKR learns a head-wise orthogonal transformation to redistribute feature magnitudes and derive more discriminative page-level logit bounds, enabling effective pruning of low-logit keys while preserving important candidates. LHP then learns a head-wise projection space that aligns Hamming distance with the true Query-Key relevance ranking for fine-grained retrieval. By combining GKR and LHP, HHR suppresses false positives and recovers false negatives, substantially improving the fidelity of hash-based sparse attention. Extensive experiments across diverse LLMs and benchmarks demonstrate that HHR achieves superior performance over existing methods. For example, on LongBench, HHR improves the average score by 1.10 points and, at a context length of 128K, achieves up to a 3.30x decoding speedup and a 2.83x end-to-end speedup for Llama-3.1-8B-Instruct. The code is publicly available at https://github.com/lianjunl13-sudo/HHR.

A compact dynamic-scene representation must retain both the surfaces seen over time and the appearance needed to render them from new viewpoints. We present Sparc4D, a feed-forward autoencoder that encodes a monocular video with known cameras into a sparse 4D scene state. Static features are shared across the clip, while spatially anchored temporal slots store time-varying features with a median $5.0\times$ fewer values than per-frame storage and negligible change in the complete model's novel-view quality. A sparse decoder produces 2D Gaussian surfels, while stored source pixels preserve fine texture through geometric re-projection. The state includes one full source frame and dynamic-region pixels sampled every fourth frame, alongside learned features and sparse occupancy. For a 32-frame MultiCamVideo clip, it averages 0.67M 32-bit-equivalent values on random windows and 0.66M on the first-32 protocol. On first-32, Sparc4D reaches 21.97 dB, compared with 20.40 dB for MoVieS. On randomly placed windows, their PSNR scores are comparable. Without fine-tuning on real data, Sparc4D transfers to DyCheck and Neu3D, where stored texture improves LPIPS while slightly reducing PSNR. Frozen Sparc4D features also support a manipulation policy that reaches 81.3% success on ManiSkill3 StackCube from 1,000 demonstrations.

Task-oriented communication conveys information that is necessary for downstream tasks. For binary decision tasks, this paradigm is information-theoretically formalized by Boolean function computation (BFC) via channels, where the receiver aims to determine the value of a function unknown to the transmitter. In this paper, we devise a practical code construction for the BFC problem based on a Reed-Solomon code. For noiseless binary channels, we derive finite-blocklength worst-case error bounds. By defining a rate function that captures how supported message length scales with channel uses, we characterize the rate-reliability tradeoff for different Boolean function families. With respect to this rate function, the proposed construction achieves an asymptotic computation rate of $1/2$. We further extend this construction to noisy channels by packing multiple BFC tasks into a single block and concatenating them with a conventional channel code. The corresponding finite-blocklength guarantees are expressed in terms of effective channel uses per function evaluation. With a channel code rate $R_c$, this construction achieves an asymptotic computation rate of $R_c/2$, yielding $C/2$ when capacity-achieving channel codes are employed. Numerical results illustrate the derived bounds and demonstrate substantial performance gains over conventional transmission. As examples, the proposed scheme achieves SNR coding gains of approximately $3.4$ and $6.4$ dB at an average task error probability of $10^{-5}$ for the exact-weight and rank-test tasks, respectively.

We present a direct experimental verification of quantum coherence for a set of quantum states in a basis-independent manner. We find that the theory of quantum coherence for a set of quantum states matches our experimental results perfectly and can be applied to protocols like BB84 and quantum secure direct communication. Using a Sagnac interferometer, we experimentally quantify the quantum coherence for two sets of experimental states. Moreover, we introduce a novel application of set coherence, illustrating that the states employed in the BB84 protocol exhibit maximal set coherence. Our results pave the way for wider applications of quantum coherence for a set of quantum states, including quantum key distribution protocols and probabilistic quantum cloning.

We present an analysis of a high-resolution optical spectrum of V1180 Cas obtained with HIRES at the W. M. Keck Observatory during a bright photometric state of the source. The spectrum is dominated by strong emission lines, including H$\alpha$, the Ca II infrared triplet, He I, and O I, along with numerous Fe I and Fe II transitions and several forbidden lines such as [O I] and [S II], indicating ongoing accretion and mass-loss activity. A weak Li I $\lambda$6708 absorption feature confirms the youth of the source. Using the Li I absorption and selected Fe I emission lines, we report for the first time a radial velocity of $-16 \pm 3$ km s$^{-1}$ for V1180 Cas. The H$\alpha$ and H$\beta$ profiles exhibit asymmetric structures with blueshifted absorption components, suggesting outflowing material along the line of sight. The He I $\lambda$5876 line displays a narrow component likely associated with post-shock accretion regions and a broad, slightly blueshifted component probably arising from magnetospheric flows and/or inner disk winds. The [O I] $\lambda$6300 profile is decomposed into low- and high-velocity components, tracing a slow disk wind and a fast jet. Using the forbidden [O I] line, we estimate for the first time a disk inclination angle of $\approx50^\circ$. The derived mass accretion and jet mass-loss rates imply $\dot{M}_{jet}/\dot{M}_{acc} \sim 0.01$–$0.03$, at the lower end of, but consistent with, the range observed for Class II YSOs. Forbidden-line diagnostics indicate densities $\sim10^{3}$ and $10^{6}$ cm$^{-3}$ with temperatures of $\sim10^{4}$ K, supporting a multi-component outflow scenario. Overall, the results support a picture in which V1180 Cas is an actively accreting, moderately inclined system hosting a multi-component outflow.

In this paper, we study boundary-driven behavior of the BGK model and the Boltzmann equation in a half-space with vacuum initial data. For any $1\leq\beta\leq2$ and $\alpha>0$, we construct a unique local-in-time BGK solution whose inflow boundary data have an arbitrarily small norm with the tangential exponential weight $e^{\alpha|v_h|^\beta}$, but whose norm with weight $e^{\alpha'|v_h|^\beta}$ is infinite for every $0<\alpha'\leq\alpha$ and every positive time of existence, where $v=(v_h,v_z)\in\mathbb{R}^n$ and $v_h\in\mathbb{R}^{n-1}$ denotes the tangential velocity. Thus, this BGK solution instantaneously leaves the exponentially weighted spaces associated with the inflow data, even when the exponential weight is weakened. The construction relies on sharp estimates for the density, bulk velocity, and temperature on a singular scale together with a fixed-point argument in a time-dependent anisotropic space. For comparison, we establish local existence and uniqueness for the cutoff Boltzmann equation under isotropic exponential weights $e^{\alpha|v|^\beta}$. In the Appendix, we further clarify the role of these different weights by showing that the macroscopic stability required for the BGK construction can fail even for Maxwellian inflow data and that it can be recovered by suitably weakening the normal velocity decay of the inflow data. These observations highlight a structural difference between local Maxwellian relaxation and the Boltzmann collision operator in the presence of boundary inflow and vacuum initial data. This work extends the whole-space analysis of D. Lee, S. Park, and S.-B. Yun \cite{LPY2024} to the half-space setting.

Latent world models plan by scoring candidate action sequences with distances in latent space. However, task success is judged by physical quantities, which we call the success-criterion quantities. In all four latent world models we examine, the end-effector position is encoded in the latent state with an error larger than the success criterion allows. Such a latent state cannot separate successful candidates from failing ones. We propose an auxiliary loss that uses success-criterion quantities as training targets, whereas existing latent world models take them only as inputs. During training, a linear head on the encoder and predictor outputs regresses the success-criterion quantities, and the regression error is added to the training loss. The head is discarded after training, so the model, its cost, and its inputs at test time are unchanged. This loss alone improves the success rate on PushT and cube by 3.5% and 3.4% (absolute), respectively, and both improvements are statistically significant. A success criterion thus specifies what a world model must retain in its latent state, and we show that it can serve directly as a training target.

Time-series anomaly detection trades off predictive accuracy, computational efficiency, and interpretability. We use a large language model not as the detector but as the author of one: an autonomous research loop in which the model repeatedly edits a single short NumPy program under a leakage-free objective, keeping the best-scoring detector it finds. The loop discovers two compact detectors, one for univariate and one for multivariate series, that describe short windows by their local spectral features and compare them with the training-region distribution through a covariance-aware distance. On the TSB-AD benchmark these detectors lead the field across metrics, ahead of the strongest classical, deep, and foundation-model baselines including Time-RCD, yet they train no network and use no GPU, and the multivariate detector is faster than every similarly performing baseline. LLM-driven program search is thus a practical route to accurate, efficient, and transparent detectors.

As generative AI (Gen AI) systems take on increasingly autonomous roles in economically and socially consequential interactions, understanding their propensity to cooperate – and the signals that shape this propensity – has become essential. We examine cooperative behavior in frontier Gen AI models using the iterated prisoner's dilemma, manipulating counterpart reputation (positive, unknown, negative), strategy (extortion vs. generosity), and non-verbal emotional signaling (facial expressions conveying competitive or cooperative appraisals). In a first study with non-reasoning models (Claude 3.5, Gemini 2.0 Flash, GPT-4o), cooperation was systematically shaped by all three factors, paralleling patterns long documented in human behavioral research, though models varied substantially in how heavily each factor was weighted. A second study with reasoning models (Claude 4.6, Gemini 3, GPT-5.2) revealed a more concentrated reliance on strategy and reputation, a near-elimination of the Potemkin effect observed in non-reasoning models (evidenced by near-uniform cooperation in a diagnostic harmony game), and a more conditional role for emotion consistent with a hierarchical cue-weighting strategy rather than a simple loss of social sensitivity. Reasoning models also showed heterogeneous end-game behavior, ranging from sustained cooperation to systematic last-round defection effect, revealing model-specific exploitability profiles with direct practical relevance for deployment in negotiation and other multi-round interactions. Together, these findings characterize Gen AI models as increasingly sophisticated, though heterogeneous, social actors, and underscore the practical value of developing standardized cooperation benchmarks to inform the responsible deployment of Gen AI in interactive, socially consequential settings.

We develop a geometric way to uniformly carry out Hörmander's $L^2$-estimates for Hermitian-Yang-Mills connections with bounded energy on Kähler surfaces. We then show the Uhlenbeck convergence of smooth HYM connections on Kähler surfaces can be realized as algebraic convergence inside an analytic flat family. As applications, we prove a continuity theorem for smoothable families and a boundedness result for $\mu$-semistable sheaves with fixed topology. We also discuss potential applications for the moduli problem.

We introduce a novel approach to model predictive control that incorporates multi-step uncertainty prediction for safely controlling systems characterized by uncertainties dependent on both state and control variables. The discrepancy between real-world systems and their control-oriented representations arises from inherent uncertainties, which frequently correlate with state and control variables, a common occurrence in modeling errors. As these uncertainties accumulate and propagate over time, they can produce substantial deviations over extended horizons, potentially compromising the integrity of safety-critical applications. Although existing stochastic control frameworks can maintain system operation within safety boundaries at specified confidence levels, they necessitate accurate prediction of state distributions throughout the control horizon. This prediction represents a significant challenge for systems where uncertainties vary with state and control inputs. Our contribution addresses this challenge through a Model Predictive Controller leveraging multi-step Gaussian Process Regression to capture and anticipate uncertainties that are state- and control-dependent. We further propose an iterative solution to the optimization problem in our MPC framework and discuss the convergence of the algorithm. To demonstrate the method in a practical application, we conduct an in-depth analysis of vehicle lateral control, particularly during lane-changing maneuvers, examining how errors propagate through the system model. The effectiveness of our proposed methodology is validated through comprehensive simulations.