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Tuesday 29 September

Quantum Physics

On Removing Interaction from Quantum Proofs

Nicholas Spooner and Max Tromanhauser

An important open question in quantum cryptography is the construction of publicly-verifiable NIZKs for QMA. Classically, one can construct NIZKs for NP in the random oracle model (and sometimes in the standard model) by compiling an honest-verifier ZK (HVZK) $\Sigma$-protocol for NP using the Fiat-Shamir transformation. Broadbent and Grilo introduced a quantum analog of a $\Sigma$-protocol (which they call a $\Xi$-protocol) in which the prover's first message is quantum, and show that HVZK $\Xi$-protocols exist for QMA. However, it is not clear how to compile such protocols into NIZKs in the (Q)ROM, because the Fiat-Shamir transformation seems to be incompatible with quantum messages. In this work we give formal evidence that this is indeed the case: we show that if generic "Fiat-Shamir-like" compilers for quantum protocols exist in the QROM (with small completeness and soundness error) then QMA = BQP.
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Artificial Intelligence

Decode-Latency Feedback Prefill: A Model-Free Controller and Its Generalization Limits

Gaurav Agarwal, Ashish Garg and Isha Singhal

Concurrent autoregressive inference creates a fundamental interference problem: prefilling a newly arrived long prompt can delay tokens for requests that are already decoding. Fixed prefill chunks reduce this interference, but the best chunk size depends on the model, hardware, load, and latency objective. We introduce Decode-Latency Feedback Prefill (DLFP), a model-free controller that changes only prefill work that overlaps active decodes. After a guarded scheduling cycle, DLFP uses the observed interval as proportional feedback to resize the next prefill chunk; isolated prefills remain unrestricted. We implement DLFP in vLLM and evaluate it with open-loop Poisson arrivals, exact token accounting, raw request traces, and NVIDIA telemetry. On Qwen3-0.6B in BF16 on one A100 80 GB GPU, three paired 100-request trials reduce P99 inter-token latency by 24.8%, 30.1%, and 28.2% (mean 27.7%, paired 95% confidence interval 21.0% to 34.3%) with exact output agreement, no failures, and unchanged SLO compliance. The benefit is not free: mean P99 time to first token increases 34.8% while remaining inside the declared SLO. Crucially, the mechanism does not generalize to Qwen3-8B, Qwen3-32B, or a two-GPU tensor-parallel configuration. We trace the failure to an asynchronous scheduler-call interval that is only a proxy for completed GPU iteration time. This negative result defines the boundary of the contribution and motivates a completion-timed controller for concurrent CPU and on-device inference. We do not claim mobile-device performance; the present work is a reproducible proof-of-concept and generalization study.
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Artificial Intelligence

Fine-Tuning Diffusion Language Models with Context Selection and Target Weighting

Loay Mualem, Lluís Pastor-Pérez, Vinh Tong et al. (+4 more)

Supervised fine-tuning of discrete diffusion language models masks some response tokens and trains the model to recover their original values from the visible context. The masking pattern therefore determines both the context available to the model and the tokens it learns to predict. Uniform random masking does not explicitly account for the interaction between these choices. We introduce GoldiMask, which selects tokens to reveal as context by approximately maximizing a submodular objective. This objective uses model signals to balance the benefit of revealing tokens against their value as prediction targets. GoldiMask then weights the remaining targets according to how they benefit from the selected context and their remaining learning potential. Across three backbones and three training datasets, GoldiMask achieves the highest average accuracy in most evaluated settings, demonstrating gains on both reasoning and code generation. Component ablations show that both context selection and target weighting contribute to the gains. GoldiMask also reduces decoding iterations on GSM8K and MATH-500 under confidence-threshold parallel decoding, while maintaining comparable accuracy at higher confidence thresholds.
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All authors Loay Mualem, Lluís Pastor-Pérez, Vinh Tong, Andrei Manolache, Tanja Bien, Steffen Staab, Mathias Niepert

Machine Learning

LeanPolish: Verified Supervision for Lean Proof Compression

Pauline Bourigault

Verified proof edits offer a natural source of supervision for improving language-model-generated Lean proofs. Yet verification establishes that an edit is correct, not that its training signal is free of search artifacts. We introduce LeanPolish, a symbolic Lean 4 pipeline that releases 33,402 accepted local edits and 65,596 same-state failed attempts, and use it to study what models learn from this supervision. First-success search admits a goal-independent rule with perfect ranking accuracy; teacher-selected evaluation sites also reward trivial deletions. Continuing menu evaluation beyond the first success removes the ordering shortcut: a trained ranker selects the best candidate on 70.1% of evaluated held-out states, versus 36.9% for the strongest frozen baseline. For compression, iterating the symbolic pass raises miniF2F savings from 19.7% to 27.5%, exceeding the neural hybrids we test there. Verified neural editing helps on other proof sources, but matched frozen-model controls show that its gains need not come from training. The supervision does improve whole-proof rewriting: fine-tuning raises verified token reduction from 2.8% to 5.5% on 19 PutnamBench proofs. Together, the released edits, complete candidate pools, and controlled evaluations separate learning to imitate a search policy from improving on that search. They provide a reproducible basis for studying proof improvement while keeping correctness, compression, and edit policy distinct.
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Machine Learning

Learning to Plan from Random Exploration

Deqian Kong, Guangyan Sun, Sheng Cheng et al. (+6 more)

Random exploration reveals how an environment can be traversed before a goal is specified. Can this experience support long-range planning without policy-improvement training? Our random-walk analysis explains what temporal relations contain: short horizons reveal geodesic geometry in the diffusion limit, while longer horizons reveal connectivity between regions before mixing removes these distinctions. We learn these relations with a conditional energy-based model that estimates temporal log-density ratios through horizon-conditioned embeddings. The model is trained on observation pairs by noise-contrastive estimation, without action or reward labels. The planner queries these learned relations at different horizons as it moves toward the goal. At test time, a separate local dynamics model predicts candidate action outcomes, and the temporal model evaluates their progress toward the goal by selecting or aggregating estimated improvements across horizons. The agent executes one action and replans with both models fixed. Experiments demonstrate long-range maze planning from random exploration using states and images. Learned score fields, embedding probes, and planned routes exhibit properties of a multiscale cognitive map. We further demonstrate egocentric navigation from random exploration and manipulation planning from suboptimal data.
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All authors Deqian Kong, Guangyan Sun, Sheng Cheng, Sirui Xie, Bo Pang, Jianwen Xie, Tony Geng, Caiwen Ding, Ying Nian Wu

Mathematical Physics

Reachable sets under Kolmogorov dynamics in the probability simplex

Alfonso Fernández de Bobadilla, Mykhailo Hontarenko, Guillem Müller-Rigat et al. (+1 more)

The finite-time reachability problem - whether two probability vectors can be transformed in a time t through a generator from a given set - is a key question in Markovian dynamics. We address this problem for normalized Kolmogorov generators with tools from differential geometry. The shortest time T connecting an ordered pair of states defines an (asymmetric) quasi-distance in the probability simplex, which distinguishes between outgoing and incoming reachable sets, and captures the inherent irreversibility of Markov dynamics. The Finsler metric corresponding to normalized generators with bounded diagonal entries is characterized, and time-independent evolutions that saturate speed limits are presented. Analytical boundaries of both reachable sets are derived and the ratio of their corresponding volumes assess the bounds obtained. The asymmetry with respect to the uniform probability vector is shown to be related to the Kullback-Leibler relative entropy.
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All authors Alfonso Fernández de Bobadilla, Mykhailo Hontarenko, Guillem Müller-Rigat, Karol Życzkowski

Cryptography and Security

LogiC-Diff: Embedding Security Properties Into AI-Enabled Cyber-Physical Systems

Ziyan An, John Stankovic and Meiyi Ma

AI-enabled Cyber-Physical Systems (CPS) are highly vulnerable to adversarial and anomalous inputs, where small perturbations can induce cascading errors and unsafe control actions. Existing approaches, such as rule-based filtering, training-time regularization, or diffusion-based reconstruction, either operate outside the model or lack mechanisms to incorporate formal security specifications into the prediction process. In this paper, we take the first step toward embedding security properties directly into AI-enabled CPS, enabling predictive models to enforce system-level constraints during inference rather than relying on external defenses. We introduce a logic-conditioned bi-stage diffusion framework that integrates Signal Temporal Logic (STL) specifications into forecasting. STL serves as a first-class conditioning signal that guides both an input repair stage and an output refinement stage, allowing the model to jointly mitigate adversarial perturbations and enforce desired temporal behaviors to satisfy security-critical properties. We evaluate our approach on two real-world multivariate CPS forecasting datasets under a diverse set of physical sensor and cyber attacks. Across sensor faults, gradient-based attacks, adaptive attacks, and varying attack strengths, our method consistently improves robustness and specification compliance, degrades more gracefully as attack strength increases, and generalizes better to unseen attacks. Ablation studies on specification coverage and quality further show that embedding logical security properties yields gains unattainable by reconstruction-based methods alone, highlighting a new direction for integrating formal methods with generative models in secure CPS.
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Networking

Priority-Aware Routing for Quantum Networks:Integrating Coherence-Time Constraints into Scheduling

Sadhgun Ram Dasi and Aswath Babu H

Quantum networks face a fundamental challenge absent in classical networks; finite memory coherence times mean that queuing delay directly degrades information quality, causing decoherence that has no classical analog. Existing routing protocols optimize for hop count or channel fidelity while treating scheduling delays as a secondary concern, leaving fidelity vulnerable to congestion-induced decoherence. We present a coherence-aware routing protocol that integrates decoherence constraints into path selection via a priority-modulated aging model derived analytically from Weighted Fair Queueing theory, where high-priority traffic receives compressed effective queue delay. We build a custom discrete-event simulator verified against NetSquid (across 104 states), and evaluate across two structurally diverse topology classes under identical physical parameters, isolating topology structure as the sole independent variable. In all experiments, our protocol is benchmarked against loss-only Dijkstra routing and FIFO scheduling as baselines. On topologies, P2 traffic achieves 96.08% fidelity under a 9x load increase with only 0.04 percentage point degradation, versus a 13.51 percentage point collapse for the loss-only baseline; P2 tail latency holds stable at 0.055 ms while Dijkstra degrades 5.5x. On Barabasi-Albert scale-free topologies, our protocol delivers a +4.12 percentage point fidelity advantage with 97.8% higher aggregate throughput at operational loads over the baseline, with a clearly characterized hub-saturation boundary at 160k QPS. FIFO scheduling provides negligible priority differentiation on both topology classes, providing strong evidence that coherence-aware routing-not scheduling alone is responsible for the observed QoS gains.
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Artificial Intelligence

Aligned Data Can Induce Misalignment via Context Confusion

Yavuz Bakman, Duygu Nur Yaldiz, Baris Askin et al. (+4 more)

Large language models are frequently updated for various use cases, where filtering out misaligned training samples is a common practice for preventing post-update misalignment. However, alignment is inherently context-dependent: a behavior that is aligned in one context may be inappropriate in another. For example, recommending that researchers retain their data for reproducibility is aligned, whereas recommending that a mobile app retain users' sensitive data may violate users' privacy. Starting from this observation, we identify a posttraining phenomenon where aligned training induces misaligned behavior in other contexts. We call this phenomenon context confusion. We demonstrate context confusion across three domains: (1) Gender Equality, (2) Privacy, and (3) Physical Safety. Unlike the broad misalignment seen in emergent misalignment, context confusion causes domain-specific misalignment that evades general alignment evaluations. Further, it is not effectively reduced by injecting general alignment training data, but can be substantially reduced by including targeted alignment data for the misaligned domain or providing in-context learning examples during inference. Lastly, we provide a mechanistic explanation of context confusion. We observe that queries from different domains can undergo similar representational shifts during the fine-tuning. Consequently, a query from a different domain may activate the same behavioral feature learned during fine-tuning, which causes the behavior to transfer to a context where it is misaligned. Based on our findings, we argue that it is difficult to predict the alignment state of a model after training by inspecting the training data alone, which highlights the importance of comprehensive post-training alignment evaluations.
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All authors Yavuz Bakman, Duygu Nur Yaldiz, Baris Askin, Swastik Roy, Morteza Ziyadi, Salman Avestimehr, Sai Praneeth Karimireddy

Numerical Analysis

An energy-based discontinuous Galerkin method for wave equations on complex geometric domains

Yangxin Fu, Yan Jiang, Siyang Wang et al. (+1 more)

This paper develops a high-order cut energy-based discontinuous Galerkin (CutEDG) method for second-order acoustic wave equations on complex domains and across stationary material interfaces. The method employs unfitted Carte- sian meshes and addresses the small-cut-cell problem by introducing ghost-penalty stabilization directly into the local bilinear forms defining the EDG energy, while leaving the original spatial coupling and numerical-flux structure unchanged. We establish semidiscrete energy stability and a priori error estimates showing that high-order accuracy is retained. The formulation is further extended to interface problems with discontinuous wave speeds. Numerical experiments confirm the pre- dicted convergence rates and demonstrate robustness with respect to arbitrarily small cut cells. In particular, the explicit time-step restriction is governed by the background mesh size rather than the smallest physical cut cell, and the stabilized energy Gram matrices exhibit cut-independent conditioning.
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All authors Yangxin Fu, Yan Jiang, Siyang Wang, Lu Zhang

Computer Vision

PhyProbe: Rethinking Physical Consistency Evaluation in Generated Videos

Max Ku, Jiaojiao Fan, Zekun Hao et al. (+5 more)

Evaluating the physical consistency of generated videos remains a fundamental challenge. Existing approaches rely on off-the-shelf vision-language models, which can often be myopic to physical dynamics, or fine-tuned evaluators trained on human annotations, which overfit to dataset-specific cues and fail to generalize. A key challenge is that existing supervision sources provide either relative ordering or absolute scores, but not both reliably and consistently across varied settings. To this end, we introduce PhyProbe, an evaluator that extracts features from a frozen pretrained spatio-temporal encoder and maps them to a scalar physical consistency violation score via a lightweight scoring head. PhyProbe is trained through a unified objective combining pairwise ranking, regression on noisy scalar annotations, and anchor-based calibration over a curated set of heterogeneous supervision sources. Experiments show that PhyProbe outperforms prior methods on most pairwise benchmarks spanning real-generated and generated-generated pairs under varying correspondence, with the largest gains in no-correspondence and generated-generated settings where existing fine-tuned evaluators degrade sharply. PhyProbe achieves strong correlation with human judgments, with close agreement between rank-based and linear metrics, indicating that scores are both well ordered and anchored to a stable [0, 1] scale. Further, despite being trained on supervision indicative of physical consistency, without explicit general-preference labels, PhyProbe also performs competitively on human preference benchmarks: consistent with the observation that physics violations are entangled with broader quality degradations.
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All authors Max Ku, Jiaojiao Fan, Zekun Hao, Francesco Ferroni, Heng Wang, Wenhu Chen, Ming-Yu Liu, Prithvijit Chattopadhyay

Quantum Algebra

Conformal blocks for modular vertex algebras

Colton Griffin

Given a vertex operator algebra $V$ over $\mathbb{C}$, it is known how to define so-called sheaves of coinvariants and conformal blocks on the moduli space $\overline{\mathcal{M}}_{g,n}$ of stable, $n$-pointed, genus $g$ curves. We extend this theory to vertex algebras equipped with a notion of change of coordinates over any algebraically closed field. As a by-product of our arguments, we also show that a number of standard assumptions in these constructions can be removed, such as being $C_1$-cofinite or CFT-type.
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Machine Learning (Statistics)

Lower Bounds for Linear-Oracle Online Learning

Mohit Sinha

Can a constant number of linear minimizations per round improve on the $T^{3/4}$ regret rate of online Frank-Wolfe on general convex sets? Weibel et al. conjectured that fixed-coefficient methods cannot. We prove their conjecture and extend the lower bound to every deterministic learner in an oracle-only model. The learner receives an initial feasible point and a diameter bound, and must remain feasible on every domain consistent with its oracle replies. For $T$ rounds, at most $b$ calls between decisions, diameter bound $D$, and gradient norm bound $L$, we construct an instance in dimension $d=2b(T-1)+1$ with regret at least $2^{-1/4}LDb^{-1/4}T^{3/4}$. The adversary fixes the domain, initial point, deterministic tie rule and linear losses before play. The vertices form a path on which every point available before a decision has zero current loss, while the final vertex has negative loss on every round. For constant $b$, the result matches the known upper rate for dimension-independent guarantees. For one-call fixed schedules with a nonzero coefficient on the newest gradient, a second construction gives regret at least $3LDT^{3/4}/4$ with unique minimizers at every issued query. Exact-arithmetic certificates for the tuned schedule of Weibel et al. closely match their finite-horizon numerical worst cases, with unique oracle replies.
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Computation and Language

Doc2LoRA Provides Decodable Representations of Scientific Ideas

Chand Sahil Mansuri, Joel Zachariah and Sadamori Kojaku

Representing scientific papers as points in a space lets us search for similar papers and inquire about how fields relate to one another and drive innovation. Beyond search, the vector space of papers invites generation: mixing papers through simple vector operations creates new points, mirroring combinatorial novelty, the recombination of existing ideas into new ones. However, a mixed point often represents an idea no paper has yet realized, with no papers nearby to identify the idea. We propose representing each paper by a LoRA adapter generated by the Doc-to-LoRA hypernetwork. Every point in the space, including mixtures, thus represents a large language model (LLM) open to questions and instructions in natural language. On papers from the American Physical Society (APS), we instruct the LLM at the average of each subfield to name the field in a few words and obtain labels closer to the official names than the labels of five baselines, as judged by word overlap and a panel of five LLM judges. We also ask the LLMs at points between two APS papers to write an abstract and obtain descriptions shifting from one paper to the other in step with the mixing weight. While Doc-to-LoRA is trained for generation, a small invertible transform makes the embeddings competitive for search, on par with SPECTER2 and EmbeddingGemma and close to SBERT. Because the transform is invertible, every point in the transformed space still maps back to an LLM. The embeddings thus serve both search and generation, enabling researchers to question the idea at any point in the space as a starting point for generating new ideas.
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High Energy Astrophysical Phenomena

NEXUS: Discovery of a Luminous Young Transient at $z=5$

Ming-Yang Zhuang, Yue Shen, Lei Hu et al. (+8 more)

We report the discovery of AT 2026abck, a young transient in a star-forming galaxy at $z=5.017\pm0.001$, identified from Year-2 observations of the NEXUS JWST treasury program. AT 2026abck was detected on 2026 Aug 7 in NIRCam F200W imaging, with contemporaneous detection from parallel NIRCam F150W+F277W imaging. It brightened by $>1.4$ mag in F200W over $\lesssim 12$ rest-frame days, as inferred from the last non-detection. AT 2026abck has nearly identical magnitudes of $\sim27.4$ mag in F150W, F200W, and F277W, and is undetected in F444W ($>27.9$ mag, 3$\sigma$). It is the first robustly detected $z\gtrsim 5$ transient in a non-lensing field. A blackbody fit yields a hot photosphere ($\sim1.7\times10^4\, \mathrm{K}$) with a radius of $\sim7\times10^{14}$ cm ($\sim46$ au) and a bolometric luminosity of $\sim3\times10^{43}\, {\rm erg\, s^{-1}}$. Its off-nucleus location and hot, UV-bright SED favor a core-collapse supernova origin, while its temperature and luminosity exceed those of normal SNe II at comparable early phases. We estimate that AT 2026abck was detected $\sim4$-10 rest-frame days after explosion. The host is an intermediate-mass ($M_*\approx10^{9.8}\,M_\odot$), star-forming (${\rm SFR}\approx20\,M_\odot\,{\rm yr^{-1}}$) galaxy on the $z\approx5$ main sequence, $\sim3.3$ dex more massive than the ultra-faint host of the lensed SN Eos at $z=5.13$. Together, the two events show that CCSNe at $z>5$ occur across a wide range of host environments, and AT 2026abck demonstrates that high-cadence blank-field JWST surveys can capture high-redshift SNe during their early, UV-bright phase.
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All authors Ming-Yang Zhuang, Yue Shen, Lei Hu, Justin D. R. Pierel, Zhiwei Pan, Zachary Stone, Adam J. Burgasser, Xiaohui Fan, Jenny E. Greene, Junyao Li, Feige Wang

Artificial Intelligence

Self-Evolving Harness on Multiple Tasks with the Agent as Its Own Optimizer

Qiankai Xu

A harness is the code around a language-model agent that organizes prompts, calls tools, manages context, and controls execution. As models grow stronger, recent work has begun to let agents improve their own harnesses, a line of work known as self-evolving harnesses. In most existing methods, a separate proposer running on a human-designed harness modifies the solver's harness, and a separate harness is evolved for each benchmark. Real-world tasks come from many domains, so both the evolution and the evaluation of a harness should cover a diverse range of tasks. We propose a framework close to recursive self-improvement: the same frozen model, on the same version of the harness, first solves tasks as the solver and then, as the proposer, reads the complete run records and directly edits the harness that runs it. Each evolution batch draws tasks from five benchmarks in different domains. To measure generalization, training and held-out tasks are strictly separated, and we additionally evaluate on five out-of-distribution benchmarks never used during evolution. We frame the evolution process as deep-learning training with two stages, multi-task pretraining and continual training. Starting from a 49-line seed harness, the harness obtained at the end of the first stage improves the average score by 4.48 points on the in-distribution benchmarks and by 12.64 points on the out-of-distribution benchmarks, surpassing Codex on the former and matching it on the latter. In the second stage, continued evolution on Claw-Eval, one of the out-of-distribution benchmarks, further raises the score on that benchmark from 66.17 to 68.06, exceeding Codex. We also provide an in-depth analysis of the mechanisms that emerged during evolution, including output truncation, history compaction, and independent review.
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Robotics

TALK-Dem: Benchmarking Embodied Task Planning under Dementia-Associated Communication Patterns

Guangxin Zhao, Yiran Hu, Yuan Cao et al. (+7 more)

Existing LLM-driven robot task planners rely on a taken-for-granted assumption of an ideal user whose instructions are clear, complete, and task-focused. However, when interacting with real-world users, especially those experiencing cognitive impairments, such as people living with dementia (PLWD), the planners often make mistakes and even pose physical safety risks. We proposed TALK-Dem (Talking Attributes and Linguistic Knowledge in Dementia), the first benchmark for evaluating LLM-driven robot task planning under dementia-associated verbal communication. TALK-Dem contains 4,800 instructions and covers five typical communication patterns, including Referential Imprecision, Object Substitution, Empty Speech, Topic Drift, and Intrusion, at three intensity levels. Experiments across six open-weight LLMs reveal a substantial robustness gap. Across communication patterns, open-weight models exhibited performance drops of up to 22.3 percentage points compared to ideal instructions. This revealed a critical gap and even danger for real-world applications, especially in assistive robotics, where locally deployable models are necessary due to privacy concerns and connectivity constraints. To mitigate this issue, we proposed the Context-Aware Retrieval from Experience (CARE) method, which retrieves relevant previously resolved tasks to provide task-specific interpretation and planning context. CARE generally outperformed standard prompting baselines across the six open-weight models, improving average task success by 18.1 percentage points over the vanilla prompt. These results highlighted the importance of both evaluating communication robustness and developing effective adaptation strategies for locally deployable assistive robots. The TALK-Dem dataset is publicly available at https://anonymous.4open.science/r/TALK-Dem-A6B3/.
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All authors Guangxin Zhao, Yiran Hu, Yuan Cao, Chenxi Jiang, Jianfei Yang, Yegang Du, Yasuyuki Taki, Yoshifumi Kitamura, Lin Gu, Zhi Zheng

Numerical Analysis

An Approximate Method for Modeling Plasmons on Graphene with Time- and Space-dependent Properties

Kaleigh Rudge and Fadil Santosa

This paper presents approximate computational methods for modeling surface plasmon propagation on a graphene sheet with time- and space-dependent material properties. Starting from Maxwell's equations, the evolution of current density under a spatially and temporally modulated Drude weight is formulated as a partial integro-differential equation (PIDE). Assuming small-amplitude perturbations of the Drude weight, a regular perturbation expansion is developed. The solvability and Fourier invertibility of the resulting order-by-order integral equations are established in appropriate Sobolev spaces. A numerical solver combining a Volterra integral equation formulation with the fast Fourier transform (FFT) is introduced, along with pointwise error estimates and computational complexity analysis. Additionally, an analytical transform-based solution using contour integration and Laplace inversion is derived for traveling-wave Drude weight modulations. Numerical simulations demonstrate diverse wave phenomena, including traveling, standing, and exponentially growing plasmonic current densities.
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Artificial Intelligence

Can an AI Agent Rediscover a Blaschke-Curve Invariant?

Yunus E. Zeytuncu

We study generalized Blaschke curves as a controlled environment for AI-assisted mathematical rediscovery. For one fixed degree-four Blaschke product, an agent receives numerical coordinates of the six pair-lines determined by each of 80 boundary configurations. The target theorem is withheld from the task instructions. The saved research log reports rejected geometric hypotheses and a homogeneous cubic fitted to polygon sides. Its frozen coefficients predict 480 lines from 80 unseen parameter values, with a recorded RMS scale-free residual of $8.88\times10^{-17}$. Discovery-set diagonals provide an out-of-fit consistency check, not a fully held-out test. A separate one-configuration run reports insufficient evidence for invariance. A post-review deterministic degree-search baseline also recovers the cubic, so the experiment does not establish an advantage over polynomial fitting. We present this single-instance case study as a protocol for separating conjecture, numerical validation, and proof, with explicit limitations concerning agent metadata, prior knowledge, and reproducibility.
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Computer Vision

Composition, Not Conversation: VLMs Lose the Scene, Not the Thread

L. D. M. S. Sai Teja, Ufaq Khan, N. Siva Gopala Krishna et al. (+5 more)

Vision-language models (VLMs) increasingly reason over visual evidence that is cropped, segmented, retrieved, or revealed over time. Yet most VQA benchmarks present the complete image and question at once. We ask what models lose when the same information is fragmented. We introduce Layered-VQA, with 93 scenes and 300 questions. Each image is decomposed into ordered RGBA layers that exactly recompose the original scene, and each question is annotated with supporting, minimal-sufficient, and distractor layers. We evaluate eleven open-weight VLMs from 3B to 32B parameters and two proprietary models with a scale of 187,200 conversations, graded by 1.74M open-model cross-judgments. We find three consistent failures. Loss in Composition: fragmenting the question has a small effect, but fragmenting the scene substantially reduces accuracy; recomposing the same layers largely restores performance. Oracle Inversion: even oracle-selected sufficient evidence can perform worse than the complete scene. Loss in Grounding: as more evidence is required, grounding degrades much faster than answer accuracy. Together, these results show that having the right visual evidence is not enough. How that evidence is composed and presented determines whether models can use and ground it. The right evidence is not enough: VLMs need the scene it came from.
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All authors L. D. M. S. Sai Teja, Ufaq Khan, N. Siva Gopala Krishna, Satyajit Tourani, Ashshak Sharifdeen, Fida Mohammad Thoker, Bernard Ghanem, Muhammad Haris Khan

Data Structures and Algorithms

Certifiable Near-Optimality: A Simple Framework for Unifying Search and Refutation for (Semi)random CSPs

Prashanti Anderson, Peter Manohar and Jeff Xu

A classical problem in average-case complexity is the study of random constraint satisfaction problems (CSPs). Random CSPs are traditionally studied in two different settings: refutation, where the instances are uniformly random and thus unsatisfiable with high probability, and search, where the instances are drawn from a planted model so that they are satisfiable. While there is no formal relationship between the refutation and search variants of random CSPs, known algorithms are strikingly similar with near-identical computational thresholds. In this work, we establish a formal relationship between the known algorithms for refutation and search by showing that in either case they achieve a stronger guarantee: they output an assignment $x$ along with a certificate $\pi$ that the fraction of constraints satisfied by $x$ is within some small $\varepsilon$ of the optimal assignment. We call this guarantee certifiable $\varepsilon$-optimality. As an application, we design new algorithms for a model of semirandom CSPs where the instance hypergraph (or scopes) is random, but the literal negation patterns are adversarially chosen and may depend on the hypergraph. For such CSPs, we give a family of algorithms that output certifiably $\varepsilon$-optimal solutions. We additionally study such semirandom CSPs in the "strong contamination model", where an adversary is allowed to corrupt an $O(\delta)$-fraction of constraints after seeing the initial CSP. For such CSPs, we give an algorithm to output a certifiably $O(\delta)$-optimal solution.
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Group Theory

On a generalization of the Reidemeister spectrum of a finite group

Marius Tărnăuceanu

Based on a recent generalization of the Reidemeister spectrum of a finite group [1], in this short note we extend the main result of our previous paper [2].

Soft Condensed Matter

Geometry and Mechanics of Ribbon Gridshells

Daniel Castro, Joo-Won Hong, Étienne Reyssat et al. (+3 more)

Mechanical metamaterials exhibit anomalous properties induced from non-trivial mesoscopic constituents. Inspired from architectural and industrial structures, we introduce arrangements of long, narrow ribbons intersecting at prescribed angles as a model thin-sheet metamaterial. These ribbon gridshells are shown to display highly non-linear behavior driven by the geometric constraints, nonetheless unlike most complex mechanical systems, we are able to explicitly write out the coarse-grained governing equations and to classify their solutions in terms of the intersection patterns of the ribbons. It is shown that the structure can assume arbitrary, tunable Gaussian curvature distributions, allowing us to formulate an inverse design problem, solvable under a suitably defined local condition. An analysis of the soft modes, confirmed by experiment and numerics, reveals rich mechanics which may exhibit both a rigid and an anomalously soft behaviors.
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All authors Daniel Castro, Joo-Won Hong, Étienne Reyssat, José Bico, Benoît Roman, Hillel Aharoni

Machine Learning (Statistics)

Acceleration of Diffusion Language Model through Discrete Average Generator

Yidong Ouyang, Zhengyan Wan, Themis Haris et al. (+8 more)

Discrete diffusion models and flow matching have emerged as powerful frameworks for generative modeling over discrete state spaces, yet efficient few-step generation remains a fundamental challenge. In this work, we introduce the Discrete Average Generator, a principled extension of MeanFlow to Continuous-Time Markov Chains (CTMCs). Analogously to how MeanFlow defines an average velocity field over a time interval in continuous spaces, we define an average generator as the normalized increment of the transition kernel over a time interval. We show that this average generator satisfies a self-consistency identity, which provides the foundation for our training objective. We further develop training strategies that align with the standard training paradigm of diffusion language models while keeping the resulting objective tractable. When projected onto per-coordinate marginals, the self-consistency identity admits a closed-form expression, enabling efficient training and inference. In Potts model simulations, our objective reduces the total variation distance of the $K$-step sampler by up to 67%. On OpenWebText, our method achieves the lowest generative perplexity among the evaluated methods for 8 to 64 sampling steps while enabling a $16\times$ acceleration, and achieves comparable performance to existing methods on ImageNet.
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All authors Yidong Ouyang, Zhengyan Wan, Themis Haris, Tian Tan, Liqian Peng, Henry Li, Ziqian Lin, Jianhang Chen, Maryam Karimzadehgan, Alec Go, George Michailidis

Machine Learning

Simulator-Refined Diffusion for Radio-Frequency Inverse Design

Jinhao Liang, Jacob K. Christopher, Michael Frei et al. (+2 more)

Diffusion models have shown potential in inverse design of printed circuit boards (PCBs), enabling the generation of layouts conditioned on target S-parameters. Despite this promise, applying diffusion models to PCB layout generation remains challenging due to their difficulty in meeting the quantitative electromagnetic specifications. A common approach is gradient-based guidance, which biases the diffusion sampling process with the gradient of an objective used for evaluation. However, full-wave electromagnetic simulators are accurate but expensive and typically non-differentiable, whereas differentiable surrogates are informative but not always reliable. To address these limitations, this paper proposes Simulator-Refined Diffusion (SRD), a novel combination of a low-fidelity differentiable surrogate and a high-fidelity non-differentiable simulator within the diffusion sampling process. Unlike standard zeroth-order optimization, which requires a great number of random perturbations, our approach uses the surrogate's gradient to propose the perturbation direction while the simulator then searches based on this direction to identify an effective design update. Experimental results across different settings show that this method consistently outperforms current state-of-the-art methods, producing layouts whose simulated S-parameters match the target specifications up to 21.2% closer for in-distribution targets and up to 19.8% for out-of-distribution targets.
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All authors Jinhao Liang, Jacob K. Christopher, Michael Frei, Tommaso Dreossi, Nando Fioretto

Computer Vision

Inductive Visual Logic for Few-Shot Out-Of-Distribution Adaptation in VLMs

Hung-Jen Chen, Yu-Heng Ho, Ting-Yao Huang et al. (+4 more)

Generative vision-language models (VLMs) such as Qwen-VL and LLaVA achieve strong zero-shot performance on tasks overlapping with their pretraining distribution, yet fail on specialized domains where the required discriminative features were never learned, a regime we term distant out-of-distribution (OOD). Standard adaptation methods cannot overcome this representational absence because they operate within the encoder's existing feature space. However, VLMs retain a robust descriptive capacity even when discrimination collapses: a model that cannot classify a medical scan can still articulate its visual patterns. Exploiting this asymmetry, we introduce Inductive Visual Logic (IVL), a training-free framework that constructs classification knowledge from the model's surviving descriptive ability. IVL extracts visual traits from few-shot support images through dual-mode prompting, combining semantic descriptions with primitive visual observations, and organizes them into per-class trait dictionaries. At inference, hierarchical filtering identifies spatially grounded trait evidence for classification. Across multiple distant-OOD benchmarks, IVL achieves the highest aggregate accuracy under two VLM backbones while producing interpretable, trait-traceable predictions.
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All authors Hung-Jen Chen, Yu-Heng Ho, Ting-Yao Huang, Po-Hsiang Hsu, Li-Yu Chen, Chun-Yi Lee, Min Sun

Statistical Methodology

Inference for Standard Trial Estimands after Data-Driven Subgroup Discovery

Larry F. Leon and Keaven M. Anderson

Data-driven subgroup identification is increasingly used in clinical trials, yet the effect reported for a discovered subgroup is typically the standard analysis: a Cox or generalized-linear-model treatment coefficient fitted within that subgroup. Selection by an effect-driven rule — rewarding large estimated effects subject to screening and size criteria — inflates the reported coefficient: a winner's curse invalidating naive intervals whether or not the identifier's internal estimand was de-biased by cross-fitting. We develop a procedure-agnostic framework for post-selection inference that separates discovery from reporting: forest search, difference-in-natural-parameters estimators, and causal forests generate interpretable candidate subgroups; selection is aligned with the coefficient to be reported; and the target is the standard-analysis effect of the selected subgroup, the candidate family held fixed — a conditional, data-adaptive estimand. Resampling the search then reduces to jointly perturbing all candidate effects, yielding refit-free multiplier resampling with an infinitesimal-jackknife interval whose coverage we characterize under standard regularity and an explicit condition on the limiting competition. It matches the full bootstrap on a fixed family; on model-generated families it remains valid for the same conditional target, which the bootstrap reproduces only under further conditions. Two trial applications and matched simulations show mitigated selection bias and improved coverage.
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Machine Learning

On the Off-Policy Teacher in On-Policy Distillation

Langlin Huang, Hao Liu, Mononito Goswami et al. (+5 more)

On-policy distillation (OPD) has recently emerged as a promising post-training paradigm in which the student learns from trajectories generated by its own policy under dense teacher supervision. However, OPD introduces a fundamental asymmetry: although the sampled trajectories are on-policy for the student, they are off-policy for the teacher. The teacher is typically optimized to continue from prefixes generated by its own policy, but during OPD it must instead supervise prefixes generated by the student. Empirically, we find that its continuation performance degrades as these prefixes grow longer. To address this issue, we propose Student-COnditioned Updates of the Teacher (SCOUT), a co-training framework that adapts the teacher to student-generated prefixes. Alongside standard OPD updates, SCOUT periodically optimizes the teacher's conditional ability using reinforcement learning with verifiable rewards, where the teacher generates continuations from student prefixes and learns from outcome rewards. Controlled experiments show that SCOUT improves the teacher's ability to continue from student-generated prefixes, supporting the intended mechanism of student-conditioned teacher adaptation. Across multiple teacher–student configurations, model scales, and reasoning domains, SCOUT also consistently improves the effectiveness of on-policy distillation.
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All authors Langlin Huang, Hao Liu, Mononito Goswami, Xinyu Li, Prithwish Jana, Nikos Kanakaris, Patrick Blöbaum, Purak Jain

Artificial Intelligence

Beyond Mode Collapse: Generating Diverse Synthetic Expert Conversations via Generative Flow Networks

Sumit Asthana, Michael Ion and Kevyn Collins Thompson

High quality synthetic data is central to post training LLMs for adaptive AI applications that represent the diverse expert strategies and decisions in conversations. Prompting LLMs directly or conditioning them on end use scenarios yields low diversity data that collapses onto dominant modes. We propose a method to generate diverse high quality synthetic data using Generative Flow Networks (GFlowNets). We show that training GFlowNets to generate latent conversation structure using a Gaussian mixture density over key interaction features (e.g., confusion episode dynamics, scaffolding directive balance) enables sampling expert strategies in proportion to their prevalence in the training data. Across two structurally distinct domains, tutoring and emotional support dialogues, our GFlow based synthetic data generation approach offers a better balance of fidelity, mode coverage and authenticity than reinforcement-learning and end to end LLM baselines, without copying training data. Evaluated on three downstream outcome prediction tasks, classifiers trained on synthetic GFlowNet generated conversations provide a stronger training signal than competitive synthesis baselines.
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Biological Physics

The Trajectory Statistics of Biological Exploratory Dynamics

Sara D. Mahdavi, Gabriel L. Salmon, Minakshi Ashok et al. (+4 more)

Biological processes, from molecules diffusing to their regulatory destinations to whales pursuing food or mates, are widely exploratory. Such behaviors are effective when some verifiable functional state or outcome can be reached regardless of initial conditions. In these cases, systems repeatedly undergo distinct and abortive trajectories; the process only ends when the system finds “right” outcomes. This dominance of the terminal condition (and indifference to the initial state) provokes a very different perspective than the conventional “dynamical systems” framework that has been a centerpiece of the quantitative sciences for centuries. We hypothesize that many of these problems defy the initial-condition driven or gradients on landscapes so useful in problems ranging from mechanics to electrodynamics to chemical kinetics to mass and heat transport. We examine several mathematical frameworks that capture and unify key aspects of exploratory dynamics. One powerful way of thinking of such processes is the geometric distribution, where repeated failures are punctuated by a successful trajectory. We develop intuitions for how random walks with resets accelerate search processes. We highlight fresh and surprising behaviors of search under drift, cues, and checkpoints. Last, appreciating the probability of trajectories conditioned on satisfying macroscopic final outcomes reveals a language for the potency of variation sculpted by selection in their broadest forms. This can give the fictitious appearance of the future making itself known in the present, but we view this as conceptually similar to the way “fictitious forces” arise in non-inertial reference frames. These approaches stress unity, open questions, and applications across a range of biological phenomena.
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All authors Sara D. Mahdavi, Gabriel L. Salmon, Minakshi Ashok, Madhav Mani, Marc Kirschner, Jane Kondev, Rob Phillips