Papers

We exhibit a cubic graph with total chromatic number equal to four and list total chromatic number five. This disproves the List Total Colouring Conjecture of Borodin–Kostochka–Woodall, Juvan–Mohar–Škrekovski and Hilton–Johnson from the late 1990s. ChatGPT 6 Astra Ultra discovered the counterexample with little input from the author.

Mechanical metamaterials owe some of their exotic effective properties to microstructural instabilities such as buckling and pattern transformation. Their fine-scale geometry, combined with the interplay of local and nonlocal effects, renders direct numerical simulation (DNS) prohibitively expensive, if not intractable. Micromorphic computational homogenization~\citep{Rokos2019} has been proposed to make macroscopic simulations feasible: a representative volume element (RVE) carrying patterning fluctuation fields resolves the microscale, while an effective micromorphic continuum describes the macroscale. Such simulations nevertheless remain costly, since the RVE problem and its associated tangent problems must be solved at every macroscopic integration point, which becomes prohibitive, especially in three dimensions. We therefore propose a reduced order model for the microscopic problem, combining proper orthogonal decomposition with a hyperreduction method tailored to the micromorphic setting. Two numerical examples quantify the reduced basis and hyperreduction errors and discuss the offline costs and attainable online speed-ups. The results show that this approach can enable engineering-scale large deformation analysis of mechanical metamaterials.

This technical report presents an alignment evaluation developed and performed by the UK AI Security Institute for assessing whether advanced AI systems take unsanctioned actions outside the scope of their assigned task. We evaluate whether frontier models conduct supply-chain attacks against out-of-scope, third-party targets when placed in difficult cybersecurity challenges, motivated by recently observed cases of models attacking real open-source repositories during evaluations. Applying our methods to GPT-6 Astra and previous OpenAI models, with cyber safeguards disabled, we find that GPT-6 Astra attempts complete supply-chain attacks in simulation at a higher rate than GPT-5.6 Sol and GPT-5.5. This includes writing malicious code as a contribution to an out-of-scope open-source codebase, creating fake identities to deceive open-source developers, and submitting benign contributions before malicious ones. GPT-6 Astra frequently reasons about the scope of the challenge in its chain-of-thought yet still proceeds to attack out-of-scope targets; it often asks for permission, and treats an automated message as as authorisation; and it continues to take unsanctioned actions, at a reduced rate, when internet access is more explicitly disallowed. Our evaluation builds on an internal version of Petri, an open-source LLM auditing tool, with all tool calls simulated by other LLMs, so that no real network access, systems or third-party repositories are reachable and no real-world harm is caused. Finally, we discuss limitations, in particular simulation awareness. We believe simulation awareness may have driven some of the observed behaviour but does not remove our concern. Our results suggest that defences beyond model alignment, such as sandboxing and monitoring, are increasingly critical for safe and secure deployment.

Synthetic data generation is dominated by the fit-then-sample paradigm: a generative model is trained on a private dataset and then sampled from. Despite its widespread adoption, this paradigm faces three challenges: (1) a new training run is required for every dataset; (2) different data modalities, such as single tables, time series, and relational databases, require task-specific models and feature engineering; and (3) the resulting model is opaque, making its behavior under data constraints difficult to inspect. We propose GENSCRIPT, an inference-only pipeline that eliminates model training. GENSCRIPT computes a deterministic statistical profile of the source data (column types, ranges, missingness, categories, correlations, etc.) and passes it–rather than raw rows–to a language model to infer field semantics and cross-column integrity constraints. A coding agent then compiles the profile and constraints into an executable, auditable sampler. This unified approach supports single-table, temporal, and relational data without task-specific modeling. Across four single-table benchmarks, GENSCRIPT builds generators in 2 minutes and samples 50k rows within 6 seconds, while remaining within a few points of leading methods in marginal fidelity. Notably, it is the only method that perfectly preserves a 1-to-1 mapping between columns in the Adult dataset. On a smart-building dataset, it produces conditional time series that more closely match the real distribution than two baselines and perfectly preserves primary- and foreign-key relationships in the corresponding relational database.

Vision-language models (VLMs) can answer questions about hour-long videos, but processing every frame is prohibitively expensive, even though the evidence for a question usually spans only a few seconds. Video agents, i.e., harness programs wrapped around a frozen VLM, address this by observing the video selectively, yet existing harnesses are hand-crafted by experts through slow build-and-test cycles. We propose VidHarness, a framework that automates harness design for cost-efficient long video understanding, in which a harness proposer iteratively evolves harnesses based on execution feedback from an evolution environment. To escape the local optima of greedy refinement, we organize the evolution as Monte Carlo tree search (MCTS), and to reduce the evaluation cost, we integrate uncertainty-aware multi-fidelity validation, which screens new harnesses on a few questions and promotes only the promising ones. Since the best harness varies with the frame budget, we further introduce a mixture-of-harness that routes each question to a harness specialized for its budget. VidHarness sets new state-of-the-art results on LongVideoBench, Video-MME, and Video-Holmes, outperforms the strongest hand-crafted video agent by up to $11.2$ points, and generalizes to the knowledge-intensive benchmarks Video-MMMU and MMVU with fewer than half of the frames of uniform sampling.

We propose a novel local-polynomial estimator of the ratio $r=f/g$ of two $d$-dimensional densities $f$ and $g$, from which independent samples are available. The estimator is shown to achieve pointwise minimax optimal rates over Hölder classes of arbitrary smoothness index without additional logarithmic factors, and with smoothness being only assumed of $r$ but not of $f$ nor $g$. Our analysis remains valid for points on the boundary of the support of the distribution associated to $g$ under a mild geometric assumption on the (unknown) boundary. We also derive a concentration inequality for the estimator, which can be useful in applications to classification, and give a rate in the supremum norm, where the supremum is also taken over boundary support points. The smoothness class over which the rate is obtained is sufficiently large that the individual densities $f$ and $g$ cannot be consistently estimated uniformly over this class. Direct estimators of the partial derivatives of $r$ together with rates of convergence are also provided. We also obtain asymptotic normality of the estimators under quite general assumptions and again including boundary points, with a consistent variance estimator allowing for data-driven studentization. Moreover, we show how our estimator can be used to estimate the Kullback-Leibler information, in a construction which additionally uses debiasing. We provide the parametric rate together with asymptotic normality under sufficient smoothness of $r$ relative to the dimension $d$.

Leading AI developers have reported agents acting beyond their approved limits, which a United Nations panel described as an early warning of loss of human control. Yet incident reports and agent-safety evaluations describe these events differently, making it difficult to compare failures, trace risk across attempts, or separate agent behavior from the environment's role in allowing an out-of-scope action to succeed. To address this gap, we introduce a common framework in which each attempt ends in approved completion, safe stopping, scope escape, or continuation. We formalize the framework as a discrete-time competing-hazards model and derive escape probability within a retry budget, a model-conditional safe-budget limit, and conditions for estimation from execution logs. We audit 22 incident reports and 102 agent-safety evaluations published from January 2025 to September 2026 using primary sources. Six incidents involved tasks that could not be completed within scope, thirteen involved agents that continued rather than stopped, and five did not report stopping behavior. Developers' figures imply a task-level incidence ratio near 47 for out-of-scope coordination in never-solved versus solved tasks. Among evaluations, 87 recorded an out-of-scope effect or specification violation, 26 treated safe stopping as a first-class outcome, only 20 recorded both, and 79 merged budget exhaustion with failure. In 20 of 22 incidents, the environment allowed an out-of-scope effect, indicating that realized loss of control often reflected persistent agent behavior interacting with permissive boundary conditions; meanwhile, no evaluation reported all fields needed to estimate the full competing-hazards process from published evidence.

We construct a separable reflexive Banach lattice $X$ and a closed sublattice $E\subseteq X$ such that every bounded linear operator from $X$ into $\ell_2$ is compact, whereas there exists a positive operator from $E$ into $\ell_2$ that does not attain its norm and admits a positive maximizing sequence converging weakly to a nonzero vector. This answers negatively the question posed by Dantas, Jung and Martínez-Cervantes in [4] concerning the inheritance of the weak maximizing property by closed subspaces of the domain. It also answers negatively the corresponding question for the positive weak maximizing property and closed sublattices of reflexive Banach lattices. Canonical lattice complexification yields a counterexample to the original question over the complex field as well.

Recent progress in large language model reasoning has been driven by benchmarks and reinforcement learning environments with automatically verifiable rewards, particularly in mathematics, code, and formal logic. These settings make model accuracy easier to evaluate and optimize, but it remains unclear how far success under fixed problem specifications and stable evaluation criteria transfers to reasoning outside such domains. Real-world reasoning often proceeds under incomplete and revisable information: conclusions may be supported provisionally, defeated by counter-evidence, reinstated by further arguments, or revised when stronger reasons become available. Reasoning of this kind is generally referred to as defeasible reasoning. We introduce ArgGYM, a procedural benchmark and RLVR-compatible training environment for structured defeasible reasoning. ArgGYM decomposes this reasoning into twelve tasks and grounds task-specific scoring in a symbolic argumentation engine that computes the formal states used to evaluate model outputs. It includes a frozen benchmark of 1,440 verified instances across fifteen curriculum configurations, two argument preference orderings (weakest-link and last-link), and two set orderings (elitist and democratic), while the same generators and verifiers can produce fresh instances for evaluation that reduces dependence on static test sets and for verifiable-reward training. On the frozen benchmark, frontier and open-weight models show sharply different reasoning profiles: they can recover substantial parts of structured answers without solving the complete task, and performance declines in later curriculum configurations with longer dependencies and more interacting structures. We release the benchmark, generators, and verifiers for reproducible evaluation and RLVR training.

Questions concerning representations of integers as the sum of a prime and a power of two go back to the correspondence between Euler and Goldbach in 1752 and to de Polignac's work of 1849. Romanoff proved that the set of integers admitting such a representation has positive lower density. Following the complementary direction studied by Kalmynin and Konyagin, we consider long intervals containing no Romanoff numbers. We use truncated products of divisor sums to derive the bound $G_{\mathcal{R}}(X)\gg\log\log X$ for the longest block in $[1,X]$ containing no integer of the form $p+2^n$, with $p$ prime and $n\ge1$. This improves the bound $G_{\mathcal{R}}(X)\gg\log\log X/\log\log\log X$ of Kalmynin and Konyagin. The key step extends a translate lemma to sets of $O(\log X)$ integer shifts of absolute value at most $X$: auxiliary primes dividing differences of shifts are removed at negligible cost. After preliminary sieving, this allows all remaining shifts to be covered simultaneously. The argument is unconditional and also applies to $p+a^n$ for every fixed integer $a\ge2$.

Purpose: Behavior cloning can accumulate errors when a learned controller visits states outside the demonstrated distribution. This study evaluates whether Disagreement-Regularized Imitation Learning (DRIL), which converts disagreement among cloned policies into a reinforcement-learning reward, improves image-based continuous control. Methods: A controlled CarRacing study combines Gaussian and Beta learner policies, demonstrations from either a clipped Gaussian expert or an intrinsically bounded Beta expert, one or 20 trajectories, deterministic and stochastic evaluation, and three retained stages: behavior cloning, the highest 10-episode training-score checkpoint, and the final DRIL checkpoint. The disagreement ensemble contains five Gaussian policies in every variant. Each retained policy is evaluated over 100 procedurally generated episodes. Results: Score-selected DRIL produced its largest gains in the few-demonstration setting, improving over the strongest behavior-cloning mean by 61% with clipped-action demonstrations and by 112% with bounded-action demonstrations. With 20 trajectories, the advantage of DRIL narrowed; in the bounded-action regime, Beta behavior cloning remained about 7% above the best DRIL checkpoint. The experiments also show that the informativeness of the disagreement reward changes with the learner representation and training stage. Conclusion: DRIL can substantially improve few-demonstration visual continuous control, while bounded Beta policies provide strong behavior-cloning performance when more demonstrations are available. The results highlight the joint importance of learner support,ensemble response, and checkpoint selection.

Access to real-world information is often noisy and fragmented. Constructing a coherent narrative from such fragments requires models to reconstruct missing spans within a broader storyline, commonly referred to as text infilling, while preserving consistency with both the local context and the global storyline. Despite using text infilling as a pre-training objective in many Large Language Models (LLMs), their actual performance on real-world narrative infilling remains underexplored. In this paper, we address this gap by introducing a multi-domain benchmark of ~9.2K instances for narrative infilling, constructed by masking one to three sentences across four narrative types: encyclopedic text, commonsense stories, news articles, and visual narratives. Using this benchmark, we evaluate 20 instruction-tuned open-source LLMs ranging from 1.5B to 70B parameters across varying levels of instruction specificity and reasoning guidance. Outputs are assessed using standard automatic metrics and a qualitative framework covering five narrative dimensions. Results show that model scale does not reliably predict infilling quality: Gemma-2-2B achieves the highest qualitative score (4.02/5), outperforming models over ten times larger, including DeepSeek-Qwen-32B (3.77/5, 6.6%) and LLaMA-3.3-70B (3.71/5, 8.3%). We further find that explicit reasoning offers limited benefits as chain-of-thought reasoning yields only a marginal improvement (+0.6%). Additionally, short narratives and domain characteristics emerge as stronger predictors of task difficulty than infill position alone for narrative infilling in current LLMs.

Robot performance is often limited by the cost of iterating on morphology and control together, since every computer-aided design (CAD) change has to be carried into a simulation-ready model before control work begins. Co-design methods attempt to close this gap, but each uses a model generator written for a single platform or lack the use of real-world data to suggest that designs are plausible. We present Draft, a parametric generation tool whose generalized engine compiles any parametric tree of serial chains into a simulation-ready MJCF model, without CAD. It allows engineers to explore design tradeoffs through easily adjustable models and evaluate how changes influence controller performance. Draft grounds the free parameters of each design using trends fitted to a survey of $114$ actuators and $49$ published robot descriptions, so that a generated robot is anchored to real-world hardware. We validate those trends wholistically by building twins of four off-the-shelf robots, whose masses agree to $1.10\times$ geometric mean fold error. Finally, we demonstrate how Draft exposes design tradeoffs by evaluating three quadrupeds through a two-stage reinforcement learning curriculum.

Integrated phase-change photonics allows non-volatile optical switching with no static power draw, but the electrical energy needed to reversibly switch the material's state limits practical scaling. Efforts to improve energy efficiency have mostly focused on device optimization, such as redesigning the integrated microheater or waveguide. Here, we take a different, materials-centered approach by alloying Sn to Ge$_2$Sb$_2$Te$_5$ (GST) without altering the device structure or CMOS compatibility. We explore Sn concentrations ranging from 0 at.% to 20 at.% on waveguide-integrated PN and PIN heaters and observe a reduction in both the amorphization and crystallization energies in the 5–10 at.% range. At higher Sn content this trend reverses and the switching energy increases, which is suggestive of phase segregation when combined with TEM compositional analysis. A 10 at.% Sn device continues to switch over 1000 cycles, with observable degradation in the extinction ratio from 4.5 $\pm$ 0.3 dB to 2.4 $\pm$ 0.3 dB. Post-cycling imaging shows PCM migration and void formation which we believe can be further improved by enhanced encapsulation. Overall, Sn alloying offers a route to lower programming energy in integrated phase-change photonics without negatively affecting the switching speed relative to un-doped GST.

Whether quantum computation can reduce the amount of data required for conventional machine learning is a central problem in quantum machine learning. In probably approximately correct (PAC) learning, a learner receives training examples sampled from an unknown probability distribution. Quantum PAC learning extends this framework by allowing access to quantum examples, which are quantum states that coherently encode this distribution, or to unitaries that prepare quantum examples, with or without inverse access. When only copies of quantum examples are available, the optimal worst-case sample complexity asymptotically matches that of classical learning. In contrast, access to both a preparation unitary and its inverse can improve the accuracy dependence of query complexity. However, it has remained open whether access to the preparation unitary alone suffices for this improvement. In this work, we resolve this question by determining the optimal query complexity with forward-only access, taking the worst case over compatible preparation unitaries and their dimensions. In both realizable and agnostic PAC learning, this complexity matches, up to constant factors, the optimal sample complexity achievable with classical examples or copies of quantum examples. To prove these results, we construct, for any algorithm with forward-only access, a simulator that approximates the algorithm's Haar-averaged output state using as many copies of the prepared state as the algorithm makes queries. These results show that inverse access is essential for the known improvement in accuracy dependence in this worst-case setting. Beyond PAC learning, our reduction provides a general tool for transferring lower bounds for state copies to query lower bounds for forward-only access to the corresponding preparation unitaries.

We introduce C2C (From Codebase to Culprit), a framework for precise bug localization that progressively reduces the debugging search space across multiple levels of granularity: files, functions, and lines of code. To mirror developer's natural top-down debugging workflows, C2C integrates semantic retrieval and Hierarchical Reinforcement Learning (HRL) in a two-stage process. First, it performs recall-oriented retrieval of buggy candidates via semantic vector similarity search using bug-report text, including available stack-trace information, against a database of embeddings, where the embeddings are fine-tuned via contrastive learning with CodeBERT. Building on this reduced search space, the HRL framework incrementally localizes bugs, reasoning from files to functions and ultimately to individual lines of code. Unlike prior approaches which operate at a single granularity, C2C enables multi-resolution localization while maintaining contextual consistency across decisions. Experiments on real-world Java and Python datasets demonstrate that C2C improves retrieval precision and localization accuracy. Ablation studies further highlight the contributions of hierarchical decomposition, structured learning signals, and reward shaping in advancing multi-level bug localization.

Training data variation, whether through designing a domain randomization (DR) scheme in simulation or curating demonstrations for imitation learning, is a primary lever for improving the robustness of robotic manipulation policies. Yet its underlying mechanisms remain poorly understood, and practitioners typically select randomization parameters through expensive trial and error. We investigate these mechanisms through a series of case studies, randomizing object size, color, and type as well as scene lighting and linguistic prompts across settings including pick-and-place RL in ManiSkill and fine-tuning of vision-language-action (VLA) models on LIBERO and RoboTwin. We examine both model behavior and internal representations, using the empirical neural tangent kernel (NTK) as our primary diagnostic tool. We show that the NTK distinguishes a shift in the internal learning mechanism from memorizing different situations with insufficient variation (e.g.\ learning what to do for a large cube, and what to do for a small cube) to adapting to the situation at hand with sufficient variation. An NTK-based signal-to-noise ratio also helps distinguish when policies have learned to ignore task-irrelevant factors (e.g.\ treating blue and red cubes identically, instead of learning a blue sub-policy and a red sub-policy). We use these diagnostics to develop practical guidance for designing DR schemes, selecting models, and detecting shortcut learning. We further compare different kinds of representations and validate our findings with real-world hardware experiments using ACT-based imitation learning.

Co-speech gestures for robots must adapt not only to speech and embodiment, but also to the workspace available for performing the motion. Since the same speech can be accompanied by different gestures, a robot can respond to workspace constraints, e.g., gestures for speech next to a wall. In these scenarios, the robot should gesture in a suitable motion rather than simply correcting an unconstrained one. To achieve this goal, we present GestAdapt, a workspace-conditioned framework that conditions co-speech gesture generation on a prescribed wrist workspace. The GestAdapt framework learns from six complementary co-speech corpora through a shared motion representation and supports retargeting to different robot embodiments. Quantitative evaluation shows that generated motions remain close to the real-motion distribution while respecting the workspace. In a user study, gestures generated under modified workspace constraints receive a mean quality score of 3.24/5, above our no-workspace variant (2.43/5) and below the reference motions (3.68/5). In a real robot evaluation, all compared motions are retargeted to the Reachy2 humanoid robot under identical workspace constraints. Motions generated with our framework rank first in 69.7% of comparisons, higher than our no-workspace variant baseline and retargeted ground-truth motions constrained afterward. Overall, the results support adapting gestures to the available workspace during generation, rather than modifying unconstrained trajectories afterward to satisfy workspace constraints, potentially compromising gesture naturalness.

We investigate the accuracy and computational efficiency of posterior approximations for gravitational-wave (GW) parameter estimation based on Fisher Matrix and its higher-order extension, the Derivative Approximation for LIkelihoods (DALI), in the context of tests of General Relativity using parameterized deviations in the inspiral waveforms (the TIGER formalism). We adopt the IMRPhenomD waveform and compare the exact posterior sampling to the following approximations in increasing order of complexity: the traditional Fisher Matrix, the Fisher sampling (singlet-DALI), the doublet-DALI and the triplet-DALI. We find that both singlet and doublet-DALI are significantly faster than the exact posterior by factors between 20 and 1000, depending on the inspiral SNRs – larger gains correspond to larger SNRs. These gains are considerably larger for more complete waveforms, such as IMRPhenomHM. To evaluate the accuracy of the approximations, we use Jensen-Shannon divergence. We conclude that both singlet and doublet-DALI systematically improves over the standard Fisher Matrix approximation, while triplet-DALI shows large variability, limiting its practical advantage. We also introduce a code with a new implementation of Fisher and DALI analysis (Symbolic DALI, SymDALI) which computes derivatives symbolically via Wolfram Language.

Homogeneous coordinate rings of Grassmannians are among the most fundamental instances of cluster algebras arising in “nature.” Despite their importance, however, the cluster variables of these cluster algebras are not well-understood, except in special cases. For the Grassmannian of 3-planes in n-space, Fomin and Pylyavskyy conjectured [FP16] that the cluster and frozen variables are exactly the indecomposable, non-elliptic web invariants which are arborizable. They proved that in particular, if an SL3 tensor diagram is a planar tree, its web invariant is a cluster or frozen variable. In this article, we give a new proof of their result for Gr(3, n) planar tree webs, and we generalize the result to Gr(4, n): if an SL4 tensor diagram for Gr(4, n) is a planar tree web, its web invariant is a cluster or frozen variable. Our proof uses some of the cluster quasihomomorphisms from [EZLP+23] and [EZPT+25] (namely, upper promotion and spurion promotion), as well as a new 6-leg pattern map.

Virtual clients offer a cost-effective approach to support applications such as A/B testing, recommender system development, and interface evaluation. However, building them requires access to large-scale, semantically faithful, fine-grained online user trajectories. These data are difficult to obtain because proprietary logs are subject to privacy restrictions and small businesses often lack sufficient traffic. Consequently, existing public datasets either abstract away fine-grained user interaction details or preserve rich context but remain platform-specific and small-scale. To address this gap, we propose SimTrace, a framework that generates faithful, fine-grained synthetic multimodal clickstreams through a computer-use client agent that is grounded in real user trajectories and the given web environment. SimTrace anonymizes real interactions and constructs a simulated twin of the given web environment, then uses both to generate synthetic interaction trajectories. Each action is paired with its corresponding web observations and user context, yielding a shareable alternative to confidential logs for developing computer-use agent-style virtual clients. We apply SimTrace to an e-commerce setting and evaluate both its fidelity and downstream utility. SimTrace outperforms competing baselines on 7 out of 8 fidelity metrics. Models trained on synthetic data achieve performance comparable to those trained on real data on downstream tasks such as purchase prediction and recommendation. For next action prediction task, augmenting real data with synthetic data further improves accuracy by 11.0% relative to training on real data alone. We release SimTrace as an open-source package to facilitate research on online user behavior modeling.

We study whether every infinite-dimensional weakly compactly generated (WCG) Banach space fails the Lotz property. The answer is affirmative in the nonseparable case: a classical decomposition theorem for WCG spaces provides a Schauder decomposition, and an explicit diagonal $C_0$-semigroup has an unbounded generator. The unrestricted assertion is false. Our main abstract result is a Calkin-algebra criterion: if $X$ fails the bounded compact approximation property and, for some fixed $m$, every noninvertible element of $\Cal(X)=\Lop(X)/\Kop(X)$ has $m$th power zero, then $X$ has the Lotz property. In particular, this applies when every operator is scalar-plus-strictly-singular and one fixed power of every strictly singular operator is compact. Combining this criterion with the Maurey–Pisier–Szankowski extraction theorem and constructions of Argyros and Motakis yields separable hereditarily indecomposable Lotz spaces over both scalar fields: reflexive examples, and, over the complex field, an example containing no infinite-dimensional reflexive subspace. Moreover, the ambient Argyros–Motakis spaces considered here are Lotz-saturated, although they themselves are non-Lotz. Thus every nonseparable WCG space is non-Lotz, while the separable WCG class contains both Lotz and non-Lotz spaces.

Stochastic differential equations (SDEs) can be studied via Itô calculus and rough path theory. For stochastic optimal control, these two frameworks give distinct Pontryagin Maximum Principle (PMP) optimality conditions with forward-backward SDEs (FBSDEs) or rough differential equations. We show that the adjoint equations of the Itô and rough PMPs are connected via the conditional expectation $p_t^{\text{It\^{o}}}=\mathbb{E}[p_t^{\text{rough}} \mid \mathcal{F}_t]$, where $\mathcal{F}_t$ represents information available at time $t$. First, we derive a rough stochastic PMP for problems with adapted controls that does not use FBSDEs. Its proof extends the rough stochastic PMP over deterministic controls by considering stochastic needle variations. Second, we derive a unified PMP connecting the Itô and rough PMPs, using Itô-Stratonovich conversion formulas and duality identities between the forward tangent and backward adjoint SDEs. As a first application, we rederive the adjoint matching method for fine-tuning generative models. As a second application, we propose an indirect shooting method for a class of feedback problems. Overall, these results give a new conditional bridge connecting two popular frameworks for stochastic optimal control.

We prove that the intersection of $2d$ halfspaces containing the Euclidean unit ball in $\mathbb{R}^d$ contains a point of norm at least $\sqrt{d}$. Equality characterizes the cube. The proof gives a lower bound for the average squared norm of the vertices, weighted by the Gaussian measures of their normal cones. The main step is an inequality for Gaussian orthant probabilities, proved by a one-dimensional comparison of mass, centroid, and boundary density. We also discuss a quadratic extension and give an independent spectral estimate.

Same-instance self-supervised learning (SSL) learns representations by enforcing consistency across two views of the same underlying instance. This principle alone, however, does not determine which downstream tasks remain recoverable from the learned representation. We study this question through semantic recoverability, defined as the amount of a task's posterior score captured by the represented function space. We show that, for centered and whitened representations, recoverability exactly determines directional class-distance-normalized variance (CDNV), controls few-shot nearest-centroid classification, and governs the strength of task-relevant semantic directions. The population linear probe and centroid axis coincide, and multiple well-recovered tasks approach a factorial centroid geometry. We then analyze a canonical two-view SSL objective and show that its population optimum spans the leading cross-view-stable modes of the associated two-view operator. This yields a closed-form spectral characterization of semantic recoverability: a downstream task is preserved to the extent that its posterior lies in the selected spectral subspace. We validate these predictions on synthetic and real datasets across several SSL methods, testing the predicted relationships among recoverability, directional geometry, spectral structure, and few-shot transfer. Together, these results give a task-level account of what information survives same-instance SSL and how the retained information appears in downstream geometry and transfer.

Personas used to seed LLM social simulations face a cold-start problem: existing methods lack a principled basis for deciding which attributes to include and how to assign their values. As a result, synthetic populations may misrepresent the demographic composition, latent attributes, and dependency structure that shape downstream behavior. We introduce MetaPersona-DB, a dataset of 11,000+ empirical human-subjects studies annotated with task-relevant variables, reported relationships, and aggregate-level population statistics. Building on this resource, we propose MetaPersona, a framework that retrieves task-relevant evidence, constructs literature-derived persona dependency graphs, and samples synthetic populations from empirical priors linking demographics, latent attributes, and outcomes. Across three downstream case studies, three baselines, and three frontier models, results vary by task and model: MetaPersona performs strongly on misinformation belief and AI-tool sentiment, while results on income redistribution are mixed. It also reduces persona-construction cost to under $0.5 per task using GPT-5.2. Finally, we present MetaPersona-Studio, a prototype interactive interface for empirically grounded persona generation.

Document text forgery has evolved beyond simple pixel-level manipulation: modern attacks alter not only the appearance of a document but also its meaning, and increasingly target the OCR & LLM pipelines that consume such documents. The ACM MM 2026 GenText-Forensics challenge therefore requires systems that not only decide whether a multilingual text image is forged, but also localize the point of manipulation, identify the attack type, and produce a human-readable forensic report with supporting evidence. We present our solution, a decomposed chain-of-thought (CoT) pipeline that combines a document tampering detector (DTD) with two Qwen3-VL-32B vision-language models, each LoRA-adapted to a distinct sub-task. DTD produces tampering probability maps that are converted into numbered candidate regions; a first model (the Filterer) validates these regions and assigns a preliminary forgery type, while a second model (the Semantic Detective) merges and re-grounds the surviving regions, searches for purely semantic anomalies that are invisible to pixel-level detectors, and writes the final report. Both models are trained by distilling chain-of-thought traces from a privileged Qwen3-VL-235B teacher that has access to ground-truth masks and reports. Our approach secured third place in the ACM MM 2026 GenText-Forensics challenge. We describe the data preparation, test-time augmentation, region rendering, distillation protocol, and training configuration in detail, and report ablations over detector thresholds, prompt designs, and pipeline decompositions.

Effective malware analysis requires understanding not only whether a program is malicious, but also which behaviors it exhibits and where those behaviors originate in the code. Existing machine-learning-based malware detectors largely operate as black boxes, providing limited insight into the malicious logic responsible for their decisions. This paper addresses malicious behavior localization and classification at the basic-block level. We propose a behavior-centric analysis framework that decomposes malware samples into behaviors and systematically links these behaviors to their originating code regions. Using context-sensitive backward slicing from security-relevant system API calls, we reconstruct control- and data-dependency chains and represent each behavior as a structured graph of related basic blocks. A Transformer-based model captures instruction-level semantics, while a Graph Neural Network models structural dependencies within behavior graphs. The resulting representations are fused to enable accurate and interpretable classification, with attention-based attribution identifying code regions responsible for malicious behaviors. We evaluate our approach using standard classification metrics and a behavior coverage metric that measures the detection of manually labeled malicious behaviors. Our results demonstrate that the proposed framework achieves accurate malware classification while providing fine-grained, behavior-aware localization of malicious logic.

Large language models (LLMs) remain vulnerable to adversarial attacks that circumvent safety alignment to elicit harmful outputs. It remains unclear how harmfulness and refusal representations evolve over the course of multi-turn attacks, and why single-turn defenses are less effective in multi-turn settings. This work investigates how the geometry and temporal dynamics of harmfulness and refusal representations evolve across multi-turn attacks. We analyzed hidden-state representations from three instruction-tuned LLMs (Llama-3.1-8B-Instruct, Qwen2.5-7B-Instruct, and Gemma-2-9B-it) using three multi-turn attack frameworks (Crescendo, ActorAttack, and X-Teaming), and examined representation behavior across conversation turns, model layers, and token positions under various context configurations. Across models and frameworks, we found that (1) each attack framework traverses different geometric directions, yet each achieves comparable success in eliciting harmful outputs; (2) multi-turn harmfulness directions became increasingly linearly separable at the end-of-turn token position across turns in middle to late model layers; and (3) harmfulness representations are weakly aligned with refusal-related representations. The results indicate that multi-turn attacks do not succeed by suppressing the model's internal representation of harmfulness. Instead, harmfulness representations become increasingly separable across conversation turns, while remaining only weakly aligned with refusal-related representations. The findings are one possible explanation for why static single-turn safety probes may degrade in multi-turn settings, and suggest that robust defenses must consider temporal representation dynamics rather than identifying harmfulness with isolated or single-turn prompts.

Two-sample tests are widely applicable in inference and generative modelling, yet users frequently fall back on heuristics and visual inspection due to lack of an accessible test that operates in multiple dimensions. I present Permutation Test using the Energy Distance (PTED), a Python implementation of a powerful two-sample test described in Székely and Rizzo [2004]. The test statistic is the energy distance, a metric on probability distributions that admits a natural sample estimator built from pairwise distances. A permutation test is run on energy distances to produce an exact two-sample test. Because the statistic depends on the data only through pairwise distances, the test applies in high dimensions, on learned feature representations, at large or small or imbalanced sample sizes, and to any data type on which a distance can be defined. An approximation to the formula allows PTED to scale linearly with both number of dimensions and samples while retaining most discriminative power. I highlight a number of instructive sensitivity tests on PTED alongside other multi-dimensional two-sample tests for comparison. PTED is the only method that is sensitive to all tests, though conventional Maximum Mean Discrepancy is identical for all but an over-fitting test.