Science & Mathematics

We establish sharp degree bounds for Putinar sum-of-squares (SOS) certificates in terms of the positivity margin $δ$. For any fixed Archimedean quadratic module with prescribed generators and any fixed degree bound on the objective, normalized polynomial objectives admit a uniform certificate-degree upper bound of $O(δ^{-1/2}\log^2(2/δ))$. The bound is sharp: we construct a matching lower-bound example in three variables. We further show that the number of inequality generators affects the optimal degree bound. For quadratic modules with at most two inequality generators, the bound improves to $O(δ^{-1/2}\log(2/δ))$, which is also sharp. This improvement is obtained by directly converting two-generator Stengle refutations into certificates for the original quadratic module. We also establish sharp degree bounds for trigonometric SOS certificates on tori. In particular, for the full torus without additional constraints, the optimal worst-case order improves to $δ^{-1/4}$, whereas additional equality constraints can lead the order to $δ^{-1/2}\log(2/δ)$. These results also yield sharp worst-case convergence rates for the Lasserre hierarchy.

Irregularly sampled multivariate time series arise in many real-world domains such as healthcare, climate science, and large-scale monitoring systems. Characterized by asynchronous observations and heterogeneity across variables, such time series pose significant challenges for forecasting. In this work, we introduce Cross-Variable Temporal Attention (CVTA), a short-term, continuous-time forecasting framework that learns prediction functions from its compact, interpretable state summarizing recent temporal dynamics across variables. CVTA uses Variable-Conditioned Embeddings to project heterogeneous variables into variable-specific latent spaces, and applies temporal attention to capture cross-variable dependencies from this state. Furthermore, we demonstrate that CVTA can be integrated as an auxiliary module into existing state-of-the-art prediction models through a dynamic meta-decision model. Extensive experiments on multiple real-world benchmarks show that CVTA achieves strong short-term predictive accuracy, supports efficient online inference, improves existing prediction models when used as an auxiliary module, and learns attention patterns that align well with domain knowledge.

Octopuses exhibit a powerful form of embodied intelligence from a highly adaptable soft body. One key mechanism is the ability to instantiate bending points at any location along the arm, which enables performant and dexterous behaviours. Taking inspiration from the octopus for its dexterity, this study focuses on changing the curvature of a tendon-actuated arm by adaptively changing the anchoring end-point along the arm. An array of inflatable shells is integrated into the arm, where inflating a shell causes an increase in friction at the location, jamming the tendon and creating a temporary new anchoring point. The novel soft actuator does not break the continuity of the arm between the actuated segment and the loose segment. Experiments show that the actuated segment has a non-constant bell-shaped curvature which is comparable to that of a real octopus arm during a reaching motion. Compared to conventional single-tendon continuum manipulators, the proposed design offers an expanded workspace and enhanced dexterity through the ability to independently shape different regions of the arm through selective curvature tuning. At the same time, it avoids the mechanical complexity typically associated with multi-segment, multi-actuator systems.

Moore's paradox \citep{moore1942} concerns sentences such as ``It is raining, but I don't believe that it is,'' which may well be true yet cannot be sensibly asserted. The absurdity lies not in the content but in the act, since to assert is to vouch for one's own belief. This makes the paradox a test of whether language models take the speech act into account when computing meaning. We present the first test of Moore's paradox in LLMs, evaluating 12 models on a curated set of Moorean sentences in varied contexts. We find that models largely recognize the infelicity of Moorean sentences, and that the judgement is not tied to a memorized form and tracks the speech act. Using the Rational Speech Act framework (RSA; \citealt{goodmanfrank2016}), we then test whether these judgements arise from a listener reasoning about a speaker. We find the models' own listeners do not reason about their own speakers, and their reasoning traces suggest that they instead recall knowledge about the paradox and apply rules therein. The models thus appear to have learned the paradox as a fact about sentences, not as a requirement on speakers.

Alignment of large language models typically relies on pairwise preference feedback, though ranked feedback can capture more comprehensive information across multiple responses within a single annotation. However, ranked-preference alignment is underexplored in practice compared to simpler pairwise approaches, potentially resulting in suboptimal behavior. Concurrently, recent research has conceptualized large language model alignment objectives as divergence estimators between aligned (preferred) and unaligned (less-preferred) response distributions, resulting in a family of objectives with an interpretable theoretical foundation and strong empirical performance. This work unifies these perspectives by introducing $f$-RPO, a $f$-divergence objective for ranked preference optimization that extends divergence-based alignment to ranked feedback and recovers pairwise preference alignment as a special case. Our theoretical analysis establishes rank-order consistency, showing that $f$-RPO preserves the underlying preference ordering at convergence. Empirical results indicate that total-variation and reverse-KL variants of the proposed objective consistently outperform ranked-alignment baselines in both ranking and generation quality across Qwen, Llama, & Gemma models ranging from 0.5B to 8B parameters.

Policy learning from observational data is fundamental to applications ranging from personalized medicine to welfare-program targeting, but standard approaches optimize empirical performance and may fail when the deployment distribution differs from the training distribution. We study \emph{distributionally-robust policy learning}: given observational data, we seek a policy $π\in Π$ that maximizes the worst-case policy value over an $f$-divergence ball of radius $ρ$ around the data-generating distribution. We propose an estimator built on cross-fitted doubly-robust scores for the conditional treatment effect, paired with a DRO solver that handles \texttt{KL}, $χ^2$, and \texttt{CVaR} ambiguity sets. We establish two convergence guarantees. First, the estimated policy attains the standard $\widetilde{O}(n^{-1/2})$ rate on its DRO regret, and inherits the doubly-robust property -- the rate continues to hold whenever either the outcome model or the propensity model is consistently estimated, even at slow nonparametric rates. We then propose a sample-splitting bias-correction algorithm derived from the Lagrangian dual, and show that under a Tsybakov-style margin condition on the treatment-effect, the estimator attains a fast rate of $\widetilde{O}(n^{-(1+α)/(2+α)})$ , interpolating between $\widetilde{O}(1/\sqrt{n})$ and $\widetilde{O}(1/n)$ as the margin parameter $α$ ranges over $[0,\infty)$. To our knowledge, this is the first work to incorporate a margin condition into the analysis of distributionally-robust policy learning, and the first to obtain fast rates in this setting. Empirically, on synthetic and semi-synthetic experiments calibrated to a welfare-to-work program, distributional robustness yields meaningful improvements over empirical welfare maximization when training and test distributions differ.

Language-guided video generation often captures scene content while missing the requested motion. We present ViMoLa (Video Motion Language), which predicts a motion prior from language and injects it into a frozen image-to-video backbone. A spatial vector-quantized autoencoder compresses dense trajectories into 64 tokens from a 512-entry codebook; a 28M-parameter transformer predicts the tokens from text; and zero-gated cross-attention adapters condition every frozen Wan~2.2 DiT block through forward hooks. Trained on 462K videos from Something-Something~v2 and Kinetics-400, ViMoLa raises directional accuracy from 0.287 to 0.442 (chance 0.250), with similar measured generative quality. Across-prompt shuffled codes achieve 0.283, supporting the importance of prompt-matched token content. A low-rank adapter reaches 0.428 at 1.45% additional forward-pass FLOPs, and reusing the tokenizer and language model with newly trained CogVideoX adapters raises accuracy from 0.301 to 0.398. Control remains imperfect: oracle codes reach 0.531, compound-motion gains are smaller, and the adapter does not explicitly preserve token-to-patch assignments.

It has long been proposed that animals construct cognitive maps to support flexible behavior in novel environments. We tested whether large language models form similar representations using relational reasoning tasks and causal "mosaic experiments" that manipulate internal activations in open-weight language models. Models beyond the ten-billion-parameter scale successfully inferred unstated relationships between entities and generalized to synthetic entity names. Across model and task families, models generated abstract representations of relational structure and combined them additively with representations of entity identity, binding entities to roles within that structure. Models stored observed relationships as pairwise links that they composed retrospectively when queried, rather than prospectively positioning each entity in a global coordinate system. Binding was mediated by a sparse, distributed set of key--value pairs; by perturbing these pairs, we implanted "false memories" that altered model behavior in predictable ways. Overall, our findings reveal an internal organization analogous to a cognitive map that explains how language models reason with limited information.

Audio LLMs deployed in settings such as crisis hotlines and customer support are only useful beyond speech-to-text pipelines if they use acoustic cues rather than the transcript alone. We test whether they prioritise transcript content over paralinguistic cues (emotion, speaker identity, sarcasm) and trace the mechanism when they do. Across six audio LLMs under LISTEN-style conflict conditions, the mean text-dominance rate on mismatched text+audio items is 0.78 (0.86 excluding sarcasm). In the most text-dominant screened model, probing shows speaker identity remains linearly decodable at ceiling at the language model's input, so the failure is not perceptual. Back-patching, reported to repair lexical text dominance, has no measurable effect here; but it also fails on its own source task in our replication (n=300), so we treat its null as uninformative rather than as evidence of non-transfer. Attention knockout partially restores audio-grounded output by blocking the claim from propagating through intermediate tokens during open-ended generation, whereas blocking the answer position's direct connection to the conflicting claim has no effect. The claim's influence therefore travels through an intermediate relay rather than a single severable edge. The effect appears only in free-form generation and not in closed-set multiple choice, suggesting that benchmarks relying on that format may be systematically blind to interventions of this kind. Code and data are publicly available at https://github.com/AdvayRoongta/audio-llm-mech-interp.

Visual world models have shown strong potential for robot planning, yet long-horizon manipulation remains challenging due to compounding prediction errors, large search complexity, and latent plans that the low-level controller cannot reliably reach. In this work, we introduce Vector-Quantized World Model (VQ-WM), a latent feedback motion planning framework that integrates discrete long-horizon search with continuous visual feedback control: a discrete latent predictor models transitions between vector-quantized latent states, allowing the planner to look far ahead and find a shortest path to the goal through discrete search and a continuous learned controller sequentially reaches the planned states through visual feedback, correcting deviations to mitigate compounding errors. Whereas most vector quantization uses Euclidean distance, we use a novel estimator of the first-passage-time as a quasi-metric, which aligns the planning abstraction with the controller's capabilities. We evaluate on the physical robot manipulation of the Tower of Hanoi puzzle: whereas existing state-of-the-art foundation models (VLAs, WAMs) only succeed when the solution trace in their training dataset, our method achieves 100\% success rate with only short-play data, demonstrate its ability to compose long-horizon solutions beyond the short demonstrated trajectories and execute them reliably. Our solution also outperforms strongest world-models by 13.3--85.3 percentage points on simulation benchmarks spanning manipulation and locomotion, demonstrating consistent progress and new capabilities.

Automated generation of end-to-end web tests remains costly: developers must identify stable selectors, encode multi-step workflows, attach assertions, and maintain scripts as interfaces evolve. Recent LLM-based web agents can complete natural-language tasks in a live browser session, but task completion is not the same as producing a test-ware artifact - code that is executable, replay-able from a reset state, inspectable by developers, and tied to an oracle. We present TESSARA, an adaptive test-script generation framework that converts natural-language test intent into Playwright scripts consisting of executable interaction code, goal-state assertions, and step-level provenance linking each step to its generated code fragment, selector evidence, execution outcome, and repair history. TESSARA grounds each planned step via Step-Aligned Scripting (SAS), enabling fine-grained failure localization, selective regeneration of failing suffixes, and reversibility-aware backtracking that avoids undoing likely commit points (e.g., form submissions). A three-level verification pipeline (syntactic, execution, and semantic/oracle), detects and repairs malformed code, interaction failures, and incorrect landing states. We evaluate TESSARA on three public web benchmarks, measuring script executability, oracle satisfaction, replay stability, and repair efficiency, and show substantial improvements over baselines and underlying VLMs used directly as script generators.

As AI voice agents get deployed in high-volume contact centers, firms can route low-intent leads to AI and allocate high-intent leads to human workers. Drawing on sequential search theory, we posit that AI-induced task allocation reshapes work, enriching opportunities facing human workers but also raising their reservation value for continuing with the lead in hand, making them less willing to persist. We study the effects of an AI voice-agent deployment at a Chinese online health-insurance brokerage using more than a half million customer outreach records surrounding the rollout. Adopting a regression-discontinuity-in-time design, we trace how worker behavior changes across the workday. Results show that the enrichment of human-facing opportunities concentrates early in the workday, raising the probability that a call is a high-intent lead by about 23 percentage points on the first three calls and fading to zero later. However, customer acquisition by human workers declines precisely where the enrichment is greatest, falling about 5 percentage points on the first three calls and flattening over the day. Consistent with the theorized reservation value mechanism, workers reallocate their earliest leads about 8 percentage points more often and persist less with them, shortening those calls by about 13%. A calibrated decomposition analysis further shows that the modest gain from improved lead ordering is outweighed by a much larger negative behavioral response. By reshaping the quality and within-workday distribution of opportunities, parallel AI deployment alters how workers pursue tasks, highlighting opportunity distribution as an important service operations state variable beyond workload and congestion.

While autoregressive foundation models trained on limit order book (LOB) data show state-of-the-art performance for market simulation, pre-training with cross-entropy neither penalizes the compounding of sampling errors over free-running rollouts nor targets desired market properties. We introduce a post-training method for LOB foundation models using a Wasserstein generative adversarial network (GAN) objective. A critic, trained online on rollouts through the true, non-differentiable matching engine, guides updates from evolution strategies over rank-4 LoRA perturbations of the pre-trained generator, under a KL trust region. For efficiency, we use EGGROLL (Evolution Guided GeneRal Optimisation via Low-rank Learning), a memory-efficient variant of evolution strategies. On a held-out panel, adversarial post-training improves LOB-Bench realism by 17.6% (WS-21) and 17.0% (Mean-$L_1$), while selection-matched random-perturbation and compute-matched continued-pre-training controls yield no improvement. Post-training is thus a necessary stage that more pre-training does not replace. Per-position divergence measurements show that it slows error accumulation over 500-message rollouts from $3.1\times$ to $2.3\times$. Adversarial post-training is also inexpensive, requiring under 50M training tokens and 12 GPU-hours per seed, three orders of magnitude below the 48B-token pre-training budget. Ablations over critic inputs, optimizers, and the population-rollout trade-off, together with an analysis of reward hacking, yield practical design guidelines for adversarial post-training.

Solubility depends on intermolecular interactions between solutes and solvents, and is central to drug discovery, chemical and materials process engineering. Its prediction requires out-of-distribution (OOD) generalization to unseen solutes, solvents, and solvent mixtures, where supervised methods suffer from data scarcity, and existing self-supervised methods do not explicitly learn chemically meaningful relations. Learning chemically meaningful relational information without labels can alleviate data scarcity and improve OOD generalization, but remains challenging. We introduce Prior Relational Information for Self-supervised Modeling (PRISM) and apply it to solubility OOD generalization. PRISM is a label-free pretraining framework that converts expert-defined chemical priors into relational teachers. For solubility prediction, it trains four encoders to preserve the population-level relational information from priors capturing hydrophobic, electrostatic, polarizability, and substructural effects, using Kullback-Leibler (KL) divergence to match distance-based neighborhood distributions during pretraining. Across scaffold, solute, and solvent OOD settings, PRISM matches or surpasses supervised and self-supervised baselines. Under mixed-solvent OOD, freezing the four PRISM encoders and training a lightweight fusion-and-composition head outperforms strong baselines and substantially reduces run-to-run variation. Ablations and control studies confirm that gains stem from chemically meaningful relational structures baked into the encoders by PRISM. We expect this strategy of turning relational priors into self-supervision signals to extend beyond solubility prediction to domains where chemically or biologically meaningful relational priors are available.

For every fixed $\varepsilon\in(0,1)$ and $η\in[0,1)$, we prove that computing an $(\varepsilon,η)$-weak approximate Nash equilibrium requires quasipolynomial time assuming deterministic PPAD-ETH, even in symmetric binary-payoff games with a constant number of players. The games are given by complete payoff tables, and the player count depends only on the tolerances. The weak approximate Nash equilibrium allows at most an $η$ fraction of players to gain more than $\varepsilon$ by deviating unilaterally. The main technical result is an unconditional error-amplification reduction from bimatrix games. For every fixed $δ\in(0,1)$, it transforms a rational bimatrix game with payoffs in $[0,1]$ into a symmetric binary-payoff game with a polynomial-size complete table and a player count depending only on $δ,\varepsilon,η$. Every $(\varepsilon,η)$-weak approximate equilibrium of the constructed game yields a $δ$-approximate Nash equilibrium of the bimatrix game. Construction and recovery take polynomial time in their explicit inputs. Combining this reduction with the bimatrix hardness result of Rubinstein [FOCS 16] gives a deterministic worst-case running-time lower bound of $N^{(\log N)^{1-o(1)}}$, where $N$ is the constructed table's binary encoding length.