Science & Mathematics

We consider the problem of setting tolls on a subset of the arcs of a congested network so as to maximize the revenue of a network authority, anticipating that users route according to a Wardrop equilibrium. This problem is naturally cast as a bilevel program in which the leader sets tolls while the followers respond by choosing an equilibrium routing. We focus on the important special case of separable affine arc cost functions. Under this assumption, Wardrop equilibria admit Beckmann's convex characterization, from which we derive three new single-level reformulations of the bilevel problem, exploiting both Beckmann's formulation and its dual: an arc-based formulation, which we solve exactly, and two path-based formulations, solved by column-and-constraint generation. Beyond the reformulations, we further derive from Beckmann's potential an upper bound on the optimal revenue that can be used to certify optimality gaps across all formulations. An extensive computational study on instances derived from the Sioux Falls and Eastern Massachusetts networks compares our formulations with the recent mixed-integer nonlinear formulation of Beck, Labbé and Schmidt. The arc-based formulation solves substantially more instances to proven optimality (within a time limit of 1800 s) than this formulation and, unlike it, returns a feasible solution on every instance. It remains effective on the largest, 74-node network, on which the formulation of Beck et al. solves none. The magnitude of the upper bounds on the tolls proves to be a major driver of tractability: the genuinely hard core of the benchmark emerges once the regulatory cap on tolls is removed. The two path-based formulations, used as heuristics, return a solution within one percent of the optimum on every instance whose optimal value is known, often in seconds where exact formulations reach the time limit.

Fine particulate matter (PM2.5) refers to particulate matter with an aerodynamic diameter of 2.5 micrometre or less. It comes from human activities, such as traffic and industry, and from wildfires, desert dust and gases emitted by vegetation. Short-term exposure to it accounts for about a million deaths a year. Operational forecasts run on grids tens of kilometres wide, which hide the pollution breathed by nearly two hundred million people a day. Machine learning has transformed weather forecasting, but data-driven forecasts of air pollution still blur extremes and lose skill as the air travels. Here we introduce Foehn, a generative model that learns from global kilometre-scale estimates of PM2.5 and computes where the air comes from. Over a year of retrospective forecasts, it outperforms the operational forecast at three stations in four and forecasts at the scale of this hidden exposure. Its ensembles are calibrated, and their mean detects local pollution extremes four days ahead as well as the operational forecast does one day ahead. Such forecasts could warn the millions whom coarse maps miss, once kilometre-scale data are available in real time.

The (111) orientation of SrTiO$_3$ (STO)-based heterostructures has emerged as a versatile platform for two-dimensional electron gases (2DEGs), yet the influence of STO's polar ferroelastic domain-wall (DW) network on charge transport remains largely unexplored. Here we study AlO$_x$/STO (111) interfaces hosting 2DEGs of different carrier densities. In the lower-density 2DEG, low-temperature transport exhibits thermal hysteresis, slow resistance relaxation, cooling-rate dependence, and memory effects, signaling glasslike electron dynamics. The relaxation is strongly non-monotonic in temperature, increasing below $\sim$80 K, peaking near 25 K, and vanishing below $\sim$12 K, tracking the established evolution of the ferroelastic DW state of bulk STO rather than any electronic energy scale, which identifies the DW network as its origin. These signatures are absent in a second, more metallic interface with much higher carrier density, demonstrating that the electron-DW coupling can be tuned. We further show that polar DWs govern the photoresponse: the persistent photoconductivity rises sharply below $\sim$80 K, coinciding with the onset of DW polarity. Together, these results establish polar ferroelastic DWs as a carrier-density-tunable electronic degree of freedom in STO (111)-based 2DEGs, opening routes to manipulate 2DEG properties through topological defects.

Existing benchmarks for text-vision embedding models report aggregate scores that obscure whether performance comes from general capabilities, task-specific adaptation, or robustness to challenging tasks. We introduce TRACE, a Training-aware Robustness and Challenge Evaluation framework that reorganizes 168 tasks from various sources of datasets into three categories: General, Adaptability, and Challenge. Through controlled experiments on two text-vision embedding models, we show that combining general and adaptation data improves Adaptability performance by 7.67 and 7.09 points, respectively, while largely preserving General performance. However, Challenge performance remains below 5.0, with limited improvements from additional training data. Further analysis identifies multilingual and visual-document tasks as major weaknesses. Our findings demonstrate that data adaptation alone is insufficient to address these challenges, highlighting the need for methodological advances beyond data-centric improvements.

Developing coordination policies for complex multi-agent systems relies on either labor-intensive algorithm design or opaque task-specific reinforcement learning. With recent advances in autonomous coding agents, we show that policy search directly in code space offers a compelling third path that combines automated optimization with explicit interpretability. We investigate a human-directed workflow in which coding agents iteratively propose, implement, evaluate, diagnose, and eventually refine algorithms guided by simulation feedback and explicit correctness verification. We conducted two case studies and found that this workflow robustly outperformed any manually engineered solutions. On a challenging map in the 2024 League of Robot Runners competition, a two-day search discovered a policy that exceeds the stronger locally reproduced competition entry by 35.0% on the densest instance and generalizes to unseen map instances. In simulated real-world warehouses with irregular lanes, continuous robot geometry, and asynchronous motion, a week-long search discovered an entirely new class of multi-agent pathfinding algorithm that outperforms a calibrated proprietary solution in throughput by 58.9%. Under stated assumptions, we further prove that the new algorithm is collision-free and completes, in finite time, every accepted goal that is not withdrawn or replaced. Together, the studies show that policy search in code space powered by state-of-the-art coding agents offers a highly competitive path to building real engineering solutions that are both effective and analytically tractable.

The increasing specialization of scientific research calls for fine-grained representations of publication content that can be applied at scale. SCALE extends the OpenAlex taxonomy with approximately 114,000 Scientific Concepts derived from author keywords, but assigning these Concepts to individual publications remains challenging. We introduce MATCH (Multi-stage Article Tagging to Concept Hierarchies), a framework that assigns SCALE Concepts using article titles, abstracts, and author keywords. MATCH combines multi-view embedding retrieval, deterministic taxonomy-aware filtering, and language-model reranking to select relevant Concepts while preserving their hierarchical paths. Its modular design supports both API-based and self-hosted inference. In a blind evaluation involving 22 domain experts across 11 fields and 110 articles, the self-hosted and API-based configurations achieved Precision of 81.5% and 83.3%, respectively, and Precision@5 of approximately 89% for both, with no statistically significant difference detected. These findings support the practical viability of the evaluated self-hosted configuration for large-scale Concept assignment without per-token API charges. Deployed on over two million MDPI publications, MATCH assigns a median of five Concepts per article, covers approximately 94% of the SCALE Concepts, and supports daily indexing of newly available publications. By operationalizing the SCALE taxonomy at publication level, MATCH provides a foundation for fine-grained scientometric analysis and monitoring of scientific developments.

Generative modeling of discrete data has two popular paradigms: autoregressive models such as GPT, which factorize a sequence in a left-to-right (L2R) order, and masked diffusion models, which are essentially any-order autoregressive modeling. Rather than competing methods, these are the two extreme points of a single axis -- the generation order. For structured discrete domains without a natural traversal, both extremes may be suboptimal, yet the intermediate choice -- a single well-adapted order -- remains largely unexplored. We introduce OrderGPT, which builds on Any-Order GPT to learn a task-level generation order without canonical-order supervision. Our key observation is that predicting variables from randomly sampled reveal prefixes produces recurring attention patterns in the backbone that provide a model-dependent signal of predictive dependencies. We aggregate this signal into a reciprocal dependency graph and use a spectral teacher to derive continuous generation priorities. A lightweight OrderMLP integrated into the GPT backbone learns to predict these priorities from attention, incorporating order learning into the architecture within a single training run. Training gradually shifts toward the learned order, which is then frozen for subsequent autoregressive training and generation. The same mechanism adapts across modalities: adaptively it recovers near-L2R dependency structure in language, learns anatomically organized factorizations on human pose, and discovers a factorization on tabular data that places statistically and semantically related fields nearby, while improving downstream modeling metrics across all domains. The code is available at https://github.com/Chenhe-yang/OrderGPT/.

Large Language Model (LLM) agents are increasingly deployed in unfamiliar and evolving environments, requiring them to proactively explore, understand, and adapt to environmental dynamics. However, existing benchmarks rarely test whether agents can proactively discover how an environment works and adapt as it evolves. To address this gap, we introduce AdaExploreBench, a benchmark for proactive exploration and test-time adaptation in evolving environments. By instantiating environmental dynamics as hidden rules, AdaExploreBench requires agents to actively acquire evidence and infer the rules. Under implicit rule drift, the latent rule changes without announcement, requiring agents to detect from degraded performance that prior knowledge is stale and re-explore. Experiments on eight leading LLMs show that proactive and adaptive exploration remain challenging: GPT-6 Sol achieves only 61.9% calibrated accuracy, while providing sufficient evidence or removing rule drift improves average performance significantly by close to 10%. These results reveal a critical bottleneck in current LLM agents: they can often reason effectively from informative evidence once it is available, but struggle to actively acquire the right evidence and recognize when previously acquired evidence is no longer valid.

In this paper, we investigate the information bottleneck problem for sources that follow discrete-time ergodic finite-state Markov chains. We propose treating observations generated by the time-varying Markov chain as if they were drawn from its unique stationary distribution, and we use the solution to the information bottleneck problem for the stationary process to compress samples from the time-varying process. The resulting error is upper bounded by several information gap terms. We establish sufficient conditions under which these gaps converge to zero and analyze the convergence rates of the different information gap terms. The proofs are based on intricate analysis using convergence of subsequences along with the derivation of properties of the optimization sets associated with the information bottleneck problem. In addition to the inequalities and convergence results we establish, our analysis offers insights into how simple properties of ergodic Markov chains give rise to results concerning the information bottleneck problem for such chains.

Tool-using language agents increasingly perform regulated customer-service workflows, where a correct final state is insufficient: agents must also provide disclosures, obtain consent, and follow required procedures. Existing tool-agent benchmarks largely score final business states, accepting trajectories that reach correct outcomes through non-compliant processes. We introduce cxbench, a benchmark that evaluates outcome and process compliance separately across six regulated domains. Each task combines a customer request, a tool-based environment, and explicit process requirements. Rule cards link cited regulatory obligations to observable trace evidence. A hybrid grader combines deterministic checks for ordering and authority with an LLM judge for semantic requirements. We define a false-pass as an outcome-pass run that fails process checks. Across seven models and 120 tasks, 55.5% of the 840 retained executions are false-passes, representing 80.1% of outcome-passing runs; only 13.8% pass both checks. Process-inclusive evaluation changes the observed model ordering and exposes differences hidden by outcome-only scoring. cxbench makes these failures inspectable through trace-linked criteria.

We study integer programs in standard form $\min\{\mathbf{c}^{\mathsf{T}}\mathbf{x}:A\mathbf{x}=\mathbf{b},\ \mathbf{l}\leq\mathbf{x}\leq\mathbf{u},\ \mathbf{x}\in\mathbb{Z}^n\}$, where $A\in\mathbb{Z}^{d\times n}$ and all entries of $\mathbf{b},\mathbf{c},\mathbf{l},\mathbf{u}$ are integers. Let $N$ be an upper bound on the absolute values of the entries of $A$. We give a deterministic algorithm running in time \[ \operatorname{poly}(L_{\rm in})+ f(d)\,N^{O(d)}\bigl(1+\log(c_{\max}+1)\bigr)^{O(1)}, \] where $c_{\max}$ bounds the absolute values of the costs and $L_{\rm in}$ is the input length. Prior to our work, the best known running time was $N^{O(d^2)}$ [Eisenbrand \& Weismantel'20], and it has been a fundamental open problem whether the exponent $O(d^2)$ can be improved to one linear in $d$. We answer this question affirmatively.

Reinforcement Learning (RL) for Large Language Model (LLM) agents in multi-turn, long-horizon environments remains challenging due to inefficient action selection and repetitive behavioral patterns. In particular, agents often become trapped in high-confidence yet unproductive behaviors, repeatedly executing invalid actions or entering action loops that hinder task completion. We observe that these frequently violate environment preconditions, revealing a mismatch between the agent's representation of the internal state and the dynamics of the underlying environment. In addition, repetitive high-confidence actions lead to cyclical behaviors that provide little to no progress towards the goal. We argue that addressing these challenges requires more productive task-aligned exploration to improve the agent's understanding of environment dynamics. Motivated by intrinsic curiosity-driven exploration, we propose a conditional state-space exploration framework that balances task completion with intrinsic information-seeking behavior. Specifically, we introduce an intrinsic reward that penalizes actions whose observation duplicates prior state memory. This provides the benefit of reducing redundant behaviors and encouraging state-space coverage without relying on a general information-theoretic measure. Strong experimental results demonstrate that our approach substantially improves policy learning in multi-turn environments, mitigating invalid actions and repetitive loops.

Building embodied agents that can perceive, reason, and act across diverse 3D worlds is a central research direction toward artificial general intelligence. Yet most existing work remains confined to specific tasks in a single scene and transfers poorly to new environments, leaving general embodied agents for open-world settings under-explored. We refer to such agents as Embodied World Agents (EWAs), whose defining property is the ability to understand diverse visual environments and execute general actions in open-world conditions. To advance EWA research, we study open-world embodied navigation-planning and release EmbodiedWorld-200K, a large-scale dataset of over 200K samples spanning diverse scenes. Each example is equipped with multi-level annotations, ranging from low-level camera-motion trajectories to high-level semantic instructions. The dataset also provides unified evaluation splits and task-specific metrics, supporting offline pretraining and fair evaluation of EWAs. Beyond offline supervision, a defining characteristic of an EWA is its interaction with the environment; training solely on offline data is therefore insufficient, especially for generalizing to scenes not covered in the training distribution. Building dedicated real interactive environments, however, is often prohibitively expensive. To address this, we propose a novel training scheme that employs a video world model as a low-cost environment proxy and performs interactive reinforcement-learning (RL) post-training of the EWA within it. Empirically, pretraining on EmbodiedWorld-200K substantially improves the open-world embodied planning ability of the EWA, and further RL post-training inside a world model yields clear gains on out-of-distribution scenes. The dataset, baseline checkpoints, and training and evaluation code are available at https://xiaokunfeng.github.io/EmbodiedWorld-200K/.

Joint 4D reconstruction of a human and object from a monocular video is essential for understanding how people interact with their environment. While recent methods have made noticeable progress, capturing such human-object interactions remains difficult due to two main challenges. First, a video typically contains composite semantic context spanning multiple interaction phases, making it difficult to track the temporal changes of the interaction in the reconstruction. Second, under human-object occlusion, a single-view observation contains incomplete visual information about the interaction, resulting in geometrically inconsistent reconstructions. To address these challenges, we introduce HORIA, built upon two core designs. First, we decompose the entire input video into temporally grounded and semantically distinct interaction phases with motion-aware captioning, obtaining a specific text description for each phase. Second, conditioned on these text descriptions of the interaction, we propose an interaction-aware re-rendering that compensates for the limited single-view observation. Specifically, we render the initially reconstructed 4D human and object from novel viewpoints and refine the renderings with a text-to-video diffusion prior, which provides auxiliary novel-view supervision beyond single-view cues. As a result, our framework produces temporally coherent and accurate 4D reconstructions under diverse interaction scenarios, achieving state-of-the-art performance.

Activation steering for ASR systems is an underexplored technique in improving both ASR performance and demographic fairness. We investigate two forms of activation steering: paired activation subtraction, and supervised optimization. We find the former to be ineffective at ameliorating ASR performance whatsoever, while the latter is quite effective at deriving steering vectors (SVs) that improve at once overall ASR performance and demographic fairness along such diverse axes as gender, age, and dialect. We also explore what types of data---from the most to the least personal---are necessary for calculating or training SVs. First, we show significant performance in performance from training SVs using an eclectic group of speakers from the same dataset. Furthermore, we find that vectors trained using acoustically similar speakers leads to ASR performances that are competitive or superior to vectors trained on the same speaker, or speakers from the same labeled demographic group. This finding shows that we can harness activation steering for few-shot adaptation given access to a speaker's demography, or zero-shot adaptation to unseen speakers without the need for any labels at all.