#01Oct 27, 2026
stat.ML
QD-PINN:A Physics-Informed Neural Network Approach to Bayesian Quickest Detection in High-Dimensional Diffusions
Hang Ye, Yi Liu, Haipeng Xing
Quickest detection problems (QDPs) arise in a wide range of applications. However, the complementarity structure of the associated variational inequalities poses substantial challenges for traditional numerical methods, particularly in high-dimensional settings. We propose a PINN-based framework for estimating the optimal stopping boundary in QDPs with high-dimensional diffusion processes and spatial dependence, while overcoming the curse of dimensionality. Theoretically, we establish a novel equivalence between the free-boundary PDE and an infinite-dimensional stochastic optimization problem, rigorously justifying the use of finite-dimensional neural networks to approximate the true solution. Furthermore, we assess the robustness of the proposed framework by quantifying uncertainty in the learned stopping boundaries using deep ensembles and Monte Carlo dropout. The results show low variability across independent training runs and stochastic forward passes, indicating stable and consistent boundary estimates. We also compare our PINN results with reference numerical solutions where available and find close agreement.
#02Oct 27, 2026
cs.LG
GAS-PFN: Graph-Aware Spatiotemporal Prior-Data Fitted Networks for Zero-Shot Traffic Forecasting
Joseph Natter, Long Vu, Yifan Zhang and 3 more
Traffic forecasting requires modeling complex temporal dynamics and the spatial dependencies imposed by road topology. Supervised graph-based models achieve strong performance, but are often trained for a particular dataset and sensor graph, making deployment to new or evolving networks costly. Prior-Data Fitted Networks (PFNs) offer a zero-shot alternative by learning in-context inference from synthetic task priors, which provide an explicit mechanism for encoding domain-specific assumptions. Existing forecasting PFNs, however, do not explicitly represent the graph-structured dependencies governing traffic dynamics. To combine graph-aware traffic modeling with zero-shot adaptation, we introduce the Graph-Aware Spatiotemporal Prior-Data Fitted Network (GAS-PFN). GAS-PFN incorporates sampled road topology into its synthetic task prior through random-walk diffusion, teaching the model to learn graph-coupled dynamics during pretraining. Its co-designed inference architecture uses two mask-conditioned passes through a shared Transformer backbone to separately model sensor-specific temporal dynamics and spatiotemporal interactions among neighboring sensors before integrating their representations for prediction. This design enables GAS-PFN to use target-network structure and context without parameter updates. Across six benchmarks at the 90-minute horizon, GAS-PFN reduces MSE by 34.0% on average relative to TimePFN, its closest PFN-based predecessor. It also reduces MSE by 27.7% on average relative to four recent industry-developed general-purpose zero-shot forecasters. In this comparison, all models receive 90 minutes of contiguous recent history, and any additional context is drawn from each dataset's chronological training split. These results indicate that aligning PFN priors and inference architectures with graph structure improves in-context learning for zero-shot traffic forecasting.
#03Oct 27, 2026
cs.SI
Spectral Braids: A Topological Descriptor for Dynamic Directed Networks
Mehmet Emin Aktas, Esra Akbas
Eigenvalues are a workhorse of graph machine learning: spectral clustering, spectral graph neural networks, and graph kernels all summarize a network by the eigenvalues of a matrix. These eigenvalues are almost always treated as a static list of numbers. When a graph changes, however, its eigenvalues move, and when the matrix is not symmetric, they move in the complex plane, where they can wind around each other. The pattern of this winding is a braid, a classical object from topology. We propose spectral braids, a methodology for dynamic directed networks: each snapshot is aggregated into a community-level transition matrix, its complex eigenvalues are tracked over time, and the braid they trace is read off as a word. The word is then mapped to a matrix by the Burau representation, which gives a fixed-size feature vector for any classifier. The braid has a concrete meaning: each eigenvalue describes how a group of communities behaves, and each crossing records one group overtaking another. We evaluate the method on dynamic network classification, using synthetic networks of online communities whose labels describe how the network evolved between the same starting and ending states. Our experimental results show that the proposed features reach 97.1% accuracy on four classes, against 44.5% for the best feature set that does not track eigenvalues, and that the Burau features also separate networks containing the same events in a different order, which simple counts of crossings cannot do. To the best of our knowledge, this is the first study that defines braids and braid monodromy on graph data and uses them as features for learning on dynamic networks.
#04Oct 27, 2026
math.ST
Regression Functions as Fields on Covariate Space: Evolution Equations, the Hessian, and Identification
Nobuaki Tanaka
For each time $t$, the regression function $m_t(x)=E[Y_t\mid X_t=x]$ of an outcome on contemporaneous covariates can be regarded as a field on covariate space. We study how this field evolves when the covariates of individual units move as a diffusion and the outcome attached to each unit changes according to its own dynamics. Under mild regularity we show that $m_t$ satisfies a second-order evolution equation whose diffusion term is $\frac12\mathrm{tr}(Σ\nabla^2 m_t)$, the trace of the Hessian of the regression function weighted by the instantaneous covariance $Σ$ of the covariate increments, whose transport term is the drift of the time-reversed covariate process, and whose source term is the conditional mean rate of change of the outcome. The equation is a regression-theoretic reading of a classical transport law, and it yields a Feynman-Kac representation of $m_t$ along reversed covariate paths. We connect the Hessian appearing in the equation to the Hessian estimated by quadratic regression (under Gaussian design the best quadratic approximation has Hessian $E[\nabla^2 m(X)]$ exactly) and to the leading bias of kernel smoothers. For binary outcomes governed by bistable replicator dynamics with imitation among units with similar covariates, the closed equation is of Nagumo type, its planar travelling fronts are exactly logistic in $(x,t)$, and a single logistic regression of the outcome on covariates and time identifies the ratio of diffusion to reaction and the direction of invasion. We discuss identification under panel versus repeated cross-sectional designs and a two-stage estimation strategy, and we illustrate the results with simulations.
#05Oct 27, 2026
cs.LG
Gym-Anything-RT: Scaling Real-Time Environments for Vision-Language Agents
Pranjal Aggarwal, Sean Welleck
AI agents have made substantial progress in domains where they have a non-trivial amount of time to deliberate between actions, such as mathematics, software engineering, and performing tasks on desktop applications. It is less clear how such models fare in settings that demand real-time interaction, such as playing a video game or operating a physical device. In these settings, the environment state may evolve as the agent is reasoning, or even as the underlying model is performing a forward pass. To gain insight into the real-time interaction capabilities of vision-language agents, we introduce Gym-Anything-RT. Our key idea is to construct visual minigames that demand a portfolio of capabilities required for interactive real-time settings. Gym-Anything-RT uses an agentic pipeline to automatically generate such environments based on a taxonomy of six capabilities required for real-time interaction, including the ability to perceive the environment and act under an evolving environment state. A key feature of Gym-Anything-RT is that it allows for controlled comparison of real-time interaction capabilities: we can run the same minigame in real time, or pause or slow down the environment to relax the requirement for real-time actions. We use Gym-Anything-RT to construct 100 real-time minigames and evaluate AI agents on them. We find large capability gaps in real-time interaction. For example, GPT-6 Astra (xHigh) achieves a pass rate of only 9.0% on the real-time minigames, which rises to 75.0% when the environment is paused. We also identify intriguing behaviors by the most powerful frontier agents: for instance, when given the ability to write code, these agents write code that bypasses the need to perceive and act in real time. We publicly release Gym-Anything-RT and the generated minigames to spur further research on AI agents in real-time interactive settings.