Human trajectory data is crucial in urban planning, traffic engineering, and public health. However, directly using real-world trajectory data often faces challenges such as privacy concerns, data acquisition costs, and data quality. A practical solution to these challenges is trajectory generation, a method developed to simulate human mobility behaviors. Existing trajectory generation methods mainly focus on capturing individual movement patterns but often overlook the influence of population distribution on trajectory generation. In reality, dynamic population distribution reflects changes in population density across different regions, significantly impacting individual mobility behavior. Thus, we propose a novel trajectory generation framework based on a diffusion model, which integrates the dynamic population distribution constraints to guide high-fidelity generation outcomes. Specifically, we construct a spatial graph to enhance the spatial correlation of trajectories. Then, we design a dynamic population distribution aware denoising network to capture the spatiotemporal dependencies of human mobility behavior as well as the impact of population distribution in the denoising process. Extensive experiments show that the trajectories generated by our model can resemble real-world trajectories in terms of some critical statistical metrics, outperforming state-of-the-art algorithms by over 54%.

Abstract-- Reliable navigation in under-canopy agricultural environments remains a challenge due to GNSS unreliability, cluttered rows, and variable lighting. T o address these limitations, we present an end-to-end learning-based navigation system that maps raw 3D LiDAR data directly to control commands using a deep reinforcement learning policy trained entirely in simulation. Our method includes a voxel-based downsampling strategy that reduces LiDAR input size by 95.83%, enabling efficient policy learning without relying on labeled datasets or manually designed control interfaces. The policy was validated in simulation, achieving a 100% success rate in straight-row plantations and showing a gradual decline in performance as row curvature increased, tested across varying sinusoidal frequencies and amplitudes. Autonomous robots have seen significant growth in modern agriculture, particularly for under-canopy tasks such as plant phenotyping, crop row harvesting, and disease scouting. These applications require platforms that are not only compact and agile but also capable of accurately navigating between dense crop rows (Figure 1) [1]. However, reliable navigation in such environments remains an active area of research due to several challenges, including clutter and occlusions caused by narrow row spacing and the high visual variability introduced by different plant growth stages [2].

Estimating causal effects from real-world relational data can be challenging when the underlying causal model and potential confounders are unknown. While several causal discovery algorithms exist for learning causal models with latent confounders from data, they assume that the data is independent and identically distributed (i.i.d.) and are not well-suited for learning from relational data. Similarly, existing relational causal discovery algorithms assume causal sufficiency, which is unrealistic for many real-world datasets. To address this gap, we propose RelFCI, a sound and complete causal discovery algorithm for relational data with latent confounders. Our work builds upon the Fast Causal Inference (FCI) and Relational Causal Discovery (RCD) algorithms and it defines new graphical models, necessary to support causal discovery in relational domains. We also establish soundness and completeness guarantees for relational d-separation with latent confounders. We present experimental results demonstrating the effectiveness of RelFCI in identifying the correct causal structure in relational causal models with latent confounders.

Sequence generation and prediction form a cornerstone of modern machine learning, with applications spanning natural language processing, program synthesis, and time-series forecasting. These tasks are typically modeled in an autoregressive fashion, where each token is generated conditional on the preceding ones, and beam search is commonly used to balance exploration and fluency during decoding. While deep learning models and Large Language Models (LLMs) excel at capturing statistical patterns in this setting, they remain ill-equipped to guarantee compliance with formal constraints. In this paper, we introduce ABS: a general and model-agnostic inference-time algorithm that guarantees compliance with any constraint that can be compiled into a Deterministic Finite Automaton (DFA), without requiring retraining. ABS leverages the DFA to guide a constrained variant of beam search: at each decoding step, transitions leading to violations are masked, while remaining paths are dynamically re-ranked according to both the model's probabilities and the automaton's acceptance structure. We formally prove that the resulting sequences are guaranteed to satisfy the given constraints, and we empirically demonstrate that ABS also improves output quality. We validate our approach on three distinct tasks: constrained image-stream classification, controlled text generation, and text infilling. In all settings, ABS achieves perfect constraint satisfaction, while outperforming or matching state-of-the-art baselines on standard quality metrics and efficiency.

Statistical analysis of corpora provides an approach to quantitatively investigate natural languages. This approach has revealed that several power laws consistently emerge across different corpora and languages, suggesting universal mechanisms underlying languages. Particularly, the power-law decay of correlation has been interpreted as evidence for underlying hierarchical structures in syntax, semantics, and discourse. This perspective has also been extended to child speeches and animal signals. However, the argument supporting this interpretation has not been empirically tested in natural languages. To address this problem, the present study examines the validity of the argument for syntactic structures. Specifically, we test whether the statistical properties of parse trees align with the assumptions in the argument. Using English and Japanese corpora, we analyze the mutual information, deviations from probabilistic context-free grammars (PCFGs), and other properties in natural language parse trees, as well as in the PCFG that approximates these parse trees. Our results indicate that the assumptions do not hold for syntactic structures and that it is difficult to apply the proposed argument to child speeches and animal signals, highlighting the need to reconsider the relationship between the power law and hierarchical structures.

We study the problem of learning a $n$-variables $k$-CNF formula $Φ$ from its i.i.d. uniform random solutions, which is equivalent to learning a Boolean Markov random field (MRF) with $k$-wise hard constraints. Revisiting Valiant's algorithm (Commun. ACM'84), we show that it can exactly learn (1) $k$-CNFs with bounded clause intersection size under Lovász local lemma type conditions, from $O(\log n)$ samples; and (2) random $k$-CNFs near the satisfiability threshold, from $\widetilde{O}(n^{\exp(-\sqrt{k})})$ samples. These results significantly improve the previous $O(n^k)$ sample complexity. We further establish new information-theoretic lower bounds on sample complexity for both exact and approximate learning from i.i.d. uniform random solutions.

This work addresses the problem of efficient sampling of Markov random fields (MRF). The sampling of Potts or Ising MRF is most often based on Gibbs sampling, and is thus computationally expensive. We consider in this work how to circumvent this bottleneck through a link with Gaussian Markov Random fields. The latter can be sampled in several cost-effective ways, and we introduce a mapping from real-valued GMRF to discrete-valued MRF. The resulting new class of MRF benefits from a few theoretical properties that validate the new model. Numerical results show the drastic performance gain in terms of computational efficiency, as we sample at least 35x faster than Gibbs sampling using at least 37x less energy, all the while exhibiting empirical properties close to classical MRFs.

Preconditioning is a key component of MCMC algorithms that improves sampling efficiency by facilitating exploration of geometrically complex target distributions through an invertible map. While linear preconditioners are often sufficient for moderately complex target distributions, recent work has explored nonlinear preconditioning with invertible neural networks as components of normalizing flows (NFs). However, empirical and theoretical studies show that overparameterized NF preconditioners can degrade sampling efficiency and fit quality. Moreover, existing NF-based approaches do not adapt their architectures to the target distribution. Related work outside of MCMC similarly finds that suitably parameterized NFs can achieve comparable or superior performance with substantially less training time or data. We propose a factorized preconditioning architecture that reduces NF complexity by combining a linear component with a conditional NF, improving adaptability to target geometry. The linear preconditioner is applied to dimensions that are approximately Gaussian, as estimated from warmup samples, while the conditional NF models more complex dimensions. Our method yields significantly better tail samples on two complex synthetic distributions and consistently better performance on a sparse logistic regression posterior across varying likelihood and prior strengths. It also achieves higher effective sample sizes on hierarchical Bayesian model posteriors with weak likelihoods and strong funnel geometries. This approach is particularly relevant for hierarchical Bayesian model analyses with limited data and could inform current theoretical and software strides in neural MCMC design.

Large language models (LLMs) can be controlled at inference time through prompts (in-context learning) and internal activations (activation steering). Different accounts have been proposed to explain these methods, yet their common goal of controlling model behavior raises the question of whether these seemingly disparate methodologies can be seen as specific instances of a broader framework. Motivated by this, we develop a unifying, predictive account of LLM control from a Bayesian perspective. Specifically, we posit that both context- and activation-based interventions impact model behavior by altering its belief in latent concepts: steering operates by changing concept priors, while in-context learning leads to an accumulation of evidence. This results in a closed-form Bayesian model that is highly predictive of LLM behavior across context- and activation-based interventions in a set of domains inspired by prior work on many-shot in-context learning. This model helps us explain prior empirical phenomena - e.g., sigmoidal learning curves as in-context evidence accumulates - while predicting novel ones - e.g., additivity of both interventions in log-belief space, which results in distinct phases such that sudden and dramatic behavioral shifts can be induced by slightly changing intervention controls. Taken together, this work offers a unified account of prompt-based and activation-based control of LLM behavior, and a methodology for empirically predicting the effects of these interventions.

We study the theoretical complexity of simulated tempering for sampling from mixtures of log-concave components differing only by location shifts. The main result establishes the first polynomial-time guarantee for simulated tempering combined with the Metropolis-adjusted Langevin algorithm (MALA) with respect to the problem dimension $d$, maximum mode displacement $D$, and logarithmic accuracy $\log ε^{-1}$. The proof builds on a general state decomposition theorem for $s$-conductance, applied to an auxiliary Markov chain constructed on an augmented space. We also obtain an improved complexity estimate for simulated tempering combined with random-walk Metropolis. Our bounds assume an inverse-temperature ladder with smallest value $β_1 = O(D^{-2})$ and spacing $β_{i+1}/β_i = 1 + O( d^{-1/2} )$, both of which are shown to be asymptotically optimal up to logarithmic factors.