Abstract--Causal relationship discovery has been drawing increasing attention due to its prevalent application. Existing methods rely on human experience, statistical methods, or graphical criteria methods which are error-prone, stuck at the idealized assumption, and rely on a huge amount of data. And there is also a serious data gap in accessing Multivariate time series(MTS) in many areas, adding difficulty in finding their causal relationship. Existing methods are easy to be over-fitting on them. T o fill the gap we mentioned above, in this paper, we propose Shylock, a novel method that can work well in both few-shot and normal MTS to find the causal relationship. Shylock can reduce the number of parameters exponentially by using group dilated convolution and a sharing kernel, but still learn a better representation of variables with time delay. By combing the global constraint and the local constraint, Shylock achieves information sharing among networks to help improve the accuracy. T o evaluate the performance of Shylock, we also design a data generation method to generate MTS with time delay. We evaluate it on commonly used benchmarks and generated datasets. Extensive experiments show that Shylock outperforms two existing state-of-art methods on both few-shot and normal MTS.

Aircraft collision avoidance systems is critical to modern aviation. These systems are designed to predict potential collisions between aircraft and recommend appropriate avoidance actions. Creating effective collision avoidance systems requires solutions to a variety of technical challenges related to surveillance, decision making, and validation. These challenges have sparked significant research and development efforts over the past several decades that have resulted in a variety of proposed solutions. This article provides an overview of these challenges and solutions with an emphasis on those that have been put through a rigorous validation process and accepted by regulatory bodies. The challenges posed by the collision avoidance problem are often present in other domains, and aircraft collision avoidance systems can serve as case studies that provide valuable insights for a wide range of safety-critical systems.

Generative models that maximize model likelihood have gained traction in many practical settings. Among them, perturbation based approaches underpin many strong likelihood estimation models, yet they often face slow convergence and limited theoretical understanding. In this paper, we derive a tighter likelihood bound for noise driven models to improve both the accuracy and efficiency of maximum likelihood learning. Our key insight extends the classical KL divergence Fisher information relationship to arbitrary noise perturbations, going beyond the Gaussian assumption and enabling structured noise distributions. This formulation allows flexible use of randomized noise distributions that naturally account for sensor artifacts, quantization effects, and data distribution smoothing, while remaining compatible with standard diffusion training. Treating the diffusion process as a Gaussian channel, we further express the mismatched entropy between data and model, showing that the proposed objective upper bounds the negative log-likelihood (NLL). In experiments, our models achieve competitive NLL on CIFAR-10 and SOTA results on ImageNet across multiple resolutions, all without data augmentation, and the framework extends naturally to discrete data.

Marked Temporal Point Process (MTPP) has been well studied to model the event distribution in marked event streams, which can be used to predict the mark and arrival time of the next event. However, existing studies overlook that the distribution of event marks is highly imbalanced in many real-world applications, with some marks being frequent but others rare. The imbalance poses a significant challenge to the performance of the next event prediction, especially for events of rare marks. To address this issue, we propose a thresholding method, which learns thresholds to tune the mark probability normalized by the mark's prior probability to optimize mark prediction, rather than predicting the mark directly based on the mark probability as in existing studies. In conjunction with this method, we predict the mark first and then the time. In particular, we develop a novel neural MTPP model to support effective time sampling and estimation of mark probability without computationally expensive numerical improper integration. Extensive experiments on real-world datasets demonstrate the superior performance of our solution against various baselines for the next event mark and time prediction. The code is available at https://github.com/undes1red/IFNMTPP.

Listwise reranking with large language models (LLMs) enhances top-ranked results in retrieval-based applications. Due to the limit in context size and high inference cost of long context, reranking is typically performed over a fixed size of small subsets, with the final ranking aggregated from these partial results. This fixed computation disregards query difficulty and document distribution, leading to inefficiencies. We propose AcuRank, an adaptive reranking framework that dynamically adjusts both the amount and target of computation based on uncertainty estimates over document relevance. Using a Bayesian TrueSkill model, we iteratively refine relevance estimates until reaching sufficient confidence levels, and our explicit modeling of ranking uncertainty enables principled control over reranking behavior and avoids unnecessary updates to confident predictions. Results on the TREC-DL and BEIR benchmarks show that our method consistently achieves a superior accuracy-efficiency trade-off and scales better with compute than fixed-computation baselines. These results highlight the effectiveness and generalizability of our method across diverse retrieval tasks and LLM-based reranking models.

Generative flow networks are able to sample, via sequential construction, high-reward, complex objects according to a reward function. However, such reward functions are often estimated approximately from noisy data, leading to epistemic uncertainty in the learnt policy. We present an approach to quantify this uncertainty by constructing a surrogate model composed of a polynomial chaos expansion, fit on a small ensemble of trained flow networks. This model learns the relationship between reward functions, parametrised in a low-dimensional space, and the probability distributions over actions at each step along a trajectory of the flow network. The surrogate model can then be used for inexpensive Monte Carlo sampling to estimate the uncertainty in the policy given uncertain rewards. We illustrate the performance of our approach on a discrete and continuous grid-world, symbolic regression, and a Bayesian structure learning task.

Recent advances such as self-consistency and test-time reinforcement learning (TTRL) improve the reliability of large language models (LLMs) without additional supervision, yet their underlying mechanisms and statistical guarantees remain poorly understood. We present a unified framework for certifiable inference in LLMs, showing that majority voting provides a statistical certificate of self-consistency: under mild assumptions, the aggregated answer coincides with the mode of the model's terminal distribution with high probability. We derive finite-sample and anytime-valid concentration bounds that quantify this confidence, and introduce the Martingale Majority Certificate (MMC), a sequential stopping rule that adaptively determines when sufficient samples have been drawn. We further prove that label-free post-training methods such as TTRL implicitly sharpen the answer distribution by exponentially tilting it toward its mode, thereby reducing the number of samples required for certification. Building on this insight, we propose new post-training objectives that explicitly optimise this trade-off between sharpness and bias. Together, these results explain and connect two central test-time scaling strategies, self-consistency and TTRL, within a single statistical framework for label-free, certifiable reliability in reasoning LLMs.

Thanks to the remarkable human-like capabilities of machine learning (ML) models in perceptual and cognitive tasks, frameworks integrating ML within rational agent architectures are gaining traction. Yet, the landscape remains fragmented and incoherent, often focusing on embedding ML into generic agent containers while overlooking the expressive power of rational architectures--such as Belief-Desire-Intention (BDI) agents. This paper presents a fine-grained systematisation of existing approaches, using the BDI paradigm as a reference. Our analysis illustrates the fast-evolving literature on rational agents enhanced by ML, and identifies key research opportunities and open challenges for designing effective rational ML agents.

In standard autoregressive generation, an LLM predicts the next-token distribution, samples a discrete token, and then discards the distribution, passing only the sampled token as new input. To preserve this distribution's rich information, we propose Mixture of Inputs (MoI), a training-free method for autoregressive generation. After generating a token following the standard paradigm, we construct a new input that blends the generated discrete token with the previously discarded token distribution. Specifically, we employ a Bayesian estimation method that treats the token distribution as the prior, the sampled token as the observation, and replaces the conventional one-hot vector with the continuous posterior expectation as the new model input. MoI allows the model to maintain a richer internal representation throughout the generation process, resulting in improved text quality and reasoning capabilities. On mathematical reasoning, code generation, and PhD-level QA tasks, MoI consistently improves performance across multiple models including QwQ-32B, Nemotron-Super-49B, Gemma-3-27B, and DAPO-Qwen-32B, with no additional training and negligible computational overhead.

The matrix normal model, i.e., the family of Gaussian matrix-variate distributions whose covariance matrices are the Kronecker product of two lower dimensional factors, is frequently used to model matrix-variate data. The tensor normal model generalizes this family to Kronecker products of three or more factors. We study the estimation of the Kronecker factors of the covariance matrix in the matrix and tensor normal models. For the above models, we show that the maximum likelihood estimator (MLE) achieves nearly optimal nonasymptotic sample complexity and nearly tight error rates in the Fisher-Rao and Thompson metrics. In contrast to prior work, our results do not rely on the factors being well-conditioned or sparse, nor do we need to assume an accurate enough initial guess. For the matrix normal model, all our bounds are minimax optimal up to logarithmic factors, and for the tensor normal model our bounds for the largest factor and for overall covariance matrix are minimax optimal up to constant factors provided there are enough samples for any estimator to obtain constant Frobenius error. In the same regimes as our sample complexity bounds, we show that the flip-flop algorithm, a practical and widely used iterative procedure to compute the MLE, converges linearly with high probability. Our main technical insight is that, given enough samples, the negative log-likelihood function is strongly geodesically convex in the geometry on positive-definite matrices induced by the Fisher information metric. This strong convexity is determined by the expansion of certain random quantum channels.