Heavy-tailed distributions, prevalent in a lot of real-world applications such as finance, telecommunications, queuing theory, and natural language processing, are challenging to model accurately owing to their slow tail decay. Bernstein phase-type (BPH) distributions, through their analytical tractability and good approximations in the non-tail region, can present a good solution, but they suffer from an inability to reproduce these heavy-tailed behaviors exactly, thus leading to inadequate performance in important tail areas. On the contrary, while highly adaptable to heavy-tailed distributions, hyperexponential (HE) models struggle in the body part of the distribution. Additionally, they are highly sensitive to initial parameter selection, significantly affecting their precision. To solve these issues, we propose a novel hybrid model of BPH and HE distributions, borrowing the most desirable features from each for enhanced approximation quality. Specifically, we leverage an optimization to set initial parameters for the HE component, significantly enhancing its robustness and reducing the possibility that the associated procedure results in an invalid HE model. Experimental validation demonstrates that the novel hybrid approach is more performant than individual application of BPH or HE models. More precisely, it can capture both the body and the tail of heavy-tailed distributions, with a considerable enhancement in matching parameters such as mean and coefficient of variation. Additional validation through experiments utilizing queuing theory proves the practical usefulness, accuracy, and precision of our hybrid approach.

Low-Rank Adaptation (LoRA) offers a cost-effective solution for fine-tuning large language models (LLMs), but it often produces overconfident predictions in data-scarce few-shot settings. To address this issue, several classical statistical learning approaches have been repurposed for scalable uncertainty-aware LoRA fine-tuning. However, these approaches neglect how input characteristics affect the predictive uncertainty estimates. To address this limitation, we propose Contextual Low-Rank Adaptation (C-LoRA) as a novel uncertainty-aware and parameter efficient fine-tuning approach, by developing new lightweight LoRA modules contextualized to each input data sample to dynamically adapt uncertainty estimates. Incorporating data-driven contexts into the parameter posteriors, C-LoRA mitigates overfitting, achieves well-calibrated uncertainties, and yields robust predictions. Extensive experiments on LLaMA2-7B models demonstrate that C-LoRA consistently outperforms the state-of-the-art uncertainty-aware LoRA methods in both uncertainty quantification and model generalization. Ablation studies further confirm the critical role of our contextual modules in capturing sample-specific uncertainties. C-LoRA sets a new standard for robust, uncertainty-aware LLM fine-tuning in few-shot regimes. Although our experiments are limited to 7B models, our method is architecture-agnostic and, in principle, applies beyond this scale; studying its scaling to larger models remains an open problem. Our code is available at https://github.com/ahra99/c_lora.

Reinforcement learning (RL) has proven effective for fine-tuning large language models (LLMs), significantly enhancing their reasoning abilities in domains such as mathematics and code generation. A crucial factor influencing RL fine-tuning success is the training curriculum: the order in which training problems are presented. While random curricula serve as common baselines, they remain suboptimal; manually designed curricula often rely heavily on heuristics, and online filtering methods can be computationally prohibitive. To address these limitations, we propose Self-Evolving Curriculum (SEC), an automatic curriculum learning method that learns a curriculum policy concurrently with the RL fine-tuning process. Our approach formulates curriculum selection as a non-stationary Multi-Armed Bandit problem, treating each problem category (e.g., difficulty level or problem type) as an individual arm. We leverage the absolute advantage from policy gradient methods as a proxy measure for immediate learning gain. At each training step, the curriculum policy selects categories to maximize this reward signal and is updated using the TD(0) method. Across three distinct reasoning domains: planning, inductive reasoning, and mathematics, our experiments demonstrate that SEC significantly improves models' reasoning capabilities, enabling better generalization to harder, out-of-distribution test problems. Additionally, our approach achieves better skill balance when fine-tuning simultaneously on multiple reasoning domains. These findings highlight SEC as a promising strategy for RL fine-tuning of LLMs.

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty - often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce neurosymbolic diffusion models (NeSyDMs), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols. Our approach reuses the independence assumption from NeSy predictors at each step of the diffusion process, enabling scalable learning while capturing symbol dependencies and uncertainty quantification. Across both synthetic and real-world benchmarks - including high-dimensional visual path planning and rule-based autonomous driving - NeSyDMs achieve state-of-the-art accuracy among NeSy predictors and demonstrate strong calibration.

Large language models (LLMs) continue to advance, with an increasing number of domain-specific variants tailored for specialised tasks. However, these models often lack transparency and explainability, can be costly to fine-tune, require substantial prompt engineering, yield inconsistent results across domains, and impose significant adverse environmental impact due to their high computational demands. To address these challenges, we propose the Bayesian network LLM fusion (BNLF) framework, which integrates predictions from three LLMs, including FinBERT, RoBERTa, and BERTweet, through a probabilistic mechanism for sentiment analysis. BNLF performs late fusion by modelling the sentiment predictions from multiple LLMs as probabilistic nodes within a Bayesian network. Evaluated across three human-annotated financial corpora with distinct linguistic and contextual characteristics, BNLF demonstrates consistent gains of about six percent in accuracy over the baseline LLMs, underscoring its robustness to dataset variability and the effectiveness of probabilistic fusion for interpretable sentiment classification.

Current evaluations of agents remain centered around one-shot task completion, failing to account for the inherently iterative and collaborative nature of many real-world problems, where human goals are often underspecified and evolve. We argue for a shift from building and assessing task completion agents to developing collaborative agents, assessed not only by the quality of their final outputs but by how well they engage with and enhance human effort throughout the problem-solving process. To support this shift, we introduce collaborative effort scaling, a framework that captures how an agent's utility grows with increasing user involvement. Through case studies and simulated evaluations, we show that state-of-the-art agents often underperform in multi-turn, real-world scenarios, revealing a missing ingredient in agent design: the ability to sustain engagement and scaffold user understanding. Collaborative effort scaling offers a lens for diagnosing agent behavior and guiding development toward more effective interactions.

Uncovering hidden graph structures underlying real-world data is a critical challenge with broad applications across scientific domains. Recently, transformer-based models leveraging the attention mechanism have demonstrated strong empirical success in capturing complex dependencies within graphs. However, the theoretical understanding of their training dynamics has been limited to tree-like graphs, where each node depends on a single parent. Extending provable guarantees to more general directed acyclic graphs (DAGs) -- which involve multiple parents per node -- remains challenging, primarily due to the difficulty in designing training objectives that enable different attention heads to separately learn multiple different parent relationships. In this work, we address this problem by introducing a novel information-theoretic metric: the kernel-guided mutual information (KG-MI), based on the $f$-divergence. Our objective combines KG-MI with a multi-head attention framework, where each head is associated with a distinct marginal transition kernel to model diverse parent-child dependencies effectively. We prove that, given sequences generated by a $K$-parent DAG, training a single-layer, multi-head transformer via gradient ascent converges to the global optimum in polynomial time. Furthermore, we characterize the attention score patterns at convergence. In addition, when particularizing the $f$-divergence to the KL divergence, the learned attention scores accurately reflect the ground-truth adjacency matrix, thereby provably recovering the underlying graph structure. Experimental results validate our theoretical findings.

In Vision-Language-Action (VLA) models, robustness to real-world perturbations is critical for deployment. Existing methods target simple visual disturbances, overlooking the broader multi-modal perturbations that arise in actions, instructions, environments, and observations. Here, we first evaluate the robustness of mainstream VLAs under 17 perturbations across four modalities. We find (1) actions as the most fragile modality, (2) Existing visual-robust VLA do not gain robustness in other modality, and (3) pi0 demonstrates superior robustness with a diffusion-based action head. To build multi-modal robust VLAs, we propose RobustVLA against perturbations in VLA inputs and outputs. For output robustness, we perform offline robust optimization against worst-case action noise that maximizes mismatch in flow matching objective. This can be seen as adversarial training, label smoothing, and outlier penalization. For input robustness, we enforce consistent actions across input variations that preserve task semantics. To account for multiple perturbations, we formulate robustness as a multi-armed bandit problem and apply an upper confidence bound algorithm to automatically identify the most harmful noise. Experiments on LIBERO demonstrate our RobustVLA delivers absolute gains over baselines of 12.6% on the pi0 backbone and 10.4% on the OpenVLA backbone across all 17 perturbations, achieving 50.6x faster inference than existing visual-robust VLAs, and a 10.4% gain under mixed perturbations. Our RobustVLA is particularly effective on real-world FR5 robot with limited demonstrations, showing absolute gains by 65.6% under perturbations of four modalities.

Uncovering cause-and-effect mechanisms from data is fundamental to scientific progress. While large language models (LLMs) show promise for enhancing causal discovery (CD) from unstructured data, their application to the increasingly prevalent multimodal setting remains a critical challenge. Even with the advent of multimodal LLMs (MLLMs), their efficacy in multimodal CD is hindered by two primary limitations: (1) difficulty in exploring intra- and inter-modal interactions for comprehensive causal variable identification; and (2) insufficiency to handle structural ambiguities with purely observational data. To address these challenges, we propose MLLM-CD, a novel framework for multimodal causal discovery from unstructured data. It consists of three key components: (1) a novel contrastive factor discovery module to identify genuine multimodal factors based on the interactions explored from contrastive sample pairs; (2) a statistical causal structure discovery module to infer causal relationships among discovered factors; and (3) an iterative multimodal counterfactual reasoning module to refine the discovery outcomes iteratively by incorporating the world knowledge and reasoning capabilities of MLLMs. Extensive experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed MLLM-CD in revealing genuine factors and causal relationships among them from multimodal unstructured data.

Modeling systems that exhibit both continuous and discontinuous state changes presents a significant challenge in machine learning. For instance, biological spiking networks feature the continuous decay of neuron potentials alongside discontinuous spikes, which cause abrupt increases in the potentials of neighboring downstream neurons. Designing appropriate objective functions and applying gradient methods that work with these discontinuities are among the difficulties of working with such systems. Traditionally, ordinary and partial differential equations (ODEs and PDEs) are used to model continuous state changes, while Markov decision processes (MDPs) are employed to capture discrete actions that drive environmental transitions. In this paper, we study Action-Driven Processes (ADPs), also known as generalized semi-Markov processes [12, 5, 16], which unify both types of dynamics within a single framework. With continuous-time states and actions at the core of ADPs, a natural question is whether it is possible to learn optimal policies for action selection using traditional reinforcement learning methods. The control-as-inference tutorial [9] elegantly demonstrated that maximum entropy reinforcement learning can be formulated as minimizing the Kullback-Leibler (KL) divergence between (a) a true trajectory distribution generated by action-state transitions and the policy, and (b) a model trajectory distribution that depends on the reward function.