Flawed planning from VLM-driven embodied agents poses significant safety hazards, hindering their deployment in real-world household tasks. However, existing static, non-interactive evaluation paradigms fail to adequately assess risks within these interactive environments, since they cannot simulate dynamic risks that emerge from an agent's actions and rely on unreliable post-hoc evaluations that ignore unsafe intermediate steps. To bridge this critical gap, we propose evaluating an agent's interactive safety: its ability to perceive emergent risks and execute mitigation steps in the correct procedural order. We thus present IS-Bench, the first multi-modal benchmark designed for interactive safety, featuring 161 challenging scenarios with 388 unique safety risks instantiated in a high-fidelity simulator. Crucially, it facilitates a novel process-oriented evaluation that verifies whether risk mitigation actions are performed before/after specific risk-prone steps. Extensive experiments on leading VLMs, including the GPT-4o and Gemini-2.5 series, reveal that current agents lack interactive safety awareness, and that while safety-aware Chain-of-Thought can improve performance, it often compromises task completion. By highlighting these critical limitations, IS-Bench provides a foundation for developing safer and more reliable embodied AI systems. Code and data are released under https://github.com/AI45Lab/IS-Bench.

The growing capabilities of large language models (LLMs) in instruction-following and context-understanding lead to the era of agents with numerous applications. Among these, task planning agents have become especially prominent in realistic scenarios involving complex internal pipelines, such as context understanding, tool management, and response generation. However, existing benchmarks predominantly evaluate agent performance based on task completion as a proxy for overall effectiveness. We hypothesize that merely improving task completion is misaligned with maximizing user satisfaction, as users interact with the entire agentic process and not only the end result. To address this gap, we propose AURA, an Agent-User inteRaction Assessment framework that conceptualizes the behavioral stages of interactive task planning agents. AURA offers a comprehensive assessment of agent through a set of atomic LLM evaluation criteria, allowing researchers and practitioners to diagnose specific strengths and weaknesses within the agent's decision-making pipeline. Our analyses show that agents excel in different behavioral stages, with user satisfaction shaped by both outcomes and intermediate behaviors. We also highlight future directions, including systems that leverage multiple agents and the limitations of user simulators in task planning.

Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the unconditioned dynamics rarely reach the terminal state. In this work, we leverage a self-consistency property of the conditioned dynamics to learn the diffusion bridge in an iterative online manner, and demonstrate promising empirical results in a range of settings.

Guided or controlled data generation with diffusion models\blfootnote{Partial preliminary results of this work appeared in International Conference on Machine Learning 2025 \citep{li2025provable}.} has become a cornerstone of modern generative modeling. Despite substantial advances in diffusion model theory, the theoretical understanding of guided diffusion samplers remains severely limited. We make progress by developing a unified algorithmic and theoretical framework that accommodates both diffusion guidance and reward-guided diffusion. Aimed at fine-tuning diffusion models to improve certain rewards, we propose injecting a reward guidance term -- constructed from the difference between the original and reward-reweighted scores -- into the backward diffusion process, and rigorously quantify the resulting reward improvement over the unguided counterpart. As a key application, our framework shows that classifier-free guidance (CFG) decreases the expected reciprocal of the classifier probability, providing the first theoretical characterization of the specific performance metric that CFG improves for general target distributions. When applied to reward-guided diffusion, our framework yields a new sampler that is easy-to-train and requires no full diffusion trajectories during training. Numerical experiments further corroborate our theoretical findings.

This thesis develops methods for causal inference and causal representation learning (CRL) in high-dimensional, time-varying data. The first contribution introduces the Causal Dynamic Variational Autoencoder (CDVAE), a model for estimating Individual Treatment Effects (ITEs) by capturing unobserved heterogeneity in treatment response driven by latent risk factors that affect only outcomes. CDVAE comes with theoretical guarantees on valid latent adjustment and generalization bounds for ITE error. Experiments on synthetic and real datasets show that CDVAE outperforms baselines, and that state-of-the-art models greatly improve when augmented with its latent substitutes, approaching oracle performance without access to true adjustment variables. The second contribution proposes an efficient framework for long-term counterfactual regression based on RNNs enhanced with Contrastive Predictive Coding (CPC) and InfoMax. It captures long-range dependencies under time-varying confounding while avoiding the computational cost of transformers, achieving state-of-the-art results and introducing CPC into causal inference. The third contribution advances CRL by addressing how latent causes manifest in observed variables. We introduce a model-agnostic interpretability layer based on the geometry of the decoder Jacobian. A sparse self-expression prior induces modular, possibly overlapping groups of observed features aligned with shared latent influences. We provide recovery guarantees in both disjoint and overlapping settings and show that meaningful latent-to-observed structure can be recovered without anchor features or single-parent assumptions. Scalable Jacobian-based regularization techniques are also developed.

The main focus of Hierarchical Reinforcement Learning (HRL) is studying how large Markov Decision Processes (MDPs) can be more efficiently solved when addressed in a modular way, by combining partial solutions computed for smaller subtasks. Despite their very intuitive role for learning, most notions of MDP abstractions proposed in the HRL literature have limited expressive power or do not possess formal efficiency guarantees. This work addresses these fundamental issues by defining Realizable Abstractions, a new relation between generic low-level MDPs and their associated high-level decision processes. The notion we propose avoids non-Markovianity issues and has desirable near-optimality guarantees. Indeed, we show that any abstract policy for Realizable Abstractions can be translated into near-optimal policies for the low-level MDP, through a suitable composition of options. As demonstrated in the paper, these options can be expressed as solutions of specific constrained MDPs. Based on these findings, we propose RARL, a new HRL algorithm that returns compositional and near-optimal low-level policies, taking advantage of the Realizable Abstraction given in the input. We show that RARL is Probably Approximately Correct, it converges in a polynomial number of samples, and it is robust to inaccuracies in the abstraction.

Across diverse domains--from complex systems and finance to high-energy physics and astrophysics--scientific inquiry often relies on deriving theoretical parameters from observational data [1]. At the core of this challenge lies the inverse problem: inferring the posterior distribution of theoretical parameters given a set of observables [2]. Traditional approaches for posterior estimation rely on sampling algorithms such as Markov Chain Monte Carlo (MCMC) [3, 4] and Nested Sampling (NS) [5]. In astrophysics and cosmology, implementations like emcee [6] and dynesty [7] have become standard tools. While these frameworks are statistically robust, they suffer significantly from the curse of dimensionality. In real-world scenarios, where the parameter space is high-dimensional and the likelihood function relies on computationally expensive simulators (e.g., in particle physics phenomenology [8]), convergence can take weeks or even months. Recent advances in machine learning have introduced Normalizing Flows (NFs) as a powerful alternative for probabilistic modelling [9, 10]. By learning a bijective mapping between a simple base distribution (e.g., a Gaussian) and the complex target distribution, NFs allow for exact density estimation and efficient sampling [11] from the target distribution. Modern architectures, such as RealNVP [12] and Neural Spline Flows [13], offer enough expressivity to model highly complex distributions.

Discovering the neural mechanisms underpinning cognition is one of the grand challenges of neuroscience. However, previous approaches for building models of RNN dynamics that explain behaviour required iterative refinement of architectures and/or optimisation objectives, resulting in a piecemeal, and mostly heuristic, human-in-the-loop process. Here, we offer an alternative approach that automates the discovery of viable RNN mechanisms by explicitly training RNNs to reproduce behaviour, including the same characteristic errors and suboptimalities, that humans and animals produce in a cognitive task. Achieving this required two main innovations. First, as the amount of behavioural data that can be collected in experiments is often too limited to train RNNs, we use a non-parametric generative model of behavioural responses to produce surrogate data for training RNNs. Second, to capture all relevant statistical aspects of the data, we developed a novel diffusion model-based approach for training RNNs. To showcase the potential of our approach, we chose a visual working memory task as our test-bed, as behaviour in this task is well known to produce response distributions that are patently multimodal (due to swap errors). The resulting network dynamics correctly qualitative features of macaque neural data. Importantly, these results were not possible to obtain with more traditional approaches, i.e., when only a limited set of behavioural signatures (rather than the full richness of behavioural response distributions) were fitted, or when RNNs were trained for task optimality (instead of reproducing behaviour). Our approach also yields novel predictions about the mechanism of swap errors, which can be readily tested in experiments. These results suggest that fitting RNNs to rich patterns of behaviour provides a powerful way to automatically discover mechanisms of important cognitive functions.

Score matching estimators have garnered significant attention in recent years because they eliminate the need to compute normalizing constants, thereby mitigating the computational challenges associated with maximum likelihood estimation (MLE).While several studies have proposed score matching estimators for point processes, this work highlights the limitations of these existing methods, which stem primarily from the lack of a mathematically rigorous analysis of how score matching behaves on finite point processes -- special random configurations on bounded spaces where many of the usual assumptions and properties of score matching no longer hold. To this end, we develop a formal framework for score matching on finite point processes via Janossy measures and, within this framework, introduce an (autoregressive) weighted score-matching estimator, whose statistical properties we analyze in classical parametric settings. For general nonparametric (e.g., deep) point process models, we show that score matching alone does not uniquely identify the ground-truth distribution due to subtle normalization issues, and we propose a simple survival-classification augmentation that yields a complete, integration-free training objective for any intensity-based point process model for spatio-temporal case. Experiments on synthetic and real-world temporal and spatio-temporal datasets, demonstrate that our method accurately recovers intensities and achieves performance comparable to MLE with better efficiency.

We introduce a unified mathematical and probabilistic framework for understanding and comparing diverse AI agent strategies. We bridge the gap between high-level agent design concepts, such as ReAct, multi-agent systems, and control flows, and a rigorous mathematical formulation. Our approach frames agentic processes as a chain of probabilities, enabling a detailed analysis of how different strategies manipulate these probabilities to achieve desired outcomes. Our framework provides a common language for discussing the trade-offs inherent in various agent architectures. One of our many key contributions is the introduction of the "Degrees of Freedom" concept, which intuitively differentiates the optimizable levers available for each approach, thereby guiding the selection of appropriate strategies for specific tasks. This work aims to enhance the clarity and precision in designing and evaluating AI agents, offering insights into maximizing the probability of successful actions within complex agentic systems.