Thermal states play a fundamental role in various areas of physics, and they are becoming increasingly important in quantum information science, with applications related to semi-definite programming, quantum Boltzmann machine learning, Hamiltonian learning, and the related task of estimating the parameters of a Hamiltonian. Here we establish formulas underlying the basic geometry of parameterized thermal states, and we delineate quantum algorithms for estimating the values of these formulas. More specifically, we prove formulas for the Fisher--Bures and Kubo--Mori information matrices of parameterized thermal states, and our quantum algorithms for estimating their matrix elements involve a combination of classical sampling, Hamiltonian simulation, and the Hadamard test. These results have applications in developing a natural gradient descent algorithm for quantum Boltzmann machine learning, which takes into account the geometry of thermal states, and in establishing fundamental limitations on the ability to estimate the parameters of a Hamiltonian, when given access to thermal-state samples. For the latter task, and for the special case of estimating a single parameter, we sketch an algorithm that realizes a measurement that is asymptotically optimal for the estimation task. We finally stress that the natural gradient descent algorithm developed here can be used for any machine learning problem that employs the quantum Boltzmann machine ansatz.

Visual reprogramming (VR) leverages the intrinsic capabilities of pretrained vision models by adapting their input or output interfaces to solve downstream tasks whose labels (i.e., downstream labels) might be totally different from the labels associated with the pretrained models (i.e., pretrained labels). When adapting the output interface, label mapping methods transform the pretrained labels to downstream labels by establishing a gradient-free one-to-one correspondence between the two sets of labels. However, in this paper, we reveal that one-to-one mappings may overlook the complex relationship between pretrained and downstream labels. Motivated by this observation, we propose a Bayesian-guided Label Mapping (BLM) method. BLM constructs an iteratively-updated probabilistic label mapping matrix, with each element quantifying a pairwise relationship between pretrained and downstream labels. The assignment of values to the constructed matrix is guided by Bayesian conditional probability, considering the joint distribution of the downstream labels and the labels predicted by the pretrained model on downstream samples. Experiments conducted on both pretrained vision models (e.g., ResNeXt) and vision-language models (e.g., CLIP) demonstrate the superior performance of BLM over existing label mapping methods. The success of BLM also offers a probabilistic lens through which to understand and analyze the effectiveness of VR. Our code is available at https://github.com/tmlr-group/BayesianLM.

Learning the structure of Directed Acyclic Graphs (DAGs) presents a significant challenge due to the vast combinatorial search space of possible graphs, which scales exponentially with the number of nodes. Recent advancements have redefined this problem as a continuous optimization task by incorporating differentiable acyclicity constraints. These methods commonly rely on algebraic characterizations of DAGs, such as matrix exponentials, to enable the use of gradient-based optimization techniques. Despite these innovations, existing methods often face optimization difficulties due to the highly non-convex nature of DAG constraints and the per-iteration computational complexity. In this work, we present a novel framework for learning DAGs, employing a Stochastic Approximation approach integrated with Stochastic Gradient Descent (SGD)-based optimization techniques. Our framework introduces new projection methods tailored to efficiently enforce DAG constraints, ensuring that the algorithm converges to a feasible local minimum. With its low iteration complexity, the proposed method is well-suited for handling large-scale problems with improved computational efficiency. We demonstrate the effectiveness and scalability of our framework through comprehensive experimental evaluations, which confirm its superior performance across various settings.

Robotic insertion tasks remain challenging due to uncertainties in perception and the need for precise control, particularly in unstructured environments. While humans seamlessly combine vision and touch for such tasks, effectively integrating these modalities in robotic systems is still an open problem. Our work presents an extensive analysis of the interplay between visual and tactile feedback during dexterous insertion tasks, showing that tactile sensing can greatly enhance success rates on challenging insertions with tight tolerances and varied hole orientations that vision alone cannot solve. These findings provide valuable insights for designing more effective multi-modal robotic control systems and highlight the critical role of tactile feedback in contact-rich manipulation tasks.

This paper investigates an under-explored challenge in large language models (LLMs): chain-of-thought prompting with noisy rationales, which include irrelevant or inaccurate reasoning thoughts within examples used for in-context learning. We construct NoRa dataset that is tailored to evaluate the robustness of reasoning in the presence of noisy rationales. Our findings on NoRa dataset reveal a prevalent vulnerability to such noise among current LLMs, with existing robust methods like self-correction and self-consistency showing limited efficacy. Notably, compared to prompting with clean rationales, base LLM drops by 1.4%-19.8% in accuracy with irrelevant thoughts and more drastically by 2.2%-40.4% with inaccurate thoughts. Addressing this challenge necessitates external supervision that should be accessible in practice. Here, we propose the method of contrastive denoising with noisy chain-of-thought (CD-CoT). It enhances LLMs' denoising-reasoning capabilities by contrasting noisy rationales with only one clean rationale, which can be the minimal requirement for denoising-purpose prompting. This method follows a principle of exploration and exploitation: (1) rephrasing and selecting rationales in the input space to achieve explicit denoising and (2) exploring diverse reasoning paths and voting on answers in the output space. Empirically, CD-CoT demonstrates an average improvement of 17.8% in accuracy over the base model and shows significantly stronger denoising capabilities than baseline methods. The source code is publicly available at: https://github.com/tmlr-group/NoisyRationales.

This chapter provides an overview of research works that present approaches with some degree of cross-fertilisation between Computational Argumentation and Machine Learning. Our review of the literature identified two broad themes representing the purpose of the interaction between these two areas: argumentation for machine learning and machine learning for argumentation. Across these two themes, we systematically evaluate the spectrum of works across various dimensions, including the type of learning and the form of argumentation framework used. Further, we identify three types of interaction between these two areas: synergistic approaches, where the Argumentation and Machine Learning components are tightly integrated; segmented approaches, where the two are interleaved such that the outputs of one are the inputs of the other; and approximated approaches, where one component shadows the other at a chosen level of detail. We draw conclusions about the suitability of certain forms of Argumentation for supporting certain types of Machine Learning, and vice versa, with clear patterns emerging from the review. Whilst the reviewed works provide inspiration for successfully combining the two fields of research, we also identify and discuss limitations and challenges that ought to be addressed in order to ensure that they remain a fruitful pairing as AI advances.

The application of reinforcement learning in traffic signal control (TSC) has been extensively researched and yielded notable achievements. However, most existing works for TSC assume that traffic data from all surrounding intersections is fully and continuously available through sensors. In real-world applications, this assumption often fails due to sensor malfunctions or data loss, making TSC with missing data a critical challenge. To meet the needs of practical applications, we introduce DiffLight, a novel conditional diffusion model for TSC under data-missing scenarios in the offline setting. Specifically, we integrate two essential sub-tasks, i.e., traffic data imputation and decision-making, by leveraging a Partial Rewards Conditioned Diffusion (PRCD) model to prevent missing rewards from interfering with the learning process. Meanwhile, to effectively capture the spatial-temporal dependencies among intersections, we design a Spatial-Temporal transFormer (STFormer) architecture. In addition, we propose a Diffusion Communication Mechanism (DCM) to promote better communication and control performance under data-missing scenarios. Extensive experiments on five datasets with various data-missing scenarios demonstrate that DiffLight is an effective controller to address TSC with missing data. The code of DiffLight is released at https://github.com/lokol5579/DiffLight-release.

We develop a generic policy gradient method with the global optimality guarantee for robust Markov Decision Processes (MDPs). While policy gradient methods are widely used for solving dynamic decision problems due to their scalable and efficient nature, adapting these methods to account for model ambiguity has been challenging, often making it impractical to learn robust policies. This paper introduces a novel policy gradient method, Double-Loop Robust Policy Mirror Descent (DRPMD), for solving robust MDPs. DRPMD employs a general mirror descent update rule for the policy optimization with adaptive tolerance per iteration, guaranteeing convergence to a globally optimal policy. We provide a comprehensive analysis of DRPMD, including new convergence results under both direct and softmax parameterizations, and provide novel insights into the inner problem solution through Transition Mirror Ascent (TMA). Additionally, we propose innovative parametric transition kernels for both discrete and continuous state-action spaces, broadening the applicability of our approach.

We present an accelerated pipeline, based on high-performance computing techniques and normalizing flows, for joint Bayesian parameter estimation and model selection and demonstrate its efficiency in gravitational wave astrophysics. We integrate the Jim inference toolkit, a normalizing flow-enhanced Markov chain Monte Carlo (MCMC) sampler, with the learned harmonic mean estimator. Our Bayesian evidence estimates run on $1$ GPU are consistent with traditional nested sampling techniques run on $16$ CPU cores, while reducing the computation time by factors of $5\times$ and $15\times$ for $4$-dimensional and $11$-dimensional gravitational wave inference problems, respectively. Our code is available in well-tested and thoroughly documented open-source packages, ensuring accessibility and reproducibility for the wider research community.

We develop EigenVI, an eigenvalue-based approach for black-box variational inference (BBVI). EigenVI constructs its variational approximations from orthogonal function expansions. For distributions over $\mathbb{R}^D$, the lowest order term in these expansions provides a Gaussian variational approximation, while higher-order terms provide a systematic way to model non-Gaussianity. These approximations are flexible enough to model complex distributions (multimodal, asymmetric), but they are simple enough that one can calculate their low-order moments and draw samples from them. EigenVI can also model other types of random variables (e.g., nonnegative, bounded) by constructing variational approximations from different families of orthogonal functions. Within these families, EigenVI computes the variational approximation that best matches the score function of the target distribution by minimizing a stochastic estimate of the Fisher divergence. Notably, this optimization reduces to solving a minimum eigenvalue problem, so that EigenVI effectively sidesteps the iterative gradient-based optimizations that are required for many other BBVI algorithms. (Gradient-based methods can be sensitive to learning rates, termination criteria, and other tunable hyperparameters.) We use EigenVI to approximate a variety of target distributions, including a benchmark suite of Bayesian models from posteriordb. On these distributions, we find that EigenVI is more accurate than existing methods for Gaussian BBVI.