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Improving the reasoning capabilities of large language models (LLMs) has attracted considerable interest. Recent approaches primarily focus on improving the reasoning process to yield a more precise final answer. However, in scenarios involving contextually aware reasoning, these methods neglect the importance of first identifying logical relationships from the context before proceeding with the reasoning. This oversight could lead to a superficial understanding and interaction with the context, potentially undermining the quality and reliability of the reasoning outcomes. In this paper, we propose an information re-organization (InfoRE) method before proceeding with the reasoning to enhance the reasoning ability of LLMs. Our re-organization method involves initially extracting logical relationships from the contextual content, such as documents or paragraphs, and subsequently pruning redundant content to minimize noise. Then, we utilize the re-organized information in the reasoning process. This enables LLMs to deeply understand the contextual content by clearly perceiving these logical relationships, while also ensuring high-quality responses by eliminating potential noise. To demonstrate the effectiveness of our approach in improving the reasoning ability, we conduct experiments using Llama2-70B, GPT-3.5, and GPT-4 on various contextually aware multi-hop reasoning tasks. Using only a zero-shot setting, our method achieves an average absolute improvement of 4% across all tasks, highlighting its potential to improve the reasoning performance of LLMs. Our source code is available at //github.com/hustcxx/InfoRE.

The study of behavioral diversity in Multi-Agent Reinforcement Learning (MARL) is a nascent yet promising field. In this context, the present work deals with the question of how to control the diversity of a multi-agent system. With no existing approaches to control diversity to a set value, current solutions focus on blindly promoting it via intrinsic rewards or additional loss functions, effectively changing the learning objective and lacking a principled measure for it. To address this, we introduce Diversity Control (DiCo), a method able to control diversity to an exact value of a given metric by representing policies as the sum of a parameter-shared component and dynamically scaled per-agent components. By applying constraints directly to the policy architecture, DiCo leaves the learning objective unchanged, enabling its applicability to any actor-critic MARL algorithm. We theoretically prove that DiCo achieves the desired diversity, and we provide several experiments, both in cooperative and competitive tasks, that show how DiCo can be employed as a novel paradigm to increase performance and sample efficiency in MARL. Multimedia results are available on the paper's website: //sites.google.com/view/dico-marl.

We study theoretical properties of a broad class of regularized algorithms with vector-valued output. These spectral algorithms include kernel ridge regression, kernel principal component regression, various implementations of gradient descent and many more. Our contributions are twofold. First, we rigorously confirm the so-called saturation effect for ridge regression with vector-valued output by deriving a novel lower bound on learning rates; this bound is shown to be suboptimal when the smoothness of the regression function exceeds a certain level. Second, we present the upper bound for the finite sample risk general vector-valued spectral algorithms, applicable to both well-specified and misspecified scenarios (where the true regression function lies outside of the hypothesis space) which is minimax optimal in various regimes. All of our results explicitly allow the case of infinite-dimensional output variables, proving consistency of recent practical applications.

This paper proposes a novel online evaluation protocol for Test Time Adaptation (TTA) methods, which penalizes slower methods by providing them with fewer samples for adaptation. TTA methods leverage unlabeled data at test time to adapt to distribution shifts. Although many effective methods have been proposed, their impressive performance usually comes at the cost of significantly increased computation budgets. Current evaluation protocols overlook the effect of this extra computation cost, affecting their real-world applicability. To address this issue, we propose a more realistic evaluation protocol for TTA methods, where data is received in an online fashion from a constant-speed data stream, thereby accounting for the method's adaptation speed. We apply our proposed protocol to benchmark several TTA methods on multiple datasets and scenarios. Extensive experiments show that, when accounting for inference speed, simple and fast approaches can outperform more sophisticated but slower methods. For example, SHOT from 2020, outperforms the state-of-the-art method SAR from 2023 in this setting. Our results reveal the importance of developing practical TTA methods that are both accurate and efficient.

Efficient inference in high-dimensional models remains a central challenge in machine learning. This paper introduces the Gaussian Ensemble Belief Propagation (GEnBP) algorithm, a fusion of the Ensemble Kalman filter and Gaussian Belief Propagation (GaBP) methods. GEnBP updates ensembles by passing low-rank local messages over a graphical model. This combination inherits favourable qualities from each method. Ensemble techniques allow GEnBP to handle high-dimensional states, parameters and intricate, noisy, black-box generation processes. The use of local messages in a graphical model structure ensures that the approach can efficiently handle complex dependence structures. GEnBP is advantageous when the ensemble size may be considerably smaller than the inference dimension. This scenario often arises in fields such as spatiotemporal modelling, image processing and physical model inversion. GEnBP can be applied to general problem structures, including data assimilation, system identification and hierarchical models. Supporting code is available at //github.com/danmackinlay/GEnBP

Gaussian Process Regression (GPR) is widely used in statistics and machine learning for prediction tasks requiring uncertainty measures. Its efficacy depends on the appropriate specification of the mean function, covariance kernel function, and associated hyperparameters. Severe misspecifications can lead to inaccurate results and problematic consequences, especially in safety-critical applications. However, a systematic approach to handle these misspecifications is lacking in the literature. In this work, we propose a general framework to address these issues. Firstly, we introduce a flexible two-stage GPR framework that separates mean prediction and uncertainty quantification (UQ) to prevent mean misspecification, which can introduce bias into the model. Secondly, kernel function misspecification is addressed through a novel automatic kernel search algorithm, supported by theoretical analysis, that selects the optimal kernel from a candidate set. Additionally, we propose a subsampling-based warm-start strategy for hyperparameter initialization to improve efficiency and avoid hyperparameter misspecification. With much lower computational cost, our subsampling-based strategy can yield competitive or better performance than training exclusively on the full dataset. Combining all these components, we recommend two GPR methods-exact and scalable-designed to match available computational resources and specific UQ requirements. Extensive evaluation on real-world datasets, including UCI benchmarks and a safety-critical medical case study, demonstrates the robustness and precision of our methods.

We introduce a novel framework for incorporating human expertise into algorithmic predictions. Our approach focuses on the use of human judgment to distinguish inputs which `look the same' to any feasible predictive algorithm. We argue that this framing clarifies the problem of human/AI collaboration in prediction tasks, as experts often have access to information -- particularly subjective information -- which is not encoded in the algorithm's training data. We use this insight to develop a set of principled algorithms for selectively incorporating human feedback only when it improves the performance of any feasible predictor. We find empirically that although algorithms often outperform their human counterparts on average, human judgment can significantly improve algorithmic predictions on specific instances (which can be identified ex-ante). In an X-ray classification task, we find that this subset constitutes nearly 30% of the patient population. Our approach provides a natural way of uncovering this heterogeneity and thus enabling effective human-AI collaboration.

We demonstrate quantum advantage with several basic assumptions, specifically based on only the existence of OWFs. We introduce inefficient-verifier proofs of quantumness (IV-PoQ), and construct it from classical bit commitments. IV-PoQ is an interactive protocol between a verifier and a quantum prover consisting of two phases. In the first phase, the verifier is probabilistic polynomial-time, and it interacts with the prover. In the second phase, the verifier becomes inefficient, and makes its decision based on the transcript of the first phase. If the prover is honest, the inefficient verifier accepts with high probability, but any classical malicious prover only has a small probability of being accepted by the inefficient verifier. Our construction demonstrates the following results: (1)If one-way functions exist, then IV-PoQ exist. (2)If distributional collision-resistant hash functions exist (which exist if hard-on-average problems in $\mathbf{SZK}$ exist), then constant-round IV-PoQ exist. We also demonstrate quantum advantage based on worst-case-hard assumptions. We define auxiliary-input IV-PoQ (AI-IV-PoQ) that only require that for any malicious prover, there exist infinitely many auxiliary inputs under which the prover cannot cheat. We construct AI-IV-PoQ from an auxiliary-input version of commitments in a similar way, showing that (1)If auxiliary-input one-way functions exist (which exist if $\mathbf{CZK}\not\subseteq\mathbf{BPP}$), then AI-IV-PoQ exist. (2)If auxiliary-input collision-resistant hash functions exist (which is equivalent to $\mathbf{PWPP}\nsubseteq \mathbf{FBPP}$) or $\mathbf{SZK}\nsubseteq \mathbf{BPP}$, then constant-round AI-IV-PoQ exist.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

With the advent of deep neural networks, learning-based approaches for 3D reconstruction have gained popularity. However, unlike for images, in 3D there is no canonical representation which is both computationally and memory efficient yet allows for representing high-resolution geometry of arbitrary topology. Many of the state-of-the-art learning-based 3D reconstruction approaches can hence only represent very coarse 3D geometry or are limited to a restricted domain. In this paper, we propose occupancy networks, a new representation for learning-based 3D reconstruction methods. Occupancy networks implicitly represent the 3D surface as the continuous decision boundary of a deep neural network classifier. In contrast to existing approaches, our representation encodes a description of the 3D output at infinite resolution without excessive memory footprint. We validate that our representation can efficiently encode 3D structure and can be inferred from various kinds of input. Our experiments demonstrate competitive results, both qualitatively and quantitatively, for the challenging tasks of 3D reconstruction from single images, noisy point clouds and coarse discrete voxel grids. We believe that occupancy networks will become a useful tool in a wide variety of learning-based 3D tasks.