Several recent unsupervised learning methods use probabilistic approaches to solve combinatorial optimization (CO) problems based on the assumption of statistically independent solution variables. We demonstrate that this assumption imposes performance limitations in particular on difficult problem instances. Our results corroborate that an autoregressive approach which captures statistical dependencies among solution variables yields superior performance on many popular CO problems. We introduce subgraph tokenization in which the configuration of a set of solution variables is represented by a single token. This tokenization technique alleviates the drawback of the long sequential sampling procedure which is inherent to autoregressive methods without sacrificing expressivity. Importantly, we theoretically motivate an annealed entropy regularization and show empirically that it is essential for efficient and stable learning.

By Lemma 5.2, this is Pr ( x K

We study fixed-design online learning where the learner is allowed to choose the order of the datapoints in order to minimize their regret (aka self-directed online learning).

The Naïve Mean Field (NMF) approximation is widely employed in modern Machine Learning due to the huge computational gains it bestows on the statistician. Despite its popularity in practice, theoretical guarantees for high-dimensional problems are only available under strong structural assumptions (e.g., sparsity). Moreover, existing theory often does not explain empirical observations noted in the existing literature. In this paper, we take a step towards addressing these problems by deriving sharp asymptotic characterizations for the NMF approximation in high-dimensional linear regression. Our results apply to a wide class of natural priors and allow for model mismatch (i.e., the underlying statistical model can be different from the fitted model).

Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields such as hyperparameter optimization, metalearning, and reinforcement learning. Recent results have shown that simple alternating (implicit) gradient-based algorithms can match the convergence rate of single-level gradient descent (GD) when addressing bilevel problems with a strongly convex lower-level objective. However, it remains unclear whether this result can be generalized to bilevel problems beyond this basic setting. In this paper, we first introduce a stationary metric for the considered bilevel problems, which generalizes the existing metric, for a nonconvex lower-level objective that satisfies the Polyak-Łojasiewicz (PL) condition.

This paper presents an innovative visual reasoning approach to enhancing instance verification and retrieval, particularly in situations where a fine-tuning set is unavailable. The widely-used SPatial verification (SP) method, despite its efficacy, relies on a spatial model and the hypothesis-testing strategy for instance recognition, leading to inherent limitations, including the assumption of planar structures and neglect of topological relations among features. To address these shortcomings, we introduce a pioneering technique that replaces the spatial model with a topological one within the RANSAC process. We propose bio-inspired saccade and fovea functions to verify the topological consistency among features, effectively circumventing the issues associated with SP's spatial model. Our experimental results demonstrate that our method significantly outperforms SP, achieving stateof-the-art performance in non-fine-tuning retrieval. Furthermore, our approach can enhance performance when used in conjunction with fine-tuned features. Importantly, our method retains high explainability and is lightweight, offering a practical and adaptable solution for a variety of real-world applications. Our code can be found through this link.

On a high level, EDGI follows Diffuser [1]. We illustrate the architecture in Figure 1 in the main paper. We use a kernel size of 5. This is essentially an equivariant version of LayerNorm. In the geometric layers, the input state is split into scalar and vector components.

Embodied agents operate in a structured world, often solving tasks with spatial, temporal, and permutation symmetries. Most algorithms for planning and modelbased reinforcement learning (MBRL) do not take this rich geometric structure into account, leading to sample inefficiency and poor generalization.