Few-shot object detection (FSOD) aims to detect new objects based on few annotated samples. To alleviate the impact of few samples, enhancing the generalization and discrimination abilities of detectors on new objects plays an important role. In this paper, we explore employing Singular Value Decomposition (SVD) to boost both the generalization and discrimination abilities. In specific, we propose a novel method, namely, SVD-Dictionary enhancement, to build two separated spaces based on the sorted singular values. Concretely, the eigenvectors corresponding to larger singular values are used to build the generalization space in which localization is performed, as these eigenvectors generally suppress certain variations (e.g., the variation of styles) and contain intrinsical characteristics of objects. Meanwhile, since the eigenvectors corresponding to relatively smaller singular values may contain richer category-related information, we can utilize them to build the discrimination space in which classification is performed.

We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely performance is measured with respect to a given hypothesis class. This allows to avoid known computational hardness results and improper algorithms based on convex relaxations. We show how several families of unsupervised learning models, which were previously only analyzed under probabilistic assumptions and are otherwise provably intractable, can be efficiently learned in our framework by convex optimization.

Given only observational data $X = g(Z)$, where both the latent variables $Z$ and the generating process $g$ are unknown, recovering $Z$ is ill-posed without additional assumptions. Existing methods often assume linearity or rely on auxiliary supervision and functional constraints. However, such assumptions are rarely verifiable in practice, and most theoretical guarantees break down under even mild violations, leaving uncertainty about how to reliably understand the hidden world. To make identifiability actionable in the real-world scenarios, we take a complementary view: in the general settings where full identifiability is unattainable, what can still be recovered with guarantees, and what biases could be universally adopted? We introduce the problem of diverse dictionary learning to formalize this view. Specifically, we show that intersections, complements, and symmetric differences of latent variables linked to arbitrary observations, along with the latent-to-observed dependency structure, are still identifiable up to appropriate indeterminacies even without strong assumptions. These set-theoretic results can be composed using set algebra to construct structured and essential views of the hidden world, such as genus-differentia definitions. When sufficient structural diversity is present, they further imply full identifiability of all latent variables. Notably, all identifiability benefits follow from a simple inductive bias during estimation that can be readily integrated into most models. We validate the theory and demonstrate the benefits of the bias on both synthetic and real-world data.

Neural Information Processing Systems http://nips.cc/

Our algorithm is a simple alternating minimization procedure that switches between $\ell_1$ minimization and gradient descent in alternate steps. Dictionary learning and specifically alternating minimization algorithms for dictionary learning are well studied both theoretically and empirically. However, in contrast to previous theoretical analyses for this problem, we replace a condition on the operator norm (that is, the largest magnitude singular value) of the true underlying dictionary $A^*$ with a condition on the matrix infinity norm (that is, the largest magnitude term). This not only allows us to get convergence rates for the error of the estimated dictionary measured in the matrix infinity norm, but also ensures that a random initialization will provably converge to the global optimum. Our guarantees are under a reasonable generative model that allows for dictionaries with growing operator norms, and can handle an arbitrary level of overcompleteness, while having sparsity that is information theoretically optimal. We also establish upper bounds on the sample complexity of our algorithm.

Visual perception plays a critical role in obtaining external information.