相关论文: Resolving the Geometric Locus Dilemma for Support …

A central goal of meta-learning is to find a learning rule that enables fast adaptation across a set of tasks, by learning the appropriate inductive bias for that set. Most meta-learning algorithms try to find a \textit{global} learning…

Linear discriminant analysis (LDA) has been a useful tool in pattern recognition and data analysis research and practice. While linearity of class boundaries cannot always be expected, nonlinear projections through pre-trained deep neural…

The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or…

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration…

Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute.…

When choosing between options, we must solve an important binding problem. The values of the options must be associated with information about the action needed to select them. We hypothesize that the brain solves this binding problem…

Graph matching can be formalized as a combinatorial optimization problem, where there are corresponding relationships between pairs of nodes that can be represented as edges. This problem becomes challenging when there are potential…

Embeddings play a pivotal role across various disciplines, offering compact representations of complex data structures. Randomized methods like Johnson-Lindenstrauss (JL) provide state-of-the-art and essentially unimprovable theoretical…

The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that areinherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2)…

Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…

A fundamental challenge in diagnostic imaging is the phenomenon of topological equivalence, where benign and malignant structures share global topology but differ in critical geometric detail, leading to diagnostic errors in both…

In many applications, one has side information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks "nearby" that…

We introduce a new numerical method based on machine learning to approximate the solution of elliptic partial differential equations with collocation using a set of sigmoidal functions. We show that a feedforward neural network with a…

A major problem in machine learning is that of inductive bias: how to choose a learner's hypothesis space so that it is large enough to contain a solution to the problem being learnt, yet small enough to ensure reliable generalization from…

The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…

We study the decidability of the Skolem Problem, the Positivity Problem, and the Ultimate Positivity Problem for linear recurrences with real number initial values and real number coefficients in the bit-model of real computation. We show…

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of…

Learning curves are a concept from social sciences that has been adopted in the context of machine learning to assess the performance of a learning algorithm with respect to a certain resource, e.g., the number of training examples or the…

Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete…

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel…