Linkages are essentially determined by similarity measures that may be derived from multiple perspectives. For example, spatial linkages are usually generated based on localities of heterogeneous data, whereas semantic linkages can come from various properties, such as different physical meanings behind social relations. Many existing metric learning models focus on spatial linkages, but leave the rich semantic factors unconsidered. Similarities based on these models are usually overdetermined on linkages.

Dropout has been witnessed with great success in training deep neural networks by independently zeroing out the outputs of neurons at random. It has also received a surge of interest for shallow learning, e.g., logistic regression. However, the independent sampling for dropout could be suboptimal for the sake of convergence. In this paper, we propose to use multinomial sampling for dropout, i.e., sampling features or neurons according to a multinomial distribution with different probabilities for different features/neurons. To exhibit the optimal dropout probabilities, we analyze the shallow learning with multinomial dropout and establish the risk bound for stochastic optimization. By minimizing a sampling dependent factor in the risk bound, we obtain a distribution-dependent dropout with sampling probabilities dependent on the second order statistics of the data distribution. To tackle the issue of evolving distribution of neurons in deep learning, we propose an efficient adaptive dropout (named evolutional dropout) that computes the sampling probabilities on-the-fly from a mini-batch of examples. Empirical studies on several benchmark datasets demonstrate that the proposed dropouts achieve not only much faster convergence and but also a smaller testing error than the standard dropout. For example, on the CIFAR-100 data, the evolutional dropout achieves relative improvements over 10% on the prediction performance and over 50% on the convergence speed compared to the standard dropout.

This paper questions the effectiveness of a modern predictive uncertainty quantification approach, called evidential deep learning (EDL), in which a single neural network model is trained to learn a meta distribution over the predictive distribution by minimizing a specific objective function. Despite their perceived strong empirical performance on downstream tasks, a line of recent studies by Bengs et al. identify limitations of the existing methods to conclude their learned epistemic uncertainties are unreliable, e.g., in that they are non-vanishing even with infinite data. Building on and sharpening such analysis, we 1) provide a sharper understanding of the asymptotic behavior of a wide class of EDL methods by unifying various objective functions; 2) reveal that the EDL methods can be better interpreted as an out-of-distribution detection algorithm based on energy-based-models; and 3) conduct extensive ablation studies to better assess their empirical effectiveness with real-world datasets. Through all these analyses, we conclude that even when EDL methods are empirically effective on downstream tasks, this occurs despite their poor uncertainty quantification capabilities. Our investigation suggests that incorporating model uncertainty can help EDL methods faithfully quantify uncertainties and further improve performance on representative downstream tasks, albeit at the cost of additional computational complexity.

In this work, we propose Asynchronous Perception Machine (APM), a computationally-efficient architecture for test-time-training (TTT). APM can process patches of an image one at a time in any order asymmetrically, and still encode semantic-awareness in the net. We demonstrate APM's ability to recognize out-of-distribution images without dataset-specific pre-training, augmentation or any-pretext task. APM offers competitive performance over existing TTT approaches. To perform TTT, APM just distills test sample's representation once.

The persistent challenge of bias in machine learning models necessitates robust solutions to ensure parity and equal treatment across diverse groups, particularly in classification tasks.

Recent work has shown how to embed differentiable optimization problems (that is, problems whose solutions can be backpropagated through) as layers within deep learning architectures. This method provides a useful inductive bias for certain problems, but existing software for differentiable optimization layers is rigid and difficult to apply to new settings. In this paper, we propose an approach to differentiating through disciplined convex programs, a subclass of convex optimization problems used by domain-specific languages (DSLs) for convex optimization. We introduce disciplined parametrized programming, a subset of disciplined convex programming, and we show that every disciplined parametrized program can be represented as the composition of an affine map from parameters to problem data, a solver, and an affine map from the solver's solution to a solution of the original problem (a new form we refer to as affine-solver-affine form). We then demonstrate how to efficiently differentiate through each of these components, allowing for end-to-end analytical differentiation through the entire convex program. We implement our methodology in version 1.1 of CVXPY, a popular Python-embedded DSL for convex optimization, and additionally implement differentiable layers for disciplined convex programs in PyTorch and TensorFlow 2.0. Our implementation significantly lowers the barrier to using convex optimization problems in differentiable programs. We present applications in linear machine learning models and in stochastic control, and we show that our layer is competitive (in execution time) compared to specialized differentiable solvers from past work.

Federated learning (FL) allows collaborative machine learning training without sharing private data. While most FL methods assume identical data domains across clients, real-world scenarios often involve heterogeneous data domains. Federated Prototype Learning (FedPL) addresses this issue, using mean feature vectors as prototypes to enhance model generalization. However, existing FedPL methods create the same number of prototypes for each client, leading to cross-domain performance gaps and disparities for clients with varied data distributions. To mitigate cross-domain feature representation variance, we introduce FedPLVM, which establishes variance-aware dual-level prototypes clustering and employs a novel α- sparsity prototype loss. The dual-level prototypes clustering strategy creates local clustered prototypes based on private data features, then performs global prototypes clustering to reduce communication complexity and preserve local data privacy.

Sequential memory, the ability to form and accurately recall a sequence of events or stimuli in the correct order, is a fundamental prerequisite for biological and artificial intelligence as it underpins numerous cognitive functions (e.g., language comprehension, planning, episodic memory formation, etc.) However, existing methods of sequential memory suffer from catastrophic forgetting, limited capacity, slow iterative learning procedures, low-order Markov memory, and, most importantly, the inability to represent and generate multiple valid future possibilities stemming from the same context. Inspired by biologically plausible neuroscience theories of cognition, we propose Predictive Attractor Models (PAM), a novel sequence memory architecture with desirable generative properties. PAM is a streaming model that learns a sequence in an online, continuous manner by observing each input only once. Additionally, we find that PAM avoids catastrophic forgetting by uniquely representing past context through lateral inhibition in cortical minicolumns, which prevents new memories from overwriting previously learned knowledge. PAM generates future predictions by sampling from a union set of predicted possibilities; this generative ability is realized through an attractor model trained alongside the predictor. We show that PAM is trained with local computations through Hebbian plasticity rules in a biologically plausible framework. Other desirable traits (e.g., noise tolerance, CPU-based learning, capacity scaling) are discussed throughout the paper. Our findings suggest that PAM represents a significant step forward in the pursuit of biologically plausible and computationally efficient sequential memory models, with broad implications for cognitive science and artificial intelligence research.

Graph neural networks (GNNs) have recently emerged as powerful tools for addressing complex optimization problems. It has been theoretically demonstrated that GNNs can universally approximate the solution mapping functions of linear programming (LP) problems. However, these theoretical results typically require GNNs to have large parameter sizes. Conversely, empirical experiments have shown that relatively small GNNs can solve LPs effectively, revealing a significant discrepancy between theoretical predictions and practical observations. In this work, we aim to bridge this gap by providing a theoretical foundation for the effectiveness of smaller GNNs. We prove that polylogarithmic-depth, constant-width GNNs are sufficient to solve packing and covering LPs, two widely used classes of LPs. Our proof leverages the capability of GNNs to simulate a variant of the gradient descent algorithm on a carefully selected potential function. Additionally, we introduce a new GNN architecture, termed GD-Net. Experimental results demonstrate that GD-Net significantly outperforms conventional GNN structures while using fewer parameters.

Operator learning problems arise in many key areas of scientific computing where Partial Differential Equations (PDEs) are used to model physical systems. In such scenarios, the operators map between Banach or Hilbert spaces. In this work, we tackle the problem of learning operators between Banach spaces, in contrast to the vast majority of past works considering only Hilbert spaces. We focus on learning holomorphic operators - an important class of problems with many applications.