ICML 2024 Papers

In this paper, we use matrix information theory as an analytical tool to analyze the dynamics of the information interplay between data representations and classification head vectors in the supervised learning process. Specifically, inspired by the theory of Neural Collapse, we introduce matrix mutual information ratio (MIR) and matrix entropy difference ratio (HDR) to assess the interactions of data representation and class classification heads in supervised learning, and we determine the theoretical optimal values for MIR and HDR when Neural Collapse happens. Our experiments show that MIR and HDR can effectively explain many phenomena occurring in neural networks, for example, the standard supervised training dynamics, linear mode connectivity, and the performance of label smoothing and pruning. Additionally, we use MIR and HDR to gain insights into the dynamics of grokking, which is an intriguing phenomenon observed in supervised training, where the model demonstrates generalization capabilities long after it has learned to fit the training data. Furthermore, we introduce MIR and HDR as loss terms in supervised and semi-supervised learning to optimize the information interactions among samples and classification heads. The empirical results provide evidence of the method's effectiveness, demonstrating that the utilization of MIR and HDR not only aids in comprehending the dynamics throughout the training process but can also enhances the training procedure itself.

Estimating mutual correlations between random variables or data streams is essential for intelligent behavior and decision-making. As a fundamental quantity for measuring statistical relationships, mutual information has been extensively studied and utilized for its generality and equitability. However, existing methods often lack the efficiency needed for real-time applications, such as test-time optimization of a neural network, or the differentiability required for end-to-end learning, like histograms. We introduce a neural network called InfoNet, which directly outputs mutual information estimations of data streams by leveraging the attention mechanism and the computational efficiency of deep learning infrastructures. By maximizing a dual formulation of mutual information through large-scale simulated training, our approach circumvents time-consuming test-time optimization and offers generalization ability. We evaluate the effectiveness and generalization of our proposed mutual information estimation scheme on various families of distributions and applications. Our results demonstrate that InfoNet and its training process provide a graceful efficiency-accuracy trade-off and order-preserving properties. We will make the code and models available as a comprehensive toolbox to facilitate studies in different fields requiring real-time mutual information estimation.

We consider the problem of localizing change points in high-dimensional linear regression. We propose an Approximate Message Passing (AMP) algorithm for estimating both the signals and the change point locations. Assuming Gaussian covariates, we give an exact asymptotic characterization of its estimation performance in the limit where the number of samples grows proportionally to the signal dimension. Our algorithm can be tailored to exploit any prior information on the signal, noise, and change points. It also enables uncertainty quantification in the form of an efficiently computable approximate posterior distribution, whose asymptotic form we characterize exactly. We validate our theory via numerical experiments, and demonstrate the favorable performance of our estimators on both synthetic data and images.

Computational screening of naturally occurring proteins has the potential to identify efficient catalysts among the hundreds of millions of sequences that remain uncharacterized. Current experimental methods remain time, cost and labor intensive, limiting the number of enzymes they can reasonably screen. In this work, we propose a computational framework for in-silico enzyme screening. Through a contrastive objective, we train CLIPZyme to encode and align representations of enzyme structures and reaction pairs. With no standard computational baseline, we compare CLIPZyme to existing EC (enzyme commission) predictors applied to virtual enzyme screening and show improved performance in scenarios where limited information on the reaction is available (BEDROC$_{85}$ of 44.69%). Additionally, we evaluate combining EC predictors with CLIPZyme and show its generalization capacity on both unseen reactions and protein clusters.