Using Cooperative Game Theory to Prune Neural Networks

We show how solution concepts from cooperative game theory can be used to tackle the problem of pruning neural networks. The ever-growing size of deep neural networks (DNNs) increases their performance, but also their computational requirements. We introduce a method called Game Theory Assisted Pruning (GTAP), which reduces the neural network's size while preserving its predictive accuracy. GTAP is based on eliminating neurons in the network based on an estimation of their joint impact on the prediction quality through game theoretic solutions. Specifically, we use a power index akin to the Shapley value or Banzhaf index, tailored using a procedure similar to Dropout (commonly used to tackle overfitting problems in machine learning). Empirical evaluation of both feedforward networks and convolutional neural networks shows that this method outperforms existing approaches in the achieved tradeoff between the number of parameters and model accuracy.

Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees

Tabular data is hard to acquire and is subject to missing values. This paper proposes a novel approach to generate and impute mixed-type (continuous and categorical) tabular data using score-based diffusion and conditional flow matching. Contrary to previous work that relies on neural networks as function approximators, we instead utilize XGBoost, a popular Gradient-Boosted Tree (GBT) method. In addition to being elegant, we empirically show on various datasets that our method i) generates highly realistic synthetic data when the training dataset is either clean or tainted by missing data and ii) generates diverse plausible data imputations. Our method often outperforms deep-learning generation methods and can trained in parallel using CPUs without the need for a GPU. To make it easily accessible, we release our code through a Python library on PyPI and an R package on CRAN.

Explainability Techniques for Chemical Language Models

Explainability techniques are crucial in gaining insights into the reasons behind the predictions of deep learning models, which have not yet been applied to chemical language models. We propose an explainable AI technique that attributes the importance of individual atoms towards the predictions made by these models. Our method backpropagates the relevance information towards the chemical input string and visualizes the importance of individual atoms. We focus on self-attention Transformers operating on molecular string representations and leverage a pretrained encoder for finetuning. We showcase the method by predicting and visualizing solubility in water and organic solvents. We achieve competitive model performance while obtaining interpretable predictions, which we use to inspect the pretrained model.

Charting the Topography of the Neural Network Landscape with Thermal-Like Noise

The training of neural networks is a complex, high-dimensional, non-convex and noisy optimization problem whose theoretical understanding is interesting both from an applicative perspective and for fundamental reasons. A core challenge is to understand the geometry and topography of the landscape that guides the optimization. In this work, we employ standard Statistical Mechanics methods, namely, phase-space exploration using Langevin dynamics, to study this landscape for an over-parameterized fully connected network performing a classification task on random data. Analyzing the fluctuation statistics, in analogy to thermal dynamics at a constant temperature, we infer a clear geometric description of the low-loss region. We find that it is a low-dimensional manifold whose dimension can be readily obtained from the fluctuations. Furthermore, this dimension is controlled by the number of data points that reside near the classification decision boundary. Importantly, we find that a quadratic approximation of the loss near the minimum is fundamentally inadequate due to the exponential nature of the decision boundary and the flatness of the low-loss region. This causes the dynamics to sample regions with higher curvature at higher temperatures, while producing quadratic-like statistics at any given temperature. We explain this behavior by a simplified loss model which is analytically tractable and reproduces the observed fluctuation statistics.

Diffusion models with location-scale noise

Diffusion Models (DMs) are powerful generative models that add Gaussian noise to the data and learn to remove it. We wanted to determine which noise distribution (Gaussian or non-Gaussian) led to better generated data in DMs. Since DMs do not work by design with non-Gaussian noise, we built a framework that allows reversing a diffusion process with non-Gaussian location-scale noise. We use that framework to show that the Gaussian distribution performs the best over a wide range of other distributions (Laplace, Uniform, t, Generalized-Gaussian).

Safe Reinforcement Learning From Pixels Using a Stochastic Latent Representation

We address the problem of safe reinforcement learning from pixel observations. Inherent challenges in such settings are (1) a trade-off between reward optimization and adhering to safety constraints, (2) partial observability, and (3) high-dimensional observations. We formalize the problem in a constrained, partially observable Markov decision process framework, where an agent obtains distinct reward and safety signals. To address the curse of dimensionality, we employ a novel safety critic using the stochastic latent actor-critic (SLAC) approach. The latent variable model predicts rewards and safety violations, and we use the safety critic to train safe policies. Using well-known benchmark environments, we demonstrate competitive performance over existing approaches with respects to computational requirements, final reward return, and satisfying the safety constraints.

Neural Payoff Machines: Predicting Fair and Stable Payoff Allocations Among Team Members

In many multi-agent settings, participants can form teams to achieve collective outcomes that may far surpass their individual capabilities. Measuring the relative contributions of agents and allocating them shares of the reward that promote long-lasting cooperation are difficult tasks. Cooperative game theory offers solution concepts identifying distribution schemes, such as the Shapley value, that fairly reflect the contribution of individuals to the performance of the team or the Core, which reduces the incentive of agents to abandon their team. Applications of such methods include identifying influential features and sharing the costs of joint ventures or team formation. Unfortunately, using these solutions requires tackling a computational barrier as they are hard to compute, even in restricted settings. In this work, we show how cooperative game-theoretic solutions can be distilled into a learned model by training neural networks to propose fair and stable payoff allocations. We show that our approach creates models that can generalize to games far from the training distribution and can predict solutions for more players than observed during training. An important application of our framework is Explainable AI: our approach can be used to speed-up Shapley value computations on many instances.

Lyapunov Exponents for Diversity in Differentiable Games

Ridge Rider (RR) is an algorithm for finding diverse solutions to optimization problems by following eigenvectors of the Hessian ("ridges"). RR is designed for conservative gradient systems (i.e., settings involving a single loss function), where it branches at saddles - easy-to-find bifurcation points. We generalize this idea to non-conservative, multi-agent gradient systems by proposing a method - denoted Generalized Ridge Rider (GRR) - for finding arbitrary bifurcation points. We give theoretical motivation for our method by leveraging machinery from the field of dynamical systems. We construct novel toy problems where we can visualize new phenomena while giving insight into high-dimensional problems of interest. Finally, we empirically evaluate our method by finding diverse solutions in the iterated prisoners' dilemma and relevant machine learning problems including generative adversarial networks.

Gradients are Not All You Need

Differentiable programming techniques are widely used in the community and are responsible for the machine learning renaissance of the past several decades. While these methods are powerful, they have limits. In this short report, we discuss a common chaos based failure mode which appears in a variety of differentiable circumstances, ranging from recurrent neural networks and numerical physics simulation to training learned optimizers. We trace this failure to the spectrum of the Jacobian of the system under study, and provide criteria for when a practitioner might expect this failure to spoil their differentiation based optimization algorithms.

Gotta Go Fast When Generating Data with Score-Based Models

Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by reversing it (thereby going from noise to data). Unfortunately, current score-based models generate data very slowly due to the sheer number of score network evaluations required by numerical SDE solvers. In this work, we aim to accelerate this process by devising a more efficient SDE solver. Existing approaches rely on the Euler-Maruyama (EM) solver, which uses a fixed step size. We found that naively replacing it with other SDE solvers fares poorly - they either result in low-quality samples or become slower than EM. To get around this issue, we carefully devise an SDE solver with adaptive step sizes tailored to score-based generative models piece by piece. Our solver requires only two score function evaluations, rarely rejects samples, and leads to high-quality samples. Our approach generates data 2 to 10 times faster than EM while achieving better or equal sample quality. For high-resolution images, our method leads to significantly higher quality samples than all other methods tested. Our SDE solver has the benefit of requiring no step size tuning.