相关论文: Relu and softplus neural nets as zero-sum turn-bas…

It has been widely assumed that a neural network cannot be recovered from its outputs, as the network depends on its parameters in a highly nonlinear way. Here, we prove that in fact it is often possible to identify the architecture,…

Verifying the input-output relationships of a neural network so as to achieve some desired performance specification is a difficult, yet important, problem due to the growing ubiquity of neural nets in many engineering applications. We use…

Attribution methods explain which input features drive a model's prediction, making them central to model debugging and mechanistic interpretability. Yet backward attribution methods, including gradients, LRP, and transformer-specific…

Markov games model interactions among multiple players in a stochastic, dynamic environment. Each player in a Markov game maximizes its expected total discounted reward, which depends upon the policies of the other players. We formulate a…

This paper addresses zero-sum ``turn'' games, in which only one player can make decisions at each state. We show that pure saddle-point state-feedback policies for turn games can be constructed from dynamic programming fixed-point equations…

We propose a novel Shapley value approach to help address neural networks' interpretability and "vanishing gradient" problems. Our method is based on an accurate analytical approximation to the Shapley value of a neuron with ReLU…

Definable zero-sum stochastic games involve a finite number of states and action sets, reward and transition functions that are definable in an o-minimal structure. Prominent examples of such games are finite, semi-algebraic or globally…

Neural networks have demonstrated a wide range of successes, but their ``black box" nature raises concerns about transparency and reliability. Previous research on ReLU networks has sought to unwrap these networks into linear models based…

Estimating the unknown reward functions driving agents' behaviors is of central interest in inverse reinforcement learning and game theory. To tackle this problem, we develop a unified framework for reward function recovery in two-player…

It is difficult to describe in mathematical terms what a neural network trained on data represents. On the other hand, there is a growing mathematical understanding of what neural networks are in principle capable of representing.…

In this paper, we formulate inverse reinforcement learning (IRL) as an expert-learner interaction whereby the optimal performance intent of an expert or target agent is unknown to a learner agent. The learner observes the states and…

Rectified linear unit (ReLU) is a widely used activation function for deep convolutional neural networks. However, because of the zero-hard rectification, ReLU networks miss the benefits from negative values. In this paper, we propose a…

This paper presents a general framework for exploiting the representational capacity of neural networks to approximate complex, nonlinear reward functions in the context of solving the inverse reinforcement learning (IRL) problem. We show…

Neural networks with ReLU activation play a key role in modern machine learning. Understanding the functions represented by ReLU networks is a major topic in current research as this enables a better interpretability of learning processes.…

We prove that, for the fundamental regression task of learning a single neuron, training a one-hidden layer ReLU network of any width by gradient flow from a small initialisation converges to zero loss and is implicitly biased to minimise…

Artificial Neural Networks have shown impressive success in very different application cases. Choosing a proper network architecture is a critical decision for a network's success, usually done in a manual manner. As a straightforward…

Neural networks can be trained to solve regression problems by using gradient-based methods to minimize the square loss. However, practitioners often prefer to reformulate regression as a classification problem, observing that training on…

Reinforcement Learning Algorithms (RLA) are useful machine learning tools to understand how decision makers react to signals. It is known that RLA converge towards the pure Nash Equilibria (NE) of finite congestion games and more generally,…

We prove several hardness results for training depth-2 neural networks with the ReLU activation function; these networks are simply weighted sums (that may include negative coefficients) of ReLUs. Our goal is to output a depth-2 neural…

In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each…