Related papers: Relu and softplus neural nets as zero-sum turn-bas…

Reverse engineering deep ReLU networks is a critical problem in understanding the complex behavior and interpretability of neural networks. In this research, we present a novel method for reconstructing deep ReLU networks by leveraging…

We present a new algorithm to generate minimal, stable, and symbolic corrections to an input that will cause a neural network with ReLU activations to change its output. We argue that such a correction is a useful way to provide feedback to…

We study a common challenge in reinforcement learning for large language models (LLMs): the Zero-Reward Assumption, where non-terminal actions (i.e., intermediate token generations) receive zero task-specific immediate reward, while only…

We study a robust optimal stopping problem with respect to a set $\cP$ of mutually singular probabilities. This can be interpreted as a zero-sum controller-stopper game in which the stopper is trying to maximize its pay-off while an adverse…

We present empirical evidence that neural networks with ReLU and Absolute Value activations learn distance-based representations. We independently manipulate both distance and intensity properties of internal activations in trained models,…

We study the transfer of rewards learned using inverse reinforcement learning from expert demonstrations in one environment to reinforcement learning in a new, different environment. This arises naturally when demonstrations are collected…

Game theory provides the gold standard for analyzing adversarial engagements, offering strong optimality guarantees. However, these guarantees often become brittle when assumptions such as perfect information are violated. Reinforcement…

A main open question in contemporary AI research is quantifying the forms of reasoning neural networks can perform when perfectly trained. This paper answers this by interpreting reasoning tasks as circuit emulation, where the gates define…

We present a novel deep graphical representation that seamlessly merges principles of game theory with laws of statistical mechanics. It performs feature extraction, dimensionality reduction, and pattern classification within a single…

Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…

Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex…

A ReLU neural network determines/is a continuous piecewise linear map from an input space to an output space. The weights in the neural network determine a decomposition of the input space into convex polytopes and on each of these…

We present a greedy-based approach to construct an efficient single hidden layer neural network with the ReLU activation that approximates a target function. In our approach we obtain a shallow network by utilizing a greedy algorithm with…

The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…

We consider a discrete-time nonatomic routing game with variable demand and uncertain costs. Given a routing network with single origin and destination, the cost function of each edge depends on some uncertain persistent state parameter. At…

The Shapley value---probably the most important normative payoff division scheme in coalitional games---has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world…

Neural networks have been widely used to solve complex real-world problems. Due to the complicate, nonlinear, non-convex nature of neural networks, formal safety guarantees for the output behaviors of neural networks will be crucial for…

Network games provide a powerful framework for modeling agent interactions in networked systems, where players are represented by nodes in a graph and their payoffs depend on the actions taken by their neighbors. Extending the framework of…

In this research, we discuss a problem of calculating the Shapley value in bankruptcy games. We show that the decision problem of computing the Shapley value in bankruptcy games is NP-complete. We also investigate the relationship between…

We develop exact representations of training two-layer neural networks with rectified linear units (ReLUs) in terms of a single convex program with number of variables polynomial in the number of training samples and the number of hidden…