Related papers: Reachability In Simple Neural Networks

Largest theoretical contribution to Neural Networks comes from VC Dimension which characterizes the sample complexity of classification model in a probabilistic view and are widely used to study the generalization error. So far in the…

In this paper we consider the limiting case of neural networks (NNs) architectures when the number of neurons in each hidden layer and the number of hidden layers tend to infinity thus forming a continuum, and we derive approximation errors…

Learning to predict solutions to real-valued combinatorial graph problems promises efficient approximations. As demonstrated based on the NP-hard edge clique cover number, recurrent neural networks (RNNs) are particularly suited for this…

A natural and informal approach to verifiable (or zero-knowledge) ML inference over floating-point data is: ``prove that each layer was computed correctly up to tolerance $\delta$; therefore the final output is a reasonable inference…

Unordered data Petri nets (UDPN) are an extension of classical Petri nets with tokens that carry data from an infinite domain and where transitions may check equality and disequality of tokens. UDPN are well-structured, so the coverability…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

We introduce two algorithms for computing tight guarantees on the probabilistic robustness of Bayesian Neural Networks (BNNs). Computing robustness guarantees for BNNs is a significantly more challenging task than verifying the robustness…

Deployment of deep neural networks (DNNs) in safety- or security-critical systems requires provable guarantees on their correct behaviour. A common requirement is robustness to adversarial perturbations in a neighbourhood around an input.…

This article contributes to the current statistical theory of deep neural networks (DNNs). It was shown that DNNs are able to circumvent the so--called curse of dimensionality in case that suitable restrictions on the structure of the…

Sustainable research on computational models of neuronal networks requires published models to be understandable, reproducible, and extendable. Missing details or ambiguities about mathematical concepts and assumptions, algorithmic…

This paper presents an algorithm for searching for the minimum number of neurons in fully connected layers of an arbitrary network solving given problem, which does not require multiple training of the network with different number of…

Imposing constraints on the output of a Deep Neural Net is one way to improve the quality of its predictions while loosening the requirements for labeled training data. Such constraints are usually imposed as soft constraints by adding new…

Modern neural networks are often quite wide, causing large memory and computation costs. It is thus of great interest to train a narrower network. However, training narrow neural nets remains a challenging task. We ask two theoretical…

Deep neural networks (DNNs) are vulnerable to shortcut learning: rather than learning the intended task, they tend to draw inconclusive relationships between their inputs and outputs. Shortcut learning is ubiquitous among many failure cases…

The ultimate goal of verification is to guarantee the safety of deployed neural networks. Here, we claim that all the state-of-the-art verifiers we are aware of fail to reach this goal. Our key insight is that theoretical soundness…

Although neural networks can achieve very high predictive performance on various different tasks such as image recognition or natural language processing, they are often considered as opaque "black boxes". The difficulty of interpreting the…

Graph Neural Networks (GNNs) have become the standard approach for learning and reasoning over relational data, leveraging the message-passing mechanism that iteratively propagates node embeddings through graph structures. While GNNs have…

Great successes of deep neural networks have been witnessed in various real applications. Many algorithmic and implementation techniques have been developed, however, theoretical understanding of many aspects of deep neural networks is far…

Bridging logical and algorithmic reasoning with modern machine learning techniques is a fundamental challenge with potentially transformative impact. On the algorithmic side, many NP-hard problems can be expressed as integer programs, in…

We present new algorithms for a posteriori verification of neural networks (NNs) approximating solutions to PDEs. These verification algorithms compute accurate estimates of $L^p$ norms of NNs and their derivatives. When combined with…