Related papers: p-Adic Statistical Field Theory and Deep Belief Ne…

We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The…

We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural…

Spiking neural networks (SNNs) are promising in a bio-plausible coding for spatio-temporal information and event-driven signal processing, which is very suited for energy-efficient implementation in neuromorphic hardware. However, the…

Large-scale deep neural networks are both memory intensive and computation-intensive, thereby posing stringent requirements on the computing platforms. Hardware accelerations of deep neural networks have been extensively investigated in…

Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…

Neural network field theory (NN-FT) formulates field theory in terms of a network architecture and a density on its parameters. We derive Schwinger--Dyson equations and Ward identities in NN-FT and utilize them to study anomalies. The…

Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…

Softmax attention is the principle backbone of foundation models for various artificial intelligence applications, yet its quadratic complexity in sequence length can limit its inference throughput in long-context settings. To address this…

In this paper, we leverage a recent deep kernel representer theorem to connect kernel based learning and (deep) neural networks in order to understand their interplay. In particular, we show that the use of special types of kernels yields…

Neural networks (NNs) are known for their high predictive accuracy in complex learning problems. Beside practical advantages, NNs also indicate favourable theoretical properties such as universal approximation (UA) theorems. Binarized…

Deep learning's performance has been extensively recognized recently. Graph neural networks (GNNs) are designed to deal with graph-structural data that classical deep learning does not easily manage. Since most GNNs were created using…

In this chapter we take a look at the universal approximation question for stochastic feedforward neural networks. In contrast to deterministic networks, which represent mappings from a set of inputs to a set of outputs, stochastic networks…

Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that…

We show that deep narrow Boltzmann machines are universal approximators of probability distributions on the activities of their visible units, provided they have sufficiently many hidden layers, each containing the same number of units as…

The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep…

Two of the most popular modelling paradigms in computer vision are feed-forward neural networks (FFNs) and probabilistic graphical models (GMs). Various connections between the two have been studied in recent works, such as e.g. expressing…

Deep learning's success has been widely recognized in a variety of machine learning tasks, including image classification, audio recognition, and natural language processing. As an extension of deep learning beyond these domains, graph…

Recent advances in neural algorithmic reasoning with graph neural networks (GNNs) are propped up by the notion of algorithmic alignment. Broadly, a neural network will be better at learning to execute a reasoning task (in terms of sample…

The power budget for embedded hardware implementations of Deep Learning algorithms can be extremely tight. To address implementation challenges in such domains, new design paradigms, like Approximate Computing, have drawn significant…

Deep-learning density functional theory (DFT) shows great promise to significantly accelerate material discovery and potentially revolutionize materials research. However, current research in this field primarily relies on data-driven…