Related papers: A Refined Difference Field Theory for Symbolic Sum…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
We discuss a systematic way to dimensionally regularize divergent sums arising in field theories with an arbitrary number of physical compact dimensions or finite temperature. The method preserves the same symmetries of the action as the…
Neural networks and other machine learning models compute continuous representations, while humans communicate with discrete symbols. Reconciling these two forms of communication is desirable to generate human-readable interpretations or to…
Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They…
An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation…
We discuss the relation of the two types of sums in the Rogers-Schur-Ramanujan identities with the Bose-Fermi correspondence of massless quantum field theory in $1+1$ dimensions. One type, which generalizes to sums which appear in the…
Using various results from extremal set theory (interpreted in the language of additive combinatorics), we prove an asyptotically sharp version of Freiman's theorem in F_2^n: if A in F_2^n is a set for which |A + A| <= K|A| then A is…
We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we…
We propose an ensemble algorithm, which provides a new approach for evaluating and summing up a set of function samples. The proposed algorithm is not a quantum algorithm, insofar it does not involve quantum entanglement. The query…
Given a truncated perturbation expansion of a physical quantity, one can, under certain circumstances, obtain lower or upper bounds (or both) to the sum of the full perturbation series by using the Borel transform and a variational…
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…
We study a model of scalar quantum field theory in which space-time is a discrete set of points obtained by repeatedly subdividing a triangle into three triangles at the centroid. By integrating out the field variable at the centroid we get…
In this note, we presented a new decomposition of elements of finite fields of even order and illustrated that it is an effective tool in evaluation of some specific exponential sums over finite fields, the explicit value of some…
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
Infrared divergences in Quantum Field Theory govern the low-energy dynamics of many physical theories, and their understanding is a crucial ingredient in predicting the outcomes of collider experiments. We present a novel approach to…
A modified interaction representation for the master field describing connected $SU(N)$-invariant Wightman's functions in the large $N$ limit of matrix fields is constructed. This construction is based on the representation of the master…
We introduce fermionic neural network field theories via Grassmann-valued neural networks. Free theories are obtained by a generalization of the Central Limit Theorem to Grassmann variables. This enables the realization of the free Dirac…
Simulation-based methods for statistical inference have evolved dramatically over the past 50 years, keeping pace with technological advancements. The field is undergoing a new revolution as it embraces the representational capacity of…
We present a method for neural network interpretability by combining feature attribution with counterfactual explanations to generate attribution maps that highlight the most discriminative features between pairs of classes. We show that…
The quantum correlations of scalar fields are examined as a power series in derivatives. Recursive algebraic equations are derived and determine the amplitudes; all loop integrations are performed. This recursion contains the same…