A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New Boolean algebra method shows knot unknotting number is (c+1)/2.
Theory of ends of spaces using linear algebra.
New algebra counts components of arborescent knots and links.
The ability to compose learned skills to solve new tasks is an important property of lifelong-learning agents. In this work, we formalise the logical composition of tasks as a Boolean algebra. This allows us to formulate new tasks in terms of the negation, disjunction and conjunction of a set of base tasks. We then sho…
Complex of cuts reveals full automorphism group for certain Stone spaces.
A new method relaxes Boolean Matrix Factorization to make it more efficient.
We consider the notion of multiple gap as a finite set of ideals that cannot be separated. We study the different types of such objects that can be found in the Boolean algebra of subsets of the natural numbers modulo finite sets.
Boolean logic used for neural network training and inference, with convergence analysis.
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate scalable sampling-based posterior inference by exploitation of the combinatorial…
Study on functions computed by deep-layered machines finds same distribution in neural networks and Boolean circuits.
In this article we give an explicit algorithm which will determine, in a discrete and computable way, whether a finite piecewise Euclidean complex is non-positively curved. In particular, given such a complex we show how to define a boolean combination of polynomial equations and inequalities in real variables, i.e. a …
New Fourier analysis method for non-uniform Boolean hypercube.
A new deep learning method using Boolean logic reduces training and inference energy.
Boolean matrix factorization and Boolean matrix completion from noisy observations are desirable unsupervised data-analysis methods due to their interpretability, but hard to perform due to their NP-hardness. We treat these problems as maximum a posteriori inference problems in a graphical model and present a message p…
Probabilistic learning for binary classification with categorical variables.
Boolean matrix factorisation aims to decompose a binary data matrix into an approximate Boolean product of two low rank, binary matrices: one containing meaningful patterns, the other quantifying how the observations can be expressed as a combination of these patterns. We introduce the OrMachine, a probabilistic genera…
Survey on learning Boolean functions in computational theory.
A Bayesian Boolean Matrix Factorization for cancer genomics
Minimalist softmax attention learns constrained Boolean functions with supervision.
New framework reduces LLM complexity by directly finetuning in Boolean domain.
GETF efficiently decomposes large-scale Boolean tensors.
While homology theory of associative structures, such as groups and rings, has been extensively studied in the past beginning with the work of Hopf, Eilenberg, and Hochschild, homology of non-associative distributive structures, such as quandles, were neglected until recently. Distributive structures have been studied …
Transformers learn sparse Boolean functions through RL and SFT, revealing distinct learning behaviors.
Paper improves variational inference on Boolean hypercube using quantum methods.
Paper proposes algorithms for BMF using integer programming.
The paper develops algorithms for Boolean matrix factorization using IP and heuristics.
Boolean matrix factorization (BMF) is a popular and powerful technique for inferring knowledge from data. The mining result is the Boolean product of two matrices, approximating the input dataset. The Boolean product is a disjunction of rank-1 binary matrices, each describing a feature-relation, called pattern, for a g…
Study examines noise sensitivity of DNNs for binary classification.
This paper explores how boolean formulas can be learned by deep neural networks.
We explain why numbers occurring in the classification of polygon spaces coincide with numbers of self-dual equivalence classes of threshold functions, or of regular Boolean functions, or of decisive weighted majority games.
This paper introduces the combinatorial Boolean model (CBM), which is defined as the class of linear combinations of conjunctions of Boolean attributes. This paper addresses the issue of learning CBM from labeled data. CBM is of high knowledge interpretability but naïve learning of it requires exponentially large compu…
Boolean matrix has been used to represent digital information in many fields, including bank transaction, crime records, natural language processing, protein-protein interaction, etc. Boolean matrix factorization (BMF) aims to find an approximation of a binary matrix as the Boolean product of two low rank Boolean matri…
It is feasible and practically-valuable to bridge the characteristics between graph neural networks (GNNs) and logical reasoning. Despite considerable efforts and successes witnessed to solve Boolean satisfiability (SAT), it remains a mystery of GNN-based solvers for more complex predicate logic formulae. In this work,…
Study links neural network inductive bias, feature learning, and generalization on Boolean functions.
New findings show that common optimization algorithms struggle with random problems.
The study explores how Matrix Product States can represent boolean and continuous functions.
During the past few years Boolean matrix factorization (BMF) has become an important direction in data analysis. The minimum description length principle (MDL) was successfully adapted in BMF for the model order selection. Nevertheless, a BMF algorithm performing good results from the standpoint of standard measures in…
Cube category simplifies set modeling.
Efficiently estimate Boolean product distribution parameters from truncated samples.
Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks, Binarized Neural Networks, using the well-developed means of Boolean satisfiability. Our…
Extends quantum learning theory to multiclass and online settings.
In this thesis, we consider semi-algebraic sets over a real closed field defined by quadratic polynomials. Semi-algebraic sets of are defined as the smallest family of sets in that contains the algebraic sets as well as the sets defined by polynomial inequalities, and which is also closed under the bool…
Data is one of the most important assets of the information age, and its societal impact is undisputed. Yet, rigorous methods of assessing the quality of data are lacking. In this paper, we propose a formal definition for the quality of a given dataset. We assess a dataset's quality by a quantity we call the expected d…
Efficiently optimizes boolean functions using multilinear polynomials and exponential weight updates.
Probabilistic approach to Boolean matrix factorization can provide solutions robustagainst noise and missing values with linear computational complexity. However,the assumption about latent factors can be problematic in real world applications.This study proposed a new probabilistic algorithm free of assumptions of lat…
We introduce a formal language IE that is a variant of the language PAL developed in [van Benthem 2011] by adding a belief operator and a common belief operator,specializing to stochastic analysis. A constant symbol in the language denotes a stochastic process so that we can represent several financial events as formul…
New algorithm learns halfspaces over hypercube with random bit flips.
Tensor decomposition has been extensively used as a tool for exploratory analysis. Motivated by neuroscience applications, we study tensor decomposition with Boolean factors. The resulting optimization problem is challenging due to the non-convex objective and the combinatorial constraints. We propose Binary Matching P…