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.
Boolean logic used for neural network training and inference, with convergence analysis.
A new deep learning method using Boolean logic reduces training and inference energy.
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,…
The paper explores how neural networks learn logical functions and their generalization error.
New algebra counts components of arborescent knots and links.
GETF efficiently decomposes large-scale Boolean tensors.
The paper explores how different network architectures learn logical functions under GOTU, finding that a min-degree-interpolator is learned.
A Bayesian Boolean Matrix Factorization for cancer genomics
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…
We build upon probabilistic models for Boolean Matrix and Boolean Tensor factorisation that have recently been shown to solve these problems with unprecedented accuracy and to enable posterior inference to scale to Billions of observation. Here, we lift the restriction of a pre-specified number of latent dimensions by …
We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively bypassing the problem of learning in large RBMs, and creating a system able to mod…
Our interest in this paper is in the construction of symbolic explanations for predictions made by a deep neural network. We will focus attention on deep relational machines (DRMs, first proposed by H. Lodhi). A DRM is a deep network in which the input layer consists of Boolean-valued functions (features) that are defi…
DNF-Net tackles tabular data challenges with neural architecture.
Deep neural networks have been successfully deployed in a wide variety of applications including computer vision and speech recognition. However, computational and storage complexity of these models has forced the majority of computations to be performed on high-end computing platforms or on the cloud. To cope with com…
We consider the quantifier-free languages, Bc and Bc0, obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected interior. These languages are interpreted over the regular closed sets of n-dimension…
Generally speaking, the goal of constructive learning could be seen as, given an example set of structured objects, to generate novel objects with similar properties. From a statistical-relational learning (SRL) viewpoint, the task can be interpreted as a constraint satisfaction problem, i.e. the generated objects must…
The exclusive or (xor) function is one of the simplest examples that illustrate why nonlinear feedforward networks are superior to linear regression for machine learning applications. We review the xor representation and approximation problems and discuss their solutions in terms of probabilistic logic and associative …
Study on functions computed by deep-layered machines finds same distribution in neural networks and Boolean circuits.
New Fourier analysis method for non-uniform Boolean hypercube.
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…
New Boolean algebra method shows knot unknotting number is (c+1)/2.
A new method relaxes Boolean Matrix Factorization to make it more efficient.
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.
Minimalist softmax attention learns constrained Boolean functions with supervision.
New framework reduces LLM complexity by directly finetuning in Boolean domain.
Research has shown that deep neural networks contain significant redundancy, and that high classification accuracies can be achieved even when weights and activations are quantised down to binary values. Network binarisation on FPGAs greatly increases area efficiency by replacing resource-hungry multipliers with lightw…
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…
Theory of ends of spaces using linear algebra.
AlphaLogics mines market logic to generate interpretable alpha factors.
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…
Study links neural network inductive bias, feature learning, and generalization on Boolean functions.
New findings show that common optimization algorithms struggle with random problems.
Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane. For complex data with multimodal distributions this transformation is difficult t…
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.
Explaining neural network computation in terms of probabilistic/fuzzy logical operations has attracted much attention due to its simplicity and high interpretability. Different choices of logical operators such as AND, OR and XOR give rise to another dimension for network optimization, and in this paper, we study the o…