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 algorithm learns disjunctions faster than previous methods.
Study links neural network inductive bias, feature learning, and generalization on Boolean functions.
DNF-Net tackles tabular data challenges with neural architecture.
As a contribution to interpretable machine learning research, we develop a novel optimization framework for learning accurate and sparse two-level Boolean rules. We consider rules in both conjunctive normal form (AND-of-ORs) and disjunctive normal form (OR-of-ANDs). A principled objective function is proposed to trade …
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…
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…
A Bayesian Boolean Matrix Factorization for cancer genomics
The diversification (generating slightly varying separating discriminators) of Support Vector Machines (SVMs) for boosting has proven to be a challenge due to the strong learning nature of SVMs. Based on the insight that perturbing the SVM kernel may help in diversifying SVMs, we propose two kernel perturbation based b…
Boolean logic used for neural network training and inference, with convergence analysis.
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.
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…
New Boolean algebra method shows knot unknotting number is (c+1)/2.
A new method relaxes Boolean Matrix Factorization to make it more efficient.
We obtain multirelative connectivity statements about spaces of smooth embeddings, deducing these from analogous results about spaces of Poincare embeddings that were established in our previous paper.
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…
Study symplectic forms on manifolds to find Lagrangian pinwheels that can be separated.
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.
GETF efficiently decomposes large-scale Boolean tensors.
We obtain multirelative connectivity statements about spaces of Poincare embeddings, as precursors to analogous statements about spaces of smooth embeddings. The latter are the key to convergence results in the functor calculus approach to spaces of embeddings.
New method solves matrix completion problems to certifiable optimality.
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.
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…
The paper develops mixed-integer formulations for neural networks using partitioning.
Theory of ends of spaces using linear algebra.
We develop theory for using heuristics to solve computationally hard problems in differential privacy. Heuristic approaches have enjoyed tremendous success in machine learning, for which performance can be empirically evaluated. However, privacy guarantees cannot be evaluated empirically, and must be proven --- without…
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…
Answering complex logical queries on large-scale incomplete knowledge graphs (KGs) is a fundamental yet challenging task. Recently, a promising approach to this problem has been to embed KG entities as well as the query into a vector space such that entities that answer the query are embedded close to the query. Howeve…
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,…
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.
We give a new approach to intersection theory. Our "cycles" are closed manifolds mapping into compact manifolds and our "intersections" are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems r…
In this paper we prove a stability theorem for block diffeomorphisms of 2d-dimensional manifolds that are connected sums of S^d x S^d. Combining this with a recent theorem of S. Galatius and O. Randal-Williams and Morlet's lemma of disjunction, we determine the homology of the classifying space of their diffeomorphism …