arXiv research

Transformer models can solve complex math problems with less data.

Improves neural network search in combinatorial spaces of mathematical symbols.

Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic regression}$. Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. …

GFN-SR uses deep learning to generate diverse mathematical expressions.

In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…

We prove Transformers can learn diverse Gröbner bases.

Bayesian symbolic regression automates model discovery from data.

This paper describes a new method for Symbolic Regression that allows to find mathematical expressions from a dataset. This method has a strong mathematical basis. As opposed to other methods such as Genetic Programming, this method is deterministic, and does not involve the creation of a population of initial solution…

PySR method automates discovering equations from data in chaotic dynamics and epidemics.

Bayesian symbolic regression uncovers missing physics from data with uncertainty quantification.

Zoetrope Genetic Programming improves symbolic regression performance.

Secure Multiparty Computation protects data privacy in Symbolic Regression.

Deep neural network generates symbolic equations from data.

Explores tensor products in hyperdimensional computing.

A hybrid algorithm combines optimization and enumeration for symbolic regression.

Neural programming involves training neural networks to learn programs, mathematics, or logic from data. Previous works have failed to achieve good generalization performance, especially on problems and programs with high complexity or on large domains. This is because they mostly rely either on black-box function eval…

SDE automatically recovers interpretable discrete distributions.

Scientific documents rely on both mathematics and text to communicate ideas. Inspired by the topical correspondence between mathematical equations and word contexts observed in scientific texts, we propose a novel topic model that jointly generates mathematical equations and their surrounding text (TopicEq). Using an e…

Reinforcement learning algorithms can solve dynamic decision-making and optimal control problems. With continuous-valued state and input variables, reinforcement learning algorithms must rely on function approximators to represent the value function and policy mappings. Commonly used numerical approximators, such as ne…

A new algorithm speeds up sparse regression for discovering equations from data.

Mathematical reasoning---a core ability within human intelligence---presents some unique challenges as a domain: we do not come to understand and solve mathematical problems primarily on the back of experience and evidence, but on the basis of inferring, learning, and exploiting laws, axioms, and symbol manipulation ru…

Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information beyond just values at some inputs, but also effectively constrain the search space. …

New model captures complex relationships from experimental data.

Neural network language models (NNLMs) have achieved ever-improving accuracy due to more sophisticated architectures and increasing amounts of training data. However, the inductive bias of these models (formed by the distributional hypothesis of language), while ideally suited to modeling most running text, results in …

The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this p…

OGRePy simplifies tensor calculations in general relativity.

Framework for verifying deep learning operators.

This paper introduces lattice representations for efficient discrete learning.

A simple text model shows word lengths follow Zipf's law.

VaSST uses soft symbolic trees for probabilistic symbolic regression.

DisCoPyro combines category theory with machine learning for program learning.

Meta-learning approach to learn interpretable models from human feedback.

We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…

While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural…

Paper closes neural-symbolic learning loop with grammar model and back-search algorithm.

Reinforcement learning and symbolic planning have both been used to build intelligent autonomous agents. Reinforcement learning relies on learning from interactions with real world, which often requires an unfeasibly large amount of experience. Symbolic planning relies on manually crafted symbolic knowledge, which may …

For an arbitrary Riemannian manifold $X$ and Hermitian vector bundles $E$ and $F$ over $X$ we define the notion of the normal symbol of a pseudodifferential operator $P$ from $E$ to $F$. The normal symbol of $P$ is a certain smooth function from the cotangent bundle $T^*X$ to the homomorphism bundle $Hom (E,F)$ and dep…

Based on the ideas of Optimal Control, we introduce the new basic characteristic of a bracket generating distribution, the Jacobi symbol. In contrast to the classical Tanaka symbol, the set of Jacobi symbols is discrete and classifiable. We give an explicit and unified algebraic procedure for the construction of the ca…

We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field $\mathbb{Q}(\sqrt{-3})$, following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and Rédei's triple symbol, and describes the decomposition…

A formula for Rademacher symbols in triangle groups is provided.

The symbolic dynamics technique is well-known for low-dimensional dynamical systems and chaotic maps, and lies at the roots of the thermodynamic formalism of dynamical systems. Here we show that this technique can also be successfully applied to time series generated by complex systems of much higher dimensionality. Ou…

Complex $b$-$6j$ symbols relate to hyperbolic tetrahedron volumes and determinants.

The paper classifies symbols of differential operators on vector bundles.

NeSS combines neural and symbolic approaches for better compositional generalization.

Defines transverse symbols for foliated manifolds and proves their K-homology class.

A new method for spotting symbols in CAD images reduces annotation costs and improves accuracy.

In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on Delaney-Dress combinatorial tiling theory using an extension of mapping class groups to …

Paper proposes a bijective approach for signal/symbol translation using variational auto-encoders.