arXiv research

Neural networks learn symbolic structure to perform compositional tasks.

VaSST uses soft symbolic trees for probabilistic symbolic regression.

In this article, we introduce symbol calculus on a projective scheme. Using holomorphic Poisson structures, we construct deformations of ring structures for structure sheaves on projective spaces.

Develops new approach to recover CR structures from their Levi foliations.

New CR hypersurfaces in complex space with specific properties.

Hybrid model learns novel handwritten characters better than neural or symbolic models alone.

Develops a Bayesian framework for symbolic regression of scientific expressions.

SE-RRMs solve structured problems like Sudoku and ARC-AGI by enforcing symbol equivariance.

Unified approach to structured prediction combining entropy regularization and neuro-symbolic logic.

Develops experimental design for discovering missing physics in bioreactors.

R2T hybrid model improves robust regression for asymmetric noise.

An absolute parallelism for $2$-nondegenerate CR manifolds $M$ of hypersurface type was recently constructed independently by Isaev-Zaitsev, Medori-Spiro, and Pocchiola in the minimal possible dimension ($\dim M=5$), and for $\dim M=7$ in certain cases by the first author. We develop a bigraded analog of Tanaka's prolo…

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…

Introduces canonical connections for sub-Riemannian manifolds with constant symbol.

CSML learns causal structures for few-shot learning.

EPSTE: A geometric token and deep learning approach to estimating transfer entropy in neuroimaging time series

We construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles (associated to irreducible representations) for a so-called AHS-structure. Outside of a finite set of critical (or resonant) weights, this procedure gives rise to a quantization, which is intrinsi…

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…

Classifies homogeneous CR hypersurfaces in low dimensions with maximal symmetry.

Generative Neuro-Symbolic model learns from raw data with rich conceptual representations.

We present the perceptor gradients algorithm -- a novel approach to learning symbolic representations based on the idea of decomposing an agent's policy into i) a perceptor network extracting symbols from raw observation data and ii) a task encoding program which maps the input symbols to output actions. We show that t…

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

We observe that the line bundle associated to the tame symbol of two invertible holomorphic functions also carries a fairly canonical hermitian metric, hence it represents a class in a Hermitian holomorphic Deligne cohomology group. We put forward an alternative definition of hermitian holomorphic structure on a gerbe …

Study shows how transformers classify symbols without naming them, proving a margin-versus-collision criterion.

Efficiently searches through Gaussian process kernels using symbolic representation and Bayesian optimization.

Extract symbolic models from deep learning with inductive biases.

Efficient algorithm for identifying causal effects in linear models.

Existing automatic music generation approaches that feature deep learning can be broadly classified into two types: raw audio models and symbolic models. Symbolic models, which train and generate at the note level, are currently the more prevalent approach; these models can capture long-range dependencies of melodic st…

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this propert…

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…

Successful human-robot cooperation hinges on each agent's ability to process and exchange information about the shared environment and the task at hand. Human communication is primarily based on symbolic abstractions of object properties, rather than precise quantitative measures. A comprehensive robotic framework thus…

A unified approach to geometric, symbol and deformation quantizations on a generalized flag manifold endowed with an invariant pseudo-Kaehler structure is proposed. The Hilbert space of states is realized via the Bott-Borel-Weil theorem in the sheaf cohomology of the geometric quantization line bundle. The correspondin…

This paper develops a novel methodology for using symbolic knowledge in deep learning. From first principles, we derive a semantic loss function that bridges between neural output vectors and logical constraints. This loss function captures how close the neural network is to satisfying the constraints on its output. An…

A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural quantization procedure. However, considering manifolds endowed with additional st…

SDE automatically recovers interpretable discrete distributions.

The paper models musical motif transformations in Beethoven's works.

ECSEL learns signomial equations for explainable classification.

Unified tensor network formalism for combining neural and symbolic AI.

Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an autoencoder-based neural network architecture. The main advantages of the proposed Dee…

Symbolic regression finds two projective invariants capturing most of the Ricci-flat metric variation.

Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.

Study evaluates clustering methods for Google Trends data.

We compute the asymptotical growth rate of a large family of $U_q(sl_2)$ $6j$-symbols and we interpret our results in geometric terms by relating them to volumes of hyperbolic truncated tetrahedra. We address a question which is strictly related with S.Gukov's generalized volume conjecture and deals with the case of hy…

Study recovers C*-algebra from fields of Toeplitz algebras on specific groups.

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…

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 …

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