arXiv research

Study robustness of polynomial neural networks using algebraic geometry.

PAN+SR tackles scalable symbolic regression for large $p$ datasets.

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

We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms of a cylindrical algebraic decomposition. From a high-level perspective, the…

Obtaining a non-parametric expression for an interventional distribution is one of the most fundamental tasks in causal inference. Such an expression can be obtained for an identifiable causal effect by an algorithm or by manual application of do-calculus. Often we are left with a complicated expression which can lead …

EB improves asset pricing by mining large strategies without lookahead bias.

VaSST uses soft symbolic trees for probabilistic symbolic regression.

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 …

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.

The Wodzicki residue and the cut-off integral extend to classical symbol-valued forms. We show that they obey a Stokes' type property and that the extended Wodzicki residue can be interpreted as a complex residue like the ordinary one. In the case of cut-off integrals, Stokes' property (i.e. vanishing on exact forms) o…

Bayesian symbolic regression automates model discovery from data.

Symbolic regression finds simple formulas for implied volatility.

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

S2KAN integrates symbolic primitives into neural network activations for improved interpretability.

Symbolic LSTM improves time series forecasting by reducing hyperparameter sensitivity.

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

Meta-learning symbolic default hyperparameters from dataset properties.

ISR creates analytical relationships from data via invertible maps.

Extraction of symbolic information from signals is an active field of research enabling numerous applications especially in the Musical Information Retrieval domain. This complex task, that is also related to other topics such as pitch extraction or instrument recognition, is a demanding subject that gave birth to nume…

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

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

Quantum $6j$-symbols linked to tetrahedra angles and volumes.

We extend projectively equivariant quantization and symbol calculus to symbols of pseudo-differential operators. An explicit expression in terms of hypergeometric functions with noncommutative arguments is given. Some examples are worked out, one of them yielding a quantum length element on $S^3$.

Transformer models can solve complex math problems with less data.

Classifies worst approximable rational numbers using hyperbolic geometry.

Improves neural network search in combinatorial spaces of mathematical symbols.

Arguments in favor of injecting symbolic knowledge into neural architectures abound. When done right, constraining a sub-symbolic model can substantially improve its performance and sample complexity and prevent it from predicting invalid configurations. Focusing on deep probabilistic (logical) graphical models -- i.e.…

MESSY estimation recovers symbolic density functions from samples using maximum entropy.

We derive an Ehrhart function for symbols from the Euler-MacLaurin formula with remainder.

Study connects boundary geometry to symbol of Dirichlet-to-Neumann operator.

Develops a Bayesian framework for symbolic regression of scientific expressions.

Secure Multiparty Computation protects data privacy in Symbolic Regression.

We define a new homology theory we call symbol homology by using decorated moduli spaces of Whitney polygons. By decorating different types of moduli spaces we obtain different flavors of this homology theory together with morphisms between them. Each of these flavors encodes the properties of a different type of Heega…

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

QABBA improves time series storage efficiency while preserving shape information.

Neural-symbolic model improves link prediction in knowledge graphs.

The seemingly infinite diversity of the natural world arises from a relatively small set of coherent rules, such as the laws of physics or chemistry. We conjecture that these rules give rise to regularities that can be discovered through primarily unsupervised experiences and represented as abstract concepts. If such r…