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.
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 …
In this paper, we present a new task that investigates how people interact with and make judgments about towers of blocks. In Experiment~1, participants in the lab solved a series of problems in which they had to re-configure three blocks from an initial to a final configuration. We recorded whether they used one hand …
One of the key challenges in applying reinforcement learning to real-life problems is that the amount of train-and-error required to learn a good policy increases drastically as the task becomes complex. One potential solution to this problem is to combine reinforcement learning with automated symbol planning and utili…
We present a framework for autonomously learning a portable representation that describes a collection of low-level continuous environments. We show that these abstract representations can be learned in a task-independent egocentric space specific to the agent that, when grounded with problem-specific information, are …
SymNet uses neural models to solve RMDPs efficiently.
problem Limited effectiveness of generalized policies in RMDPs.
method SymNet trains shared parameters for an RDDL domain, converts instances to graphs, uses relational neural models for node embeddings, and scores actions based on embeddings.
result SymNet policies outperform random and state-of-the-art deep reactive policies on nine RDDL domains.
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…
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 Q(−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…
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…
The paper classifies symbols of differential operators on vector bundles.
problem Classifying symbols of linear differential operators on vector bundles.
method Associated tuples of linear operators to non-degenerate symbols and used C. Procesi's results to find rational invariants and equivalence criteria.
result Generators for rational invariants and a criterion for symbol equivalence.
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…
S2KAN integrates symbolic primitives into neural network activations for improved interpretability.
problem Training activations in KANs often lack symbolic fidelity, leading to unintelligible models.
method Softly Symbolified Kolmogorov-Arnold Networks (S2KAN) integrates symbolic primitives into training with learnable gates and a Minimum Description Length objective.
result S2KAN discovers interpretable forms when symbolic terms suffice, gracefully degrading to dense splines when necessary.
Quantum 6j-symbols linked to tetrahedra angles and volumes.
problem Understanding quantum 6j-symbols and their geometric interpretation.
method Establishing the geometric connection between quantum 6j-symbols and tetrahedra angles, including spherical, Euclidean, and hyperbolic cases.
result Quantum 6j-symbols correspond to dihedral angles of specific tetrahedra, including generalized hyperbolic ones, with exponential growth rates tied to their 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 S3.
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…