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We study mathematical discovery through the lens of neurosymbolic reasoning, where an AI agent powered by a large language model (LLM), coupled with symbolic computation tools, and human strategic direction, jointly produced a new result in…
Real-world observational datasets and machine learning have revolutionized data-driven decision-making, yet many models rely on empirical associations that may be misleading due to confounding and subgroup heterogeneity. Simpson's paradox…
Despite the rise to dominance of deep learning in unstructured data domains, tree-based methods such as Random Forests (RF) and Gradient Boosted Decision Trees (GBDT) are still the workhorses for handling discriminative tasks on tabular…
With the recent proliferation of open-source packages for computing, power system differential-algebraic equation (DAE) modeling and simulation are being revisited to reduce the programming efforts. Existing open-source tools require manual…
The traditional abstract domain framework for imperative programs suffers from several shortcomings; in particular it does not allow precise symbolic abstractions. To solve these problems, we propose a new abstract interpretation framework,…
Universal approximation theorem suggests that a shallow neural network can approximate any function. The input to neurons at each layer is a weighted sum of previous layer neurons and then an activation is applied. These activation…
Decision Trees (DTs) and Random Forests (RFs) are powerful discriminative learners and tools of central importance to the everyday machine learning practitioner and data scientist. Due to their discriminative nature, however, they lack…
Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…
Statement autoformalization acts as a critical bridge between human mathematics and formal mathematics by translating natural language problems into formal language. While prior works have focused on data synthesis and diverse training…
In a previous paper (of which this is a prosecution) we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended…
Deep neural networks based on layer-stacking architectures have historically suffered from poor inherent interpretability. Meanwhile, symbolic probabilistic models function with clear interpretability, but how to combine them with neural…
Generating mathematical equations from natural language requires an accurate understanding of the relations among math expressions. Existing approaches can be broadly categorized into token-level and expression-level generation. The former…
In this paper, we extend a symbolic association framework for being able to handle missing elements in multimodal sequences. The general scope of the work is the symbolic associations of object-word mappings as it happens in language…
Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown…
Alpha mining, which discovers signals that predict asset returns, has long been attractive for automatic quantitative investment. This problem is typically formulated as a tree-based symbolic regression with handcrafted market data features…
Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…
Derivative-based algorithms are ubiquitous in statistics, machine learning, and applied mathematics. Automatic differentiation offers an algorithmic way to efficiently evaluate these derivatives from computer programs that execute relevant…
The symbolic-heap fragment of separation logic has been actively developed and advocated for verifying the memory-safety property of computer programs. At present, one of its biggest challenges is to effectively prove entailments containing…
The work in ICML'09 showed that the derivatives of the classical multi-class logistic regression loss function could be re-written in terms of a pre-chosen "base class" and applied the new derivatives in the popular boosting framework. In…
In verified generic programming, one cannot exploit the structure of concrete data types but has to rely on well chosen sets of specifications or abstract data types (ADTs). Functors and monads are at the core of many applications of…