Related papers: CoNSoLe: Convex Neural Symbolic Learning
We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as…
Symbolic rule learners generate interpretable solutions, however they require the input to be encoded symbolically. Neuro-symbolic approaches overcome this issue by mapping raw data to latent symbolic concepts using a neural network.…
Abstract symbolic reasoning, as required in domains such as mathematics and logic, is a key component of human intelligence. Solvers for these domains have important applications, especially to computer-assisted education. But learning to…
Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural…
We leverage convex and bilevel optimization techniques to develop a general gradient-based parameter learning framework for neural-symbolic (NeSy) systems. We demonstrate our framework with NeuPSL, a state-of-the-art NeSy architecture. To…
We propose CoNSAL (Combining Neural networks and Symbolic regression for Analytical Lyapunov function) to construct analytical Lyapunov functions for nonlinear dynamic systems. This framework contains a neural Lyapunov function and a…
Symbolic regression is a powerful technique that can discover analytical equations that describe data, which can lead to explainable models and generalizability outside of the training data set. In contrast, neural networks have achieved…
Due to the non-convex nature of training Deep Neural Network (DNN) models, their effectiveness relies on the use of non-convex optimization heuristics. Traditional methods for training DNNs often require costly empirical methods to produce…
This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA)…
One of the ultimate goals of Artificial Intelligence is to assist humans in complex decision making. A promising direction for achieving this goal is Neuro-Symbolic AI, which aims to combine the interpretability of symbolic techniques with…
This paper proposed a new explicit nonlinear dimensionality reduction using neural networks for image retrieval tasks. We first proposed a Quasi-curvature Locally Linear Embedding (QLLE) for training set. QLLE guarantees the linear…
We improve zero-shot learning (ZSL) by incorporating common-sense knowledge in DNNs. We propose Common-Sense based Neuro-Symbolic Loss (CSNL) that formulates prior knowledge as novel neuro-symbolic loss functions that regularize…
We prove that finding all globally optimal two-layer ReLU neural networks can be performed by solving a convex optimization program with cone constraints. Our analysis is novel, characterizes all optimal solutions, and does not leverage…
Symbolic regression is a technique that can automatically derive analytic models from data. Traditionally, symbolic regression has been implemented primarily through genetic programming that evolves populations of candidate solutions…
Quantitative Susceptibility Mapping (QSM) estimates tissue magnetic susceptibility distributions from Magnetic Resonance (MR) phase measurements by solving an ill-posed dipole inversion problem. Conventional single orientation QSM methods…
Neuro-symbolic learning (NSL) models complex symbolic rule patterns into latent variable distributions by neural networks, which reduces rule search space and generates unseen rules to improve downstream task performance. Centralized NSL…
The goal of neural-symbolic computation is to integrate the connectionist and symbolist paradigms. Prior methods learn the neural-symbolic models using reinforcement learning (RL) approaches, which ignore the error propagation in the…
Deep neural networks (DNNs), particularly those using Rectified Linear Unit (ReLU) activation functions, have achieved remarkable success across diverse machine learning tasks, including image recognition, audio processing, and language…
We develop a general approach to distill symbolic representations of a learned deep model by introducing strong inductive biases. We focus on Graph Neural Networks (GNNs). The technique works as follows: we first encourage sparse latent…
Inner product-based convolution has been the founding stone of convolutional neural networks (CNNs), enabling end-to-end learning of visual representation. By generalizing inner product with a bilinear matrix, we propose the neural…