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Found 16 papers, 2 papers with code
Unification of Symmetries Inside Neural Networks: Transformer, Feedforward and Neural ODE
Understanding the inner workings of neural networks, including transformers, remains one of the most challenging puzzles in machine learning.
Integrating Large Language Models in Causal Discovery: A Statistical Causal Approach
In practical statistical causal discovery (SCD), embedding domain expert knowledge as constraints into the algorithm is widely accepted as significant for creating consistent meaningful causal models, despite the recognized challenges in systematic acquisition of the background knowledge.
A Policy Gradient Primal-Dual Algorithm for Constrained MDPs with Uniform PAC Guarantees
We study a primal-dual reinforcement learning (RL) algorithm for the online constrained Markov decision processes (CMDP) problem, wherein the agent explores an optimal policy that maximizes return while satisfying constraints.
LPML: LLM-Prompting Markup Language for Mathematical Reasoning
In this paper, we propose a novel framework that integrates the Chain-of-Thought (CoT) method with an external tool (Python REPL).
Bézier Flow: a Surface-wise Gradient Descent Method for Multi-objective Optimization
In this paper, we propose a strategy to construct a multi-objective optimization algorithm from a single-objective optimization algorithm by using the B\'ezier simplex model.
Equivariant and Invariant Reynolds Networks
We construct learning models based on the reductive Reynolds operator called equivariant and invariant Reynolds networks (ReyNets) and prove that they have universal approximation property.
Reynolds Equivariant and Invariant Networks
To overcome this difficulty, we consider representing the Reynolds operator as a sum over a subset instead of a sum over the whole group.
Approximate Bayesian Computation of Bézier Simplices
B\'ezier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems.
Group Equivariant Conditional Neural Processes
We present the group equivariant conditional neural process (EquivCNP), a meta-learning method with permutation invariance in a data set as in conventional conditional neural processes (CNPs), and it also has transformation equivariance in data space.
Universal Approximation Theorem for Equivariant Maps by Group CNNs
However, universal approximation theorems for CNNs have been separately derived with individual techniques according to each group and setting.
On the Number of Linear Functions Composing Deep Neural Network: Towards a Refined Definition of Neural Networks Complexity
The classical approach to measure the expressive power of deep neural networks with piecewise linear activations is based on counting their maximum number of linear regions.
Improved Generalization Bounds of Group Invariant / Equivariant Deep Networks via Quotient Feature Spaces
To describe the effect of invariance and equivariance on generalization, we develop a notion of a \textit{quotient feature space}, which measures the effect of group actions for the properties.
Improved Generalization Bound of Permutation Invariant Deep Neural Networks
Learning problems with data that are invariant to permutations are frequently observed in various applications, for example, point cloud data and graph neural networks.
Asymptotic Risk of Bezier Simplex Fitting
In this paper, we analyze the asymptotic risks of those B\'ezier simplex fitting methods and derive the optimal subsample ratio for the inductive skeleton fitting.
Universal approximations of permutation invariant/equivariant functions by deep neural networks
In this paper, we develop a theory about the relationship between $G$-invariant/equivariant functions and deep neural networks for finite group $G$.
Reconstruction of training samples from loss functions
Furthermore, as as application of this theory, we prove that the loss functions can reconstruct the inputs of the training samples up to scalar multiplication (as vectors) and can provide the number of layers and nodes of the deep neural network.
