Understanding neural network's (NN) generalizability remains a central question in deep learning research. The special phenomenon of grokking, where NNs abruptly generalize long after the training performance reaches a near-perfect level, offers a unique window to investigate the underlying mechanisms of NNs' generalizability. Here we propose an interpretation for grokking by framing it as a computational glass relaxation: viewing NNs as a physical system where parameters are the degrees of freedom and train loss is the system energy, we find memorization process resembles a rapid cooling of liquid into non-equilibrium glassy state at low temperature and the later generalization is like a slow relaxation towards a more stable configuration. This mapping enables us to sample NNs' Boltzmann entropy (density of states) landscape as a function of training loss and test accuracy.

Neural Information Processing Systems http://nips.cc/

We present elsciRL, an open-source Python library to facilitate the application of language solutions on reinforcement learning problems. We demonstrate the potential of our software by extending the Language Adapter with Self-Completing Instruction framework defined in (Osborne, 2024) with the use of LLMs. Our approach can be re-applied to new applications with minimal setup requirements. We provide a novel GUI that allows a user to provide text input for an LLM to generate instructions which it can then self-complete. Empirical results indicate that these instructions \textit{can} improve a reinforcement learning agent's performance. Therefore, we present this work to accelerate the evaluation of language solutions on reward based environments to enable new opportunities for scientific discovery.

Multi-scale DeepOnet (Mscale-DeepOnet) for Mitigating Spectral Bias in Learning High Frequency Operators of Oscillatory Functions B. Wang a, Lizuo Liu b, Wei Cai c, a LCSM(MOE), School of Mathematics and Statistics, Hunan Normal University, Changsha, China b Department of Mathematics, Dartmouth College, Hanover, NH, USA c Department of Mathematics, Southern Methodist University, Dallas, TX, USAAbstract In this paper, a multi-scale DeepOnet (Mscale-DeepOnet) is proposed to reduce the spectral bias of the DeepOnet in learning high-frequency mapping between highly oscillatory functions, with an application to the nonlinear mapping between the coefficient of the Helmholtz equation and its solution. The Mscale-DeepOnet introduces the multiscale neural network in the branch and trunk networks of the original DeepOnet, the resulting Mscale-DeepOnet is shown to be able to capture various high-frequency components of the mapping itself and its image. Numerical results demonstrate the substantial improvement of the Mscale-DeepOnet for the problem of wave scattering in the high-frequency regime over the normal DeepOnet with a similar number of network parameters.1. Introduction The DeepONet has shown its ability to learn not only explicit mathematical operators like integration and fractional derivatives, but also PDE operators [1, 3, 4, 7, 9]. However, like neural networks such as PINN in solving PDEs, neural operators including DeepOnet and FNO demonstrates the behaviour of spectral bias where learning is preferred for low frequency component of the approximation [11, 12, 14].

Generative networks have shown remarkable success in learning complex data distributions, particularly in generating high-dimensional data from lower-dimensional inputs. While this capability is well-documented empirically, its theoretical underpinning remains unclear. One common theoretical explanation appeals to the widely accepted manifold hypothesis, which suggests that many real-world datasets, such as images and signals, often possess intrinsic low-dimensional geometric structures. Under this manifold hypothesis, it is widely believed that to approximate a distribution on a $d$-dimensional Riemannian manifold, the latent dimension needs to be at least $d$ or $d+1$. In this work, we show that this requirement on the latent dimension is not necessary by demonstrating that generative networks can approximate distributions on $d$-dimensional Riemannian manifolds from inputs of any arbitrary dimension, even lower than $d$, taking inspiration from the concept of space-filling curves. This approach, in turn, leads to a super-exponential complexity bound of the deep neural networks through expanded neurons. Our findings thus challenge the conventional belief on the relationship between input dimensionality and the ability of generative networks to model data distributions. This novel insight not only corroborates the practical effectiveness of generative networks in handling complex data structures, but also underscores a critical trade-off between approximation error, dimensionality, and model complexity.

This paper presents the use of Kolmogorov-Arnold Networks (KANs) for forecasting the CBOE Volatility Index (VIX). Unlike traditional MLP-based neural networks that are often criticized for their black-box nature, KAN offers an interpretable approach via learnable spline-based activation functions and symbolification. Based on a parsimonious architecture with symbolic functions, KAN expresses a forecast of the VIX as a closed-form in terms of explanatory variables, and provide interpretable insights into key characteristics of the VIX, including mean reversion and the leverage effect. Through in-depth empirical analysis across multiple datasets and periods, we show that KANs achieve competitive forecasting performance while requiring significantly fewer parameters compared to MLP-based neural network models. Our findings demonstrate the capacity and potential of KAN as an interpretable financial time-series forecasting method.

Epilepsy and epileptiform discharges are common harmful brain activities, and electroencephalogram (EEG) signals are widely used to monitor the onset status of patients. However, due to the lack of unified EEG signal acquisition standards, there are many obstacles in practical applications, especially the difficulty in transferring and using models trained on different numbers of channels. To address this issue, we proposes a neural network architecture with a single-channel feature extraction (Singal Channel Feature) model backend fusion (SCFNet). The feature extractor of the model is an RCNN network with single-channel input, which does not depend on other channels, thereby enabling easier migration to data with different numbers of channels. Experimental results show that on the IIIC-Seizure dataset, the accuracy of EEG-SCFNet has improved by 4% compared to the baseline model and also increased by 1.3% compared to the original RCNN neural network model. Even with only fine-tuning the classification head, its performance can still maintain a level comparable to the baseline. In addition, in terms of cross-dataset transfer, EEG-SCFNet can still maintain certain performance even if the channel leads are different.

In Reinforcement Learning (RL), agents have no incentive to exhibit predictable behaviors, and are often pushed (through e.g. policy entropy regularization) to randomize their actions in favor of exploration. From a human perspective, this makes RL agents hard to interpret and predict, and from a safety perspective, even harder to formally verify. We propose a novel method to induce predictable behavior in RL agents, referred to as Predictability-Aware RL (PA-RL), which employs the state sequence entropy rate as a predictability measure. We show how the entropy rate can be formulated as an average reward objective, and since its entropy reward function is policy-dependent, we introduce an action-dependent surrogate entropy enabling the use of PG methods. We prove that deterministic policies minimizing the average surrogate reward exist and also minimize the actual entropy rate, and show how, given a learned dynamical model, we are able to approximate the value function associated to the true entropy rate. Finally, we demonstrate the effectiveness of the approach in RL tasks inspired by human-robot use-cases, and show how it produces agents with more predictable behavior while achieving near-optimal rewards.

Reducing and detecting hallucinations in large language models is an open research problem. In this project, we attempt to leverage recent advances in the field of uncertainty estimation to reduce hallucinations in frozen large language models. Epistemic neural networks have recently been proposed to improve output joint distributions for large pre-trained models. ENNs are small networks attached to large, frozen models to improve the model's joint distributions and uncertainty estimates. In this work, we train an epistemic neural network on top of the Llama-2 7B model combined with a contrastive decoding feature enhancement technique. We are the first to train an ENN for the next token prediction task and explore the efficacy of this method in reducing hallucinations on the TruthfulQA dataset. In essence, we provide a method that leverages a pre-trained model's latent embeddings to reduce hallucinations. Recently, Large Language Models have become more and more capable of a wide range of language processing tasks such as summarization, sentiment analysis (Scaria et al., 2023), event detection (Anantheswaran et al., 2023), finance (Gupta et al., 2021), synthetic data generation (Gupta et al., 2023b).

Active Simultaneous Localisation and Mapping (SLAM) is a critical problem in autonomous robotics, enabling robots to navigate to new regions while building an accurate model of their surroundings. Visual SLAM is a popular technique that uses virtual elements to enhance the experience. However, existing frontier-based exploration strategies can lead to a non-optimal path in scenarios where there are multiple frontiers with similar distance. This issue can impact the efficiency and accuracy of Visual SLAM, which is crucial for a wide range of robotic applications, such as search and rescue, exploration, and mapping. To address this issue, this research combines both an existing Visual-Graph SLAM known as ExploreORB with reinforcement learning. The proposed algorithm allows the robot to learn and optimize exploration routes through a reward-based system to create an accurate map of the environment with proper frontier selection. Frontier-based exploration is used to detect unexplored areas, while reinforcement learning optimizes the robot's movement by assigning rewards for optimal frontier points. Graph SLAM is then used to integrate the robot's sensory data and build an accurate map of the environment. The proposed algorithm aims to improve the efficiency and accuracy of ExploreORB by optimizing the exploration process of frontiers to build a more accurate map. To evaluate the effectiveness of the proposed approach, experiments will be conducted in various virtual environments using Gazebo, a robot simulation software. Results of these experiments will be compared with existing methods to demonstrate the potential of the proposed approach as an optimal solution for SLAM in autonomous robotics.