Self-evolving Autoencoder Embedded Q-Network

In the realm of sequential decision-making tasks, the exploration capability of a reinforcement learning (RL) agent is paramount for achieving high rewards through interactions with the environment. To enhance this crucial ability, we propose SAQN, a novel approach wherein a self-evolving autoencoder (SA) is embedded with a Q-Network (QN). In SAQN, the self-evolving autoencoder architecture adapts and evolves as the agent explores the environment. This evolution enables the autoencoder to capture a diverse range of raw observations and represent them effectively in its latent space. By leveraging the disentangled states extracted from the encoder generated latent space, the QN is trained to determine optimal actions that improve rewards. During the evolution of the autoencoder architecture, a bias-variance regulatory strategy is employed to elicit the optimal response from the RL agent. This strategy involves two key components: (i) fostering the growth of nodes to retain previously acquired knowledge, ensuring a rich representation of the environment, and (ii) pruning the least contributing nodes to maintain a more manageable and tractable latent space. Extensive experimental evaluations conducted on three distinct benchmark environments and a real-world molecular environment demonstrate that the proposed SAQN significantly outperforms state-of-the-art counterparts. The results highlight the effectiveness of the self-evolving autoencoder and its collaboration with the Q-Network in tackling sequential decision-making tasks.

Evolving Restricted Boltzmann Machine-Kohonen Network for Online Clustering

A novel online clustering algorithm is presented where an Evolving Restricted Boltzmann Machine (ERBM) is embedded with a Kohonen Network called ERBM-KNet. The proposed ERBM-KNet efficiently handles streaming data in a single-pass mode using the ERBM, employing a bias-variance strategy for neuron growing and pruning, as well as online clustering based on a cluster update strategy for cluster prediction and cluster center update using KNet. Initially, ERBM evolves its architecture while processing unlabeled image data, effectively disentangling the data distribution in the latent space. Subsequently, the KNet utilizes the feature extracted from ERBM to predict the number of clusters and updates the cluster centers. By overcoming the common challenges associated with clustering algorithms, such as prior initialization of the number of clusters and subpar clustering accuracy, the proposed ERBM-KNet offers significant improvements. Extensive experimental evaluations on four benchmarks and one industry dataset demonstrate the superiority of ERBM-KNet compared to state-of-the-art approaches.

Bounding the Excess Risk for Linear Models Trained on Marginal-Preserving, Differentially-Private, Synthetic Data

The growing use of machine learning (ML) has raised concerns that an ML model may reveal private information about an individual who has contributed to the training dataset. To prevent leakage of sensitive data, we consider using differentially-private (DP), synthetic training data instead of real training data to train an ML model. A key desirable property of synthetic data is its ability to preserve the low-order marginals of the original distribution. Our main contribution comprises novel upper and lower bounds on the excess empirical risk of linear models trained on such synthetic data, for continuous and Lipschitz loss functions. We perform extensive experimentation alongside our theoretical results.

Discovering Mathematical Formulas from Data via GPT-guided Monte Carlo Tree Search

Finding a concise and interpretable mathematical formula that accurately describes the relationship between each variable and the predicted value in the data is a crucial task in scientific research, as well as a significant challenge in artificial intelligence. This problem is referred to as symbolic regression, which is an NP-hard problem. In the previous year, a novel symbolic regression methodology utilizing Monte Carlo Tree Search (MCTS) was advanced, achieving state-of-the-art results on a diverse range of datasets. although this algorithm has shown considerable improvement in recovering target expressions compared to previous methods, the lack of guidance during the MCTS process severely hampers its search efficiency. Recently, some algorithms have added a pre-trained policy network to guide the search of MCTS, but the pre-trained policy network generalizes poorly. To optimize the trade-off between efficiency and versatility, we introduce SR-GPT, a novel algorithm for symbolic regression that integrates Monte Carlo Tree Search (MCTS) with a Generative Pre-Trained Transformer (GPT). By using GPT to guide the MCTS, the search efficiency of MCTS is significantly improved. Next, we utilize the MCTS results to further refine the GPT, enhancing its capabilities and providing more accurate guidance for the MCTS. MCTS and GPT are coupled together and optimize each other until the target expression is successfully determined. We conducted extensive evaluations of SR-GPT using 222 expressions sourced from over 10 different symbolic regression datasets. The experimental results demonstrate that SR-GPT outperforms existing state-of-the-art algorithms in accurately recovering symbolic expressions both with and without added noise.

Explaining Time Series via Contrastive and Locally Sparse Perturbations

Explaining multivariate time series is a compound challenge, as it requires identifying important locations in the time series and matching complex temporal patterns. Although previous saliency-based methods addressed the challenges, their perturbation may not alleviate the distribution shift issue, which is inevitable especially in heterogeneous samples. We present ContraLSP, a locally sparse model that introduces counterfactual samples to build uninformative perturbations but keeps distribution using contrastive learning. Furthermore, we incorporate sample-specific sparse gates to generate more binary-skewed and smooth masks, which easily integrate temporal trends and select the salient features parsimoniously. Empirical studies on both synthetic and real-world datasets show that ContraLSP outperforms state-of-the-art models, demonstrating a substantial improvement in explanation quality for time series data. The source code is available at \url{https://github.com/zichuan-liu/ContraLSP}.

PruneSymNet: A Symbolic Neural Network and Pruning Algorithm for Symbolic Regression

Symbolic regression aims to derive interpretable symbolic expressions from data in order to better understand and interpret data. %which plays an important role in knowledge discovery and interpretable machine learning. In this study, a symbolic network called PruneSymNet is proposed for symbolic regression. This is a novel neural network whose activation function consists of common elementary functions and operators. The whole network is differentiable and can be trained by gradient descent method. Each subnetwork in the network corresponds to an expression, and our goal is to extract such subnetworks to get the desired symbolic expression. Therefore, a greedy pruning algorithm is proposed to prune the network into a subnetwork while ensuring the accuracy of data fitting. The proposed greedy pruning algorithm preserves the edge with the least loss in each pruning, but greedy algorithm often can not get the optimal solution. In order to alleviate this problem, we combine beam search during pruning to obtain multiple candidate expressions each time, and finally select the expression with the smallest loss as the final result. It was tested on the public data set and compared with the current popular algorithms. The results showed that the proposed algorithm had better accuracy.

Marabou 2.0: A Versatile Formal Analyzer of Neural Networks

This paper serves as a comprehensive system description of version 2.0 of the Marabou framework for formal analysis of neural networks. We discuss the tool's architectural design and highlight the major features and components introduced since its initial release.

A Novel Paradigm for Neural Computation: X-Net with Learnable Neurons and Adaptable Structure

Artificial neural networks (ANNs) have permeated various disciplinary domains, ranging from bioinformatics to financial analytics, where their application has become an indispensable facet of contemporary scientific research endeavors. However, the inherent limitations of traditional neural networks arise due to their relatively fixed network structures and activation functions. 1, The type of activation function is single and relatively fixed, which leads to poor "unit representation ability" of the network, and it is often used to solve simple problems with very complex networks; 2, the network structure is not adaptive, it is easy to cause network structure redundant or insufficient. To address the aforementioned issues, this study proposes a novel neural network called X-Net. By utilizing our designed Alternating Backpropagation mechanism, X-Net dynamically selects appropriate activation functions based on derivative information during training to enhance the network's representation capability for specific tasks. Simultaneously, it accurately adjusts the network structure at the neuron level to accommodate tasks of varying complexities and reduce computational costs. Through a series of experiments, we demonstrate the dual advantages of X-Net in terms of reducing model size and improving representation power. Specifically, in terms of the number of parameters, X-Net is only 3$\%$ of baselines on average, and only 1.4$\%$ under some tasks. In terms of representation ability, X-Net can achieve an average $R^2$=0.985 on the fitting task by only optimizing the activation function without introducing any parameters. Finally, we also tested the ability of X-Net to help scientific discovery on data from multiple disciplines such as society, energy, environment, and aerospace, and achieved concise and good results.

Towards Efficient Verification of Quantized Neural Networks

Quantization replaces floating point arithmetic with integer arithmetic in deep neural network models, providing more efficient on-device inference with less power and memory. In this work, we propose a framework for formally verifying properties of quantized neural networks. Our baseline technique is based on integer linear programming which guarantees both soundness and completeness. We then show how efficiency can be improved by utilizing gradient-based heuristic search methods and also bound-propagation techniques. We evaluate our approach on perception networks quantized with PyTorch. Our results show that we can verify quantized networks with better scalability and efficiency than the previous state of the art.

Understanding Concepts in Graph Signal Processing for Neurophysiological Signal Analysis

Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these multivariate signals, while at the same time taking the spatial structure between the time signals into account. A central idea in GSP is the graph Fourier transform, which projects a multivariate signal onto frequency-ordered graph Fourier modes, and can therefore be regarded as a spatial analog of the temporal Fourier transform. This chapter derives and discusses key concepts in GSP, with a specific focus on how the various concepts relate to one another. The experimental section focuses on the role of graph frequency in data classification, with applications to neuroimaging. To address the limited sample size of neurophysiological datasets, we introduce a minimalist simulation framework that can generate arbitrary amounts of data. Using this artificial data, we find that lower graph frequency signals are less suitable for classifying neurophysiological data as compared to higher graph frequency signals. Finally, we introduce a baseline testing framework for GSP. Employing this framework, our results suggest that GSP applications may attenuate spectral characteristics in the signals, highlighting current limitations of GSP for neuroimaging.