Finding separatrices of dynamical flows with Deep Koopman Eigenfunctions

Many natural systems, including neural circuits involved in decision making, can be modeled as high-dimensional dynamical systems with multiple stable states. While existing analytical tools primarily describe behavior near stable equilibria, characterizing separatrices -- the manifolds that delineate boundaries between different basins of attraction -- remains challenging, particularly in high-dimensional settings. Here, we introduce a numerical framework leveraging Koopman Theory combined with Deep Neural Networks to effectively characterize separatrices. Specifically, we approximate Koopman Eigenfunctions (KEFs) associated with real positive eigenvalues, which vanish precisely at the separatrices. Utilizing these scalar KEFs, optimization methods efficiently locate separatrices even in complex systems. We demonstrate our approach on synthetic benchmarks, ecological network models, and recurrent neural networks trained on neuroscience-inspired tasks. Moreover, we illustrate the practical utility of our method by designing optimal perturbations that can shift systems across separatrices, enabling predictions relevant to optogenetic stimulation experiments in neuroscience.

A self-regulated convolutional neural network for classifying variable stars

Over the last two decades, machine learning models have been widely applied and have proven effective in classifying variable stars, particularly with the adoption of deep learning architectures such as convolutional neural networks, recurrent neural networks, and transformer models. While these models have achieved high accuracy, they require high-quality, representative data and a large number of labelled samples for each star type to generalise well, which can be challenging in time-domain surveys. This challenge often leads to models learning and reinforcing biases inherent in the training data, an issue that is not easily detectable when validation is performed on subsamples from the same catalogue. The problem of biases in variable star data has been largely overlooked, and a definitive solution has yet to be established. In this paper, we propose a new approach to improve the reliability of classifiers in variable star classification by introducing a self-regulated training process. This process utilises synthetic samples generated by a physics-enhanced latent space variational autoencoder, incorporating six physical parameters from Gaia Data Release 3. Our method features a dynamic interaction between a classifier and a generative model, where the generative model produces ad-hoc synthetic light curves to reduce confusion during classifier training and populate underrepresented regions in the physical parameter space. Experiments conducted under various scenarios demonstrate that our self-regulated training approach outperforms traditional training methods for classifying variable stars on biased datasets, showing statistically significant improvements.

RLBenchNet: The Right Network for the Right Reinforcement Learning Task

Reinforcement learning (RL) has seen significant advancements through the application of various neural network architectures. In this study, we systematically investigate the performance of several neural networks in RL tasks, including Long Short-Term Memory (LSTM), Multi-Layer Perceptron (MLP), Mamba/Mamba-2, Transformer-XL, Gated Transformer-XL, and Gated Recurrent Unit (GRU). Through comprehensive evaluation across continuous control, discrete decision-making, and memory-based environments, we identify architecture-specific strengths and limitations. Our results reveal that: (1) MLPs excel in fully observable continuous control tasks, providing an optimal balance of performance and efficiency; (2) recurrent architectures like LSTM and GRU offer robust performance in partially observable environments with moderate memory requirements; (3) Mamba models achieve a 4.5x higher throughput compared to LSTM and a 3.9x increase over GRU, all while maintaining comparable performance; and (4) only Transformer-XL, Gated Transformer-XL, and Mamba-2 successfully solve the most challenging memory-intensive tasks, with Mamba-2 requiring 8x less memory than Transformer-XL. These findings provide insights for researchers and practitioners, enabling more informed architecture selection based on specific task characteristics and computational constraints. Code is available at: https://github.com/SafeRL-Lab/RLBenchNet

A Comprehensive Benchmarking Platform for Deep Generative Models in Molecular Design

The development of novel pharmaceuticals represents a significant challenge in modern science, with substantial costs and time investments. Deep generative models have emerged as promising tools for accelerating drug discovery by efficiently exploring the vast chemical space. However, this rapidly evolving field lacks standardized evaluation protocols, impeding fair comparison between approaches. This research presents an extensive analysis of the Molecular Sets (MOSES) platform, a comprehensive benchmarking framework designed to standardize evaluation of deep generative models in molecular design. Through rigorous assessment of multiple generative architectures, including recurrent neural networks, variational autoencoders, and generative adversarial networks, we examine their capabilities in generating valid, unique, and novel molecular structures while maintaining specific chemical properties. Our findings reveal that different architectures exhibit complementary strengths across various metrics, highlighting the complex trade-offs between exploration and exploitation in chemical space. This study provides detailed insights into the current state of the art in molecular generation and establishes a foundation for future advancements in AI-driven drug discovery.

Conversational Recommendation System using NLP and Sentiment Analysis

In today's digitally-driven world, the demand for personalized and context-aware recommendations has never been greater. Traditional recommender systems have made significant strides in this direction, but they often lack the ability to tap into the richness of conversational data. This paper represents a novel approach to recommendation systems by integrating conversational insights into the recommendation process. The Conversational Recommender System integrates cutting-edge technologies such as deep learning, leveraging machine learning algorithms like Apriori for Association Rule Mining, Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), and Long Short-Term Memory (LTSM). Furthermore, sophisticated voice recognition technologies, including Hidden Markov Models (HMMs) and Dynamic Time Warping (DTW) algorithms, play a crucial role in accurate speech-to-text conversion, ensuring robust performance in diverse environments. The methodology incorporates a fusion of content-based and collaborative recommendation approaches, enhancing them with NLP techniques. This innovative integration ensures a more personalized and context-aware recommendation experience, particularly in marketing applications.

The Logical Expressiveness of Temporal GNNs via Two-Dimensional Product Logics

In recent years, the expressive power of various neural architectures -- including graph neural networks (GNNs), transformers, and recurrent neural networks -- has been characterised using tools from logic and formal language theory. As the capabilities of basic architectures are becoming well understood, increasing attention is turning to models that combine multiple architectural paradigms. Among them particularly important, and challenging to analyse, are temporal extensions of GNNs, which integrate both spatial (graph-structure) and temporal (evolution over time) dimensions. In this paper, we initiate the study of logical characterisation of temporal GNNs by connecting them to two-dimensional product logics. We show that the expressive power of temporal GNNs depends on how graph and temporal components are combined. In particular, temporal GNNs that apply static GNNs recursively over time can capture all properties definable in the product logic of (past) propositional temporal logic PTL and the modal logic K. In contrast, architectures such as graph-and-time TGNNs and global TGNNs can only express restricted fragments of this logic, where the interaction between temporal and spatial operators is syntactically constrained. These results yield the first logical characterisations of temporal GNNs and establish new relative expressiveness results for temporal GNNs.

Neuromorphic Imaging Flow Cytometry combined with Adaptive Recurrent Spiking Neural Networks

We present an experimental imaging flow cytometer using a 1 {\mu}s temporal resolution event-based CMOS camera, with data processed by adaptive feedforward and recurrent spiking neural networks. Our study classifies PMMA particles (12, 16, 20 {\mu}m) flowing at 0.7 m/s in a microfluidic channel. Processing of experimental data highlighted that spiking recurrent networks, including LSTM and GRU models, achieved 98.4% accuracy by leveraging temporal dependencies. Additionally, adaptation mechanisms in lightweight feedforward spiking networks improved accuracy by 4.3%. This work outlines a technological roadmap for neuromorphic-assisted biomedical applications, enhancing classification performance while maintaining low latency and sparsity.

ASRC-SNN: Adaptive Skip Recurrent Connection Spiking Neural Network

In recent years, Recurrent Spiking Neural Networks (RSNNs) have shown promising potential in long-term temporal modeling. Many studies focus on improving neuron models and also integrate recurrent structures, leveraging their synergistic effects to improve the long-term temporal modeling capabilities of Spiking Neural Networks (SNNs). However, these studies often place an excessive emphasis on the role of neurons, overlooking the importance of analyzing neurons and recurrent structures as an integrated framework. In this work, we consider neurons and recurrent structures as an integrated system and conduct a systematic analysis of gradient propagation along the temporal dimension, revealing a challenging gradient vanishing problem. To address this issue, we propose the Skip Recurrent Connection (SRC) as a replacement for the vanilla recurrent structure, effectively mitigating the gradient vanishing problem and enhancing long-term temporal modeling performance. Additionally, we propose the Adaptive Skip Recurrent Connection (ASRC), a method that can learn the skip span of skip recurrent connection in each layer of the network. Experiments show that replacing the vanilla recurrent structure in RSNN with SRC significantly improves the model's performance on temporal benchmark datasets. Moreover, ASRC-SNN outperforms SRC-SNN in terms of temporal modeling capabilities and robustness.

Anomaly Detection for Non-stationary Time Series using Recurrent Wavelet Probabilistic Neural Network

In this paper, an unsupervised Recurrent Wavelet Probabilistic Neural Network (RWPNN) is proposed, which aims at detecting anomalies in non-stationary environments by modelling the temporal features using a nonparametric density estimation network. The novel framework consists of two components, a Stacked Recurrent Encoder-Decoder (SREnc-Dec) module that captures temporal features in a latent space, and a Multi-Receptive-field Wavelet Probabilistic Network (MRWPN) that creates an ensemble probabilistic model to characterise the latent space. This formulation extends the standard wavelet probabilistic networks to wavelet deep probabilistic networks, which can handle higher data dimensionality. The MRWPN module can adapt to different rates of data variation in different datasets without imposing strong distribution assumptions, resulting in a more robust and accurate detection for Time Series Anomaly Detection (TSAD) tasks in the non-stationary environment. We carry out the assessment on 45 real-world time series datasets from various domains, verify the performance of RWPNN in TSAD tasks with several constraints, and show its ability to provide early warnings for anomalous events.

Concept-Guided Interpretability via Neural Chunking

Neural networks are often black boxes, reflecting the significant challenge of understanding their internal workings. We propose a different perspective that challenges the prevailing view: rather than being inscrutable, neural networks exhibit patterns in their raw population activity that mirror regularities in the training data. We refer to this as the Reflection Hypothesis and provide evidence for this phenomenon in both simple recurrent neural networks (RNNs) and complex large language models (LLMs). Building on this insight, we propose to leverage cognitively-inspired methods of chunking to segment high-dimensional neural population dynamics into interpretable units that reflect underlying concepts. We propose three methods to extract these emerging entities, complementing each other based on label availability and dimensionality. Discrete sequence chunking (DSC) creates a dictionary of entities; population averaging (PA) extracts recurring entities that correspond to known labels; and unsupervised chunk discovery (UCD) can be used when labels are absent. We demonstrate the effectiveness of these methods in extracting entities across varying model sizes, ranging from inducing compositionality in RNNs to uncovering recurring neural population states in large models with diverse architectures, and illustrate their advantage over other methods. Throughout, we observe a robust correspondence between the extracted entities and concrete or abstract concepts. Artificially inducing the extracted entities in neural populations effectively alters the network's generation of associated concepts. Our work points to a new direction for interpretability, one that harnesses both cognitive principles and the structure of naturalistic data to reveal the hidden computations of complex learning systems, gradually transforming them from black boxes into systems we can begin to understand.