Learning Locally Interacting Discrete Dynamical Systems: Towards Data-Efficient and Scalable Prediction

Locally interacting dynamical systems, such as epidemic spread, rumor propagation through crowd, and forest fire, exhibit complex global dynamics originated from local, relatively simple, and often stochastic interactions between dynamic elements. Their temporal evolution is often driven by transitions between a finite number of discrete states. Despite significant advancements in predictive modeling through deep learning, such interactions among many elements have rarely explored as a specific domain for predictive modeling. We present Attentive Recurrent Neural Cellular Automata (AR-NCA), to effectively discover unknown local state transition rules by associating the temporal information between neighboring cells in a permutation-invariant manner. AR-NCA exhibits the superior generalizability across various system configurations (i.e., spatial distribution of states), data efficiency and robustness in extremely data-limited scenarios even in the presence of stochastic interactions, and scalability through spatial dimension-independent prediction.

Topological Representations of Heterogeneous Learning Dynamics of Recurrent Spiking Neural Networks

Spiking Neural Networks (SNNs) have become an essential paradigm in neuroscience and artificial intelligence, providing brain-inspired computation. Recent advances in literature have studied the network representations of deep neural networks. However, there has been little work that studies representations learned by SNNs, especially using unsupervised local learning methods like spike-timing dependent plasticity (STDP). Recent work by \cite{barannikov2021representation} has introduced a novel method to compare topological mappings of learned representations called Representation Topology Divergence (RTD). Though useful, this method is engineered particularly for feedforward deep neural networks and cannot be used for recurrent networks like Recurrent SNNs (RSNNs). This paper introduces a novel methodology to use RTD to measure the difference between distributed representations of RSNN models with different learning methods. We propose a novel reformulation of RSNNs using feedforward autoencoder networks with skip connections to help us compute the RTD for recurrent networks. Thus, we investigate the learning capabilities of RSNN trained using STDP and the role of heterogeneity in the synaptic dynamics in learning such representations. We demonstrate that heterogeneous STDP in RSNNs yield distinct representations than their homogeneous and surrogate gradient-based supervised learning counterparts. Our results provide insights into the potential of heterogeneous SNN models, aiding the development of more efficient and biologically plausible hybrid artificial intelligence systems.

Sparse Spiking Neural Network: Exploiting Heterogeneity in Timescales for Pruning Recurrent SNN

Recurrent Spiking Neural Networks (RSNNs) have emerged as a computationally efficient and brain-inspired learning model. The design of sparse RSNNs with fewer neurons and synapses helps reduce the computational complexity of RSNNs. Traditionally, sparse SNNs are obtained by first training a dense and complex SNN for a target task, and, then, pruning neurons with low activity (activity-based pruning) while maintaining task performance. In contrast, this paper presents a task-agnostic methodology for designing sparse RSNNs by pruning a large randomly initialized model. We introduce a novel Lyapunov Noise Pruning (LNP) algorithm that uses graph sparsification methods and utilizes Lyapunov exponents to design a stable sparse RSNN from a randomly initialized RSNN. We show that the LNP can leverage diversity in neuronal timescales to design a sparse Heterogeneous RSNN (HRSNN). Further, we show that the same sparse HRSNN model can be trained for different tasks, such as image classification and temporal prediction. We experimentally show that, in spite of being task-agnostic, LNP increases computational efficiency (fewer neurons and synapses) and prediction performance of RSNNs compared to traditional activity-based pruning of trained dense models.

Studying the Impact of Stochasticity on the Evaluation of Deep Neural Networks for Forest-Fire Prediction

This paper presents the first systematic study of the evaluation of Deep Neural Networks (DNNs) for discrete dynamical systems under stochastic assumptions, with a focus on wildfire prediction. We develop a framework to study the impact of stochasticity on two classes of evaluation metrics: classification-based metrics, which assess fidelity to observed ground truth (GT), and proper scoring rules, which test fidelity-to-statistic. Our findings reveal that evaluating for fidelity-to-statistic is a reliable alternative in highly stochastic scenarios. We extend our analysis to real-world wildfire data, highlighting limitations in traditional wildfire prediction evaluation methods, and suggest interpretable stochasticity-compatible alternatives.

Brain-Inspired Spiking Neural Network for Online Unsupervised Time Series Prediction

Energy and data-efficient online time series prediction for predicting evolving dynamical systems are critical in several fields, especially edge AI applications that need to update continuously based on streaming data. However, current DNN-based supervised online learning models require a large amount of training data and cannot quickly adapt when the underlying system changes. Moreover, these models require continuous retraining with incoming data making them highly inefficient. To solve these issues, we present a novel Continuous Learning-based Unsupervised Recurrent Spiking Neural Network Model (CLURSNN), trained with spike timing dependent plasticity (STDP). CLURSNN makes online predictions by reconstructing the underlying dynamical system using Random Delay Embedding by measuring the membrane potential of neurons in the recurrent layer of the RSNN with the highest betweenness centrality. We also use topological data analysis to propose a novel methodology using the Wasserstein Distance between the persistence homologies of the predicted and observed time series as a loss function. We show that the proposed online time series prediction methodology outperforms state-of-the-art DNN models when predicting an evolving Lorenz63 dynamical system.

Unsupervised 3D Object Learning through Neuron Activity aware Plasticity

We present an unsupervised deep learning model for 3D object classification. Conventional Hebbian learning, a well-known unsupervised model, suffers from loss of local features leading to reduced performance for tasks with complex geometric objects. We present a deep network with a novel Neuron Activity Aware (NeAW) Hebbian learning rule that dynamically switches the neurons to be governed by Hebbian learning or anti-Hebbian learning, depending on its activity. We analytically show that NeAW Hebbian learning relieves the bias in neuron activity, allowing more neurons to attend to the representation of the 3D objects. Empirical results show that the NeAW Hebbian learning outperforms other variants of Hebbian learning and shows higher accuracy over fully supervised models when training data is limited.

Heterogeneous Neuronal and Synaptic Dynamics for Spike-Efficient Unsupervised Learning: Theory and Design Principles

This paper shows that the heterogeneity in neuronal and synaptic dynamics reduces the spiking activity of a Recurrent Spiking Neural Network (RSNN) while improving prediction performance, enabling spike-efficient (unsupervised) learning. We analytically show that the diversity in neurons' integration/relaxation dynamics improves an RSNN's ability to learn more distinct input patterns (higher memory capacity), leading to improved classification and prediction performance. We further prove that heterogeneous Spike-Timing-Dependent-Plasticity (STDP) dynamics of synapses reduce spiking activity but preserve memory capacity. The analytical results motivate Heterogeneous RSNN design using Bayesian optimization to determine heterogeneity in neurons and synapses to improve $\mathcal{E}$, defined as the ratio of spiking activity and memory capacity. The empirical results on time series classification and prediction tasks show that optimized HRSNN increases performance and reduces spiking activity compared to a homogeneous RSNN.

Forecasting local behavior of multi-agent system and its application to forest fire model

In this paper, we study a CNN-LSTM model to forecast the state of a specific agent in a large multi-agent system. The proposed model consists of a CNN encoder to represent the system into a low-dimensional vector, a LSTM module to learn the agent dynamics in the vector space, and a MLP decoder to predict the future state of an agent. A forest fire model is considered as an example where we need to predict when a specific tree agent will be burning. We observe that the proposed model achieves higher AUC with less computation than a frame-based model and significantly saves computational costs such as the activation than ConvLSTM.

Learning Point Processes using Recurrent Graph Network

We present a novel Recurrent Graph Network (RGN) approach for predicting discrete marked event sequences by learning the underlying complex stochastic process. Using the framework of Point Processes, we interpret a marked discrete event sequence as the superposition of different sequences each of a unique type. The nodes of the Graph Network use LSTM to incorporate past information whereas a Graph Attention Network (GAT Network) introduces strong inductive biases to capture the interaction between these different types of events. By changing the self-attention mechanism from attending over past events to attending over event types, we obtain a reduction in time and space complexity from $\mathcal{O}(N^2)$ (total number of events) to $\mathcal{O}(|\mathcal{Y}|^2)$ (number of event types). Experiments show that the proposed approach improves performance in log-likelihood, prediction and goodness-of-fit tasks with lower time and space complexity compared to state-of-the art Transformer based architectures.

Radar Guided Dynamic Visual Attention for Resource-Efficient RGB Object Detection

An autonomous system's perception engine must provide an accurate understanding of the environment for it to make decisions. Deep learning based object detection networks experience degradation in the performance and robustness for small and far away objects due to a reduction in object's feature map as we move to higher layers of the network. In this work, we propose a novel radar-guided spatial attention for RGB images to improve the perception quality of autonomous vehicles operating in a dynamic environment. In particular, our method improves the perception of small and long range objects, which are often not detected by the object detectors in RGB mode. The proposed method consists of two RGB object detectors, namely the Primary detector and a lightweight Secondary detector. The primary detector takes a full RGB image and generates primary detections. Next, the radar proposal framework creates regions of interest (ROIs) for object proposals by projecting the radar point cloud onto the 2D RGB image. These ROIs are cropped and fed to the secondary detector to generate secondary detections which are then fused with the primary detections via non-maximum suppression. This method helps in recovering the small objects by preserving the object's spatial features through an increase in their receptive field. We evaluate our fusion method on the challenging nuScenes dataset and show that our fusion method with SSD-lite as primary and secondary detector improves the baseline primary yolov3 detector's recall by 14% while requiring three times fewer computational resources.