Bridging Autoencoders and Dynamic Mode Decomposition for Reduced-order Modeling and Control of PDEs

Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper explores a deep autoencoding learning method for reduced-order modeling and control of dynamical systems governed by spatiotemporal PDEs. We first analytically show that an optimization objective for learning a linear autoencoding reduced-order model can be formulated to yield a solution closely resembling the result obtained through the dynamic mode decomposition with control algorithm. We then extend this linear autoencoding architecture to a deep autoencoding framework, enabling the development of a nonlinear reduced-order model. Furthermore, we leverage the learned reduced-order model to design controllers using stability-constrained deep neural networks. Numerical experiments are presented to validate the efficacy of our approach in both modeling and control using the example of a reaction-diffusion system.

RoboKoop: Efficient Control Conditioned Representations from Visual Input in Robotics using Koopman Operator

Developing agents that can perform complex control tasks from high-dimensional observations is a core ability of autonomous agents that requires underlying robust task control policies and adapting the underlying visual representations to the task. Most existing policies need a lot of training samples and treat this problem from the lens of two-stage learning with a controller learned on top of pre-trained vision models. We approach this problem from the lens of Koopman theory and learn visual representations from robotic agents conditioned on specific downstream tasks in the context of learning stabilizing control for the agent. We introduce a Contrastive Spectral Koopman Embedding network that allows us to learn efficient linearized visual representations from the agent's visual data in a high dimensional latent space and utilizes reinforcement learning to perform off-policy control on top of the extracted representations with a linear controller. Our method enhances stability and control in gradient dynamics over time, significantly outperforming existing approaches by improving efficiency and accuracy in learning task policies over extended horizons.

Exploiting Heterogeneity in Timescales for Sparse Recurrent Spiking Neural Networks for Energy-Efficient Edge Computing

Spiking Neural Networks (SNNs) represent the forefront of neuromorphic computing, promising energy-efficient and biologically plausible models for complex tasks. This paper weaves together three groundbreaking studies that revolutionize SNN performance through the introduction of heterogeneity in neuron and synapse dynamics. We explore the transformative impact of Heterogeneous Recurrent Spiking Neural Networks (HRSNNs), supported by rigorous analytical frameworks and novel pruning methods like Lyapunov Noise Pruning (LNP). Our findings reveal how heterogeneity not only enhances classification performance but also reduces spiking activity, leading to more efficient and robust networks. By bridging theoretical insights with practical applications, this comprehensive summary highlights the potential of SNNs to outperform traditional neural networks while maintaining lower computational costs. Join us on a journey through the cutting-edge advancements that pave the way for the future of intelligent, energy-efficient neural computing.

Real-time Digital RF Emulation -- I: The Direct Path Computational Model

In this paper we consider the problem of developing a computational model for emulating an RF channel. The motivation for this is that an accurate and scalable emulator has the potential to minimize the need for field testing, which is expensive, slow, and difficult to replicate. Traditionally, emulators are built using a tapped delay line model where long filters modeling the physical interactions of objects are implemented directly. For an emulation scenario consisting of $M$ objects all interacting with one another, the tapped delay line model's computational requirements scale as $O(M^3)$ per sample: there are $O(M^2)$ channels, each with $O(M)$ complexity. In this paper, we develop a new ``direct path" model that, while remaining physically faithful, allows us to carefully factor the emulator operations, resulting in an $O(M^2)$ per sample scaling of the computational requirements. The impact of this is drastic, a $200$ object scenario sees about a $100\times$ reduction in the number of per sample computations. Furthermore, the direct path model gives us a natural way to distribute the computations for an emulation: each object is mapped to a computational node, and these nodes are networked in a fully connected communication graph. Alongside a discussion of the model and the physical phenomena it emulates, we show how to efficiently parameterize antenna responses and scattering profiles within this direct path framework. To verify the model and demonstrate its viability in hardware, we provide several numerical experiments produced using a cycle level C++ simulator of a hardware implementation of the model.

Real-time Digital RF Emulation -- II: A Near Memory Custom Accelerator

A near memory hardware accelerator, based on a novel direct path computational model, for real-time emulation of radio frequency systems is demonstrated. Our evaluation of hardware performance uses both application-specific integrated circuits (ASIC) and field programmable gate arrays (FPGA) methodologies: 1). The ASIC testchip implementation, using TSMC 28nm CMOS, leverages distributed autonomous control to extract concurrency in compute as well as low latency. It achieves a $518$ MHz per channel bandwidth in a prototype $4$-node system. The maximum emulation range supported in this paradigm is $9.5$ km with $0.24$ $\mu$s of per-sample emulation latency. 2). The FPGA-based implementation, evaluated on a Xilinx ZCU104 board, demonstrates a $9$-node test case (two Transmitters, one Receiver, and $6$ passive reflectors) with an emulation range of $1.13$ km to $27.3$ km at $215$ MHz bandwidth.

Towards Robust Real-Time Hardware-based Mobile Malware Detection using Multiple Instance Learning Formulation

This study introduces RT-HMD, a Hardware-based Malware Detector (HMD) for mobile devices, that refines malware representation in segmented time-series through a Multiple Instance Learning (MIL) approach. We address the mislabeling issue in real-time HMDs, where benign segments in malware time-series incorrectly inherit malware labels, leading to increased false positives. Utilizing the proposed Malicious Discriminative Score within the MIL framework, RT-HMD effectively identifies localized malware behaviors, thereby improving the predictive accuracy. Empirical analysis, using a hardware telemetry dataset collected from a mobile platform across 723 benign and 1033 malware samples, shows a 5% precision boost while maintaining recall, outperforming baselines affected by mislabeled benign segments.

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.