The rise of mobility, IoT and wearables has shifted processing to the edge of the sensors, driven by the need to reduce latency, communication costs and overall energy consumption. While deep learning models have achieved remarkable results in various domains, their deployment at the edge for real-time applications remains computationally expensive. Neuromorphic computing emerges as a promising paradigm shift, characterized by co-localized memory and computing as well as event-driven asynchronous sensing and processing. In this work, we demonstrate the possibility of solving the ubiquitous computer vision task of object detection at the edge with low-power requirements, using the event-based N-Caltech101 dataset. We present the first instance of an on-chip spiking neural network for event-based face detection deployed on the SynSense Speck neuromorphic chip, which comprises both an event-based sensor and a spike-based asynchronous processor implementing Integrate-and-Fire neurons. We show how to reduce precision discrepancies between off-chip clock-driven simulation used for training and on-chip event-driven inference. This involves using a multi-spike version of the Integrate-and-Fire neuron on simulation, where spikes carry values that are proportional to the extent the membrane potential exceeds the firing threshold. We propose a robust strategy to train spiking neural networks with back-propagation through time using multi-spike activation and firing rate regularization and demonstrate how to decode output spikes into bounding boxes. We show that the power consumption of the chip is directly proportional to the number of synaptic operations in the spiking neural network, and we explore the trade-off between power consumption and detection precision with different firing rate regularization, achieving an on-chip face detection mAP[0.5] of ~0.6 while consuming only ~20 mW.
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The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time. To this end, algorithmically, the standard adaptive finite element method (AFEM) integrates an inexact solver and nested iterations with discerning stopping criteria balancing the different error components. The analysis ensuring optimal convergence order of AFEM with respect to the overall computational cost critically hinges on the concept of R-linear convergence of a suitable quasi-error quantity. This work tackles several shortcomings of previous approaches by introducing a new proof strategy. First, the algorithm requires several fine-tuned parameters in order to make the underlying analysis work. A redesign of the standard line of reasoning and the introduction of a summability criterion for R-linear convergence allows us to remove restrictions on those parameters. Second, the usual assumption of a (quasi-)Pythagorean identity is replaced by the generalized notion of quasi-orthogonality from [Feischl, Math. Comp., 91 (2022)]. Importantly, this paves the way towards extending the analysis to general inf-sup stable problems beyond the energy minimization setting. Numerical experiments investigate the choice of the adaptivity parameters.
The dynamic mode decomposition (DMD) is a simple and powerful data-driven modeling technique that is capable of revealing coherent spatiotemporal patterns from data. The method's linear algebra-based formulation additionally allows for a variety of optimizations and extensions that make the algorithm practical and viable for real-world data analysis. As a result, DMD has grown to become a leading method for dynamical system analysis across multiple scientific disciplines. PyDMD is a Python package that implements DMD and several of its major variants. In this work, we expand the PyDMD package to include a number of cutting-edge DMD methods and tools specifically designed to handle dynamics that are noisy, multiscale, parameterized, prohibitively high-dimensional, or even strongly nonlinear. We provide a complete overview of the features available in PyDMD as of version 1.0, along with a brief overview of the theory behind the DMD algorithm, information for developers, tips regarding practical DMD usage, and introductory coding examples. All code is available at //github.com/PyDMD/PyDMD .
The beta distribution serves as a canonical tool for modeling probabilities and is extensively used in statistics and machine learning, especially in the field of Bayesian nonparametrics. Despite its widespread use, there is limited work on flexible and computationally convenient stochastic process extensions for modeling dependent random probabilities. We propose a novel stochastic process called the logistic-beta process, whose logistic transformation yields a stochastic process with common beta marginals. Similar to the Gaussian process, the logistic-beta process can model dependence on both discrete and continuous domains, such as space or time, and has a highly flexible dependence structure through correlation kernels. Moreover, its normal variance-mean mixture representation leads to highly effective posterior inference algorithms. The flexibility and computational benefits of logistic-beta processes are demonstrated through nonparametric binary regression simulation studies. Furthermore, we apply the logistic-beta process in modeling dependent Dirichlet processes, and illustrate its application and benefits through Bayesian density regression problems in a toxicology study.
Multi-product formulas (MPF) are linear combinations of Trotter circuits offering high-quality simulation of Hamiltonian time evolution with fewer Trotter steps. Here we report two contributions aimed at making multi-product formulas more viable for near-term quantum simulations. First, we extend the theory of Trotter error with commutator scaling developed by Childs, Su, Tran et al. to multi-product formulas. Our result implies that multi-product formulas can achieve a quadratic reduction of Trotter error in 1-norm (nuclear norm) on arbitrary time intervals compared with the regular product formulas without increasing the required circuit depth or qubit connectivity. The number of circuit repetitions grows only by a constant factor. Second, we introduce dynamic multi-product formulas with time-dependent coefficients chosen to minimize a certain efficiently computable proxy for the Trotter error. We use a minimax estimation method to make dynamic multi-product formulas robust to uncertainty from algorithmic errors, sampling and hardware noise. We call this method Minimax MPF and we provide a rigorous bound on its error.
Deep neural networks are widely deployed in many fields. Due to the in-situ computation (known as processing in memory) capacity of the Resistive Random Access Memory (ReRAM) crossbar, ReRAM-based accelerator shows potential in accelerating DNN with low power and high performance. However, despite power advantage, such kind of accelerators suffer from the high power consumption of peripheral circuits, especially Analog-to-Digital Converter (ADC), which account for over 60 percent of total power consumption. This problem hinders the ReRAM-based accelerator to achieve higher efficiency. Some redundant Analog-to-Digital conversion operations have no contribution to maintaining inference accuracy, and such operations can be eliminated by modifying the ADC searching logic. Based on such observations, we propose an algorithm-hardware co-design method and explore the co-design approach in both hardware design and quantization algorithms. Firstly, we focus on the distribution output along the crossbar's bit-lines and identify the fine-grained redundant ADC sampling bits. % of weight and To further compress ADC bits, we propose a hardware-friendly quantization method and coding scheme, in which different quantization strategy was applied to the partial results in different intervals. To support the two features above, we propose a lightweight architectural design based on SAR-ADC\@. It's worth mentioning that our method is not only more energy efficient but also retains the flexibility of the algorithm. Experiments demonstrate that our method can reduce about $1.6 \sim 2.3 \times$ ADC power reduction.
Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formulation such as droplet merging, splitting, and transport. This paper studies a class of mean field control formulation towards these droplet dynamics. They are used to control and maintain the manipulation of droplets in applications. We first formulate the droplet dynamics as gradient flows of free energies in modified optimal transport metrics with nonlinear mobilities. We then design an optimal control problem for these gradient flows. We lastly apply the primal-dual hybrid gradient algorithm with high-order finite element methods to simulate the proposed mean field control problems. Numerical examples, including droplet formation, bead-up/spreading, transport, and merging/splitting on a two-dimensional spatial domain, demonstrate the effectiveness of the proposed mean field control mechanism.
Deep denoisers have shown excellent performance in solving inverse problems in signal and image processing. In order to guarantee the convergence, the denoiser needs to satisfy some Lipschitz conditions like non-expansiveness. However, enforcing such constraints inevitably compromises recovery performance. This paper introduces a novel training strategy that enforces a weaker constraint on the deep denoiser called pseudo-contractiveness. By studying the spectrum of the Jacobian matrix, relationships between different denoiser assumptions are revealed. Effective algorithms based on gradient descent and Ishikawa process are derived, and further assumptions of strict pseudo-contractiveness yield efficient algorithms using half-quadratic splitting and forward-backward splitting. The proposed algorithms theoretically converge strongly to a fixed point. A training strategy based on holomorphic transformation and functional calculi is proposed to enforce the pseudo-contractive denoiser assumption. Extensive experiments demonstrate superior performance of the pseudo-contractive denoiser compared to related denoisers. The proposed methods are competitive in terms of visual effects and quantitative values.
We propose a new loss function for supervised and physics-informed training of neural networks and operators that incorporates a posteriori error estimate. More specifically, during the training stage, the neural network learns additional physical fields that lead to rigorous error majorants after a computationally cheap postprocessing stage. Theoretical results are based upon the theory of functional a posteriori error estimates, which allows for the systematic construction of such loss functions for a diverse class of practically relevant partial differential equations. From the numerical side, we demonstrate on a series of elliptic problems that for a variety of architectures and approaches (physics-informed neural networks, physics-informed neural operators, neural operators, and classical architectures in the regression and physics-informed settings), we can reach better or comparable accuracy and in addition to that cheaply recover high-quality upper bounds on the error after training.
We formulate a uniform tail bound for empirical processes indexed by a class of functions, in terms of the individual deviations of the functions rather than the worst-case deviation in the considered class. The tail bound is established by introducing an initial "deflation" step to the standard generic chaining argument. The resulting tail bound is the sum of the complexity of the "deflated function class" in terms of a generalization of Talagrand's $\gamma$ functional, and the deviation of the function instance, both of which are formulated based on the natural seminorm induced by the corresponding Cram\'{e}r functions. We also provide certain approximations for the mentioned seminorm when the function class lies in a given (exponential type) Orlicz space, that can be used to make the complexity term and the deviation term more explicit.
Anomaly detection in SDN using data flow prediction is a difficult task. This problem is included in the category of time series and regression problems. Machine learning approaches are challenging in this field due to the manual selection of features. On the other hand, deep learning approaches have important features due to the automatic selection of features. Meanwhile, RNN-based approaches have been used the most. The LSTM and GRU approaches learn dependent entities well; on the other hand, the IndRNN approach learns non-dependent entities in time series. The proposed approach tried to use a combination of IndRNN and LSTM approaches to learn dependent and non-dependent features. Feature selection approaches also provide a suitable view of features for the models; for this purpose, four feature selection models, Filter, Wrapper, Embedded, and Autoencoder were used. The proposed IndRNNLSTM algorithm, in combination with Embedded, was able to achieve MAE=1.22 and RMSE=9.92 on NSL-KDD data.
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