Training much deeper spiking neural networks with a small number of time-steps.

Spiking Neural Network (SNN) is a promising energy-efficient neural architecture when implemented on neuromorphic hardware. The Artificial Neural Network (ANN) to SNN conversion method, which is the most effective SNN training method, has successfully converted moderately deep ANNs to SNNs with satisfactory performance. However, this method requires a large number of time-steps, which hurts the energy efficiency of SNNs. How to effectively covert a very deep ANN (e.g., more than 100 layers) to an SNN with a small number of time-steps remains a difficult task. To tackle this challenge, this paper makes the first attempt to propose a novel error analysis framework that takes both the "quantization error" and the "deviation error" into account, which comes from the discretization of SNN dynamicsthe neuron's coding scheme and the inconstant input currents at intermediate layers, respectively. Particularly, our theories reveal that the "deviation error" depends on both the spike threshold and the input variance. Based on our theoretical analysis, we further propose the Threshold Tuning and Residual Block Restructuring (TTRBR) method that can convert very deep ANNs (>100 layers) to SNNs with negligible accuracy degradation while requiring only a small number of time-steps. With very deep networks, our TTRBR method achieves state-of-the-art (SOTA) performance on the CIFAR-10, CIFAR-100, and ImageNet classification tasks.

Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications.

The heavy-tailed distributions of corrupted outliers and singular values of all channels in low-level vision have proven effective priors for many applications such as background modeling, photometric stereo and image alignment. And they can be well modeled by a hyper-Laplacian. However, the use of such distributions generally leads to challenging non-convex, non-smooth and non-Lipschitz problems, and makes existing algorithms very slow for large-scale applications. Together with the analytic solutions to $\ell _{p}$ -norm minimization with two specific values of $p$ , i.e., $p=1/2$ and $p=2/3$ , we propose two novel bilinear factor matrix norm minimization models for robust principal component analysis. We first define the double nuclear norm and Frobenius/nuclear hybrid norm penalties, and then prove that they are in essence the Schatten- $1/2$ and $2/3$ quasi-norms, respectively, which lead to much more tractable and scalable Lipschitz optimization problems. Our experimental analysis shows that both our methods yield more accurate solutions than original Schatten quasi-norm minimization, even when the number of observations is very limited. Finally, we apply our penalties to various low-level vision problems, e.g., text removal, moving object detection, image alignment and inpainting, and show that our methods usually outperform the state-of-the-art methods.

Online clustering algorithms for radar emitter classification.

Radar emitter classification is a special application of data clustering for classifying unknown radar emitters from received radar pulse samples. The main challenges of this task are the high dimensionality of radar pulse samples, small sample group size, and closely located radar pulse clusters. In this paper, two new online clustering algorithms are developed for radar emitter classification: One is model-based using the Minimum Description Length (MDL) criterion and the other is based on competitive learning. Computational complexity is analyzed for each algorithm and then compared. Simulation results show the superior performance of the model-based algorithm over competitive learning in terms of better classification accuracy, flexibility, and stability.

On the Convergence of the LMS Algorithm with Adaptive Learning Rate for Linear Feedforward Networks.

We consider the problem of training a linear feedforward neural network by using a gradient descent-like LMS learning algorithm. The objective is to find a weight matrix for the network, by repeatedly presenting to it a finite set of examples, so that the sum of the squares of the errors is minimized. Kohonen showed that with a small but fixed learning rate (or stepsize) some subsequences of the weight matrices generated by the algorithm will converge to certain matrices close to the optimal weight matrix. In this paper, we show that, by dynamically decreasing the learning rate during each training cycle, the sequence of matrices generated by the algorithm will converge to the optimal weight matrix. We also show that for any given ∊ > 0 the LMS algorithm, with decreasing learning rates, will generate an ∊-optimal weight matrix (i.e., a matrix of distance at most ∊ away from the optimal matrix) after O(1/∊) training cycles. This is in contrast to Ω(1/∊log 1/∊) training cycles needed to generate an ∊-optimal weight matrix when the learning rate is kept fixed. We also give a general condition for the learning rates under which the LMS learning algorithm is guaranteed to converge to the optimal weight matrix.