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Subitizing, or the sense of small natural numbers, is an innate cognitive function of humans and primates; it responds to visual stimuli prior to the development of any symbolic skills, language or arithmetic. Given successes of deep learning (DL) in tasks of visual intelligence and given the primitivity of number sense, a tantalizing question is whether DL can comprehend numbers and perform subitizing. But somewhat disappointingly, extensive experiments of the type of cognitive psychology demonstrate that the examples-driven black box DL cannot see through superficial variations in visual representations and distill the abstract notion of natural number, a task that children perform with high accuracy and confidence. The failure is apparently due to the learning method not the CNN computational machinery itself. A recurrent neural network capable of subitizing does exist, which we construct by encoding a mechanism of mathematical morphology into the CNN convolutional kernels. Also, we investigate, using subitizing as a test bed, the ways to aid the black box DL by cognitive priors derived from human insight. Our findings are mixed and interesting, pointing to both cognitive deficit of pure DL, and some measured successes of boosting DL by predetermined cognitive implements. This case study of DL in cognitive computing is meaningful for visual numerosity represents a minimum level of human intelligence.
Spiking neural networks (SNNs) that enables energy efficient implementation on emerging neuromorphic hardware are gaining more attention. Yet now, SNNs have not shown competitive performance compared with artificial neural networks (ANNs), due to the lack of effective learning algorithms and efficient programming frameworks. We address this issue from two aspects: (1) We propose a neuron normalization technique to adjust the neural selectivity and develop a direct learning algorithm for deep SNNs. (2) Via narrowing the rate coding window and converting the leaky integrate-and-fire (LIF) model into an explicitly iterative version, we present a Pytorch-based implementation method towards the training of large-scale SNNs. In this way, we are able to train deep SNNs with tens of times speedup. As a result, we achieve significantly better accuracy than the reported works on neuromorphic datasets (N-MNIST and DVSCIFAR10), and comparable accuracy as existing ANNs and pre-trained SNNs on non-spiking datasets (CIFAR10). To our best knowledge, this is the first work that demonstrates direct training of deep SNNs with high performance on CIFAR10, and the efficient implementation provides a new way to explore the potential of SNNs.
Continuous-valued deep convolutional networks (DNNs) can be converted into accurate rate-coding based spike neural networks (SNNs). However, the substantial computational and energy costs, which is caused by multiple spikes, limit their use in mobile and embedded applications. And recent works have shown that the newly emerged temporal-coding based SNNs converted from DNNs can reduce the computational load effectively. In this paper, we propose a novel method to convert DNNs to temporal-coding SNNs, called TDSNN. Combined with the characteristic of the leaky integrate-andfire (LIF) neural model, we put forward a new coding principle Reverse Coding and design a novel Ticking Neuron mechanism. According to our evaluation, our proposed method achieves 42% total operations reduction on average in large networks comparing with DNNs with no more than 0.5% accuracy loss. The evaluation shows that TDSNN may prove to be one of the key enablers to make the adoption of SNNs widespread.
One of the long-standing questions in biology and machine learning is how neural networks may learn important features from the input activities with a delayed feedback, commonly known as the temporal credit-assignment problem. The aggregate-label learning is proposed to resolve this problem by matching the spike count of a neuron with the magnitude of a feedback signal. However, the existing threshold-driven aggregate-label learning algorithms are computationally intensive, resulting in relatively low learning efficiency hence limiting their usability in practical applications. In order to address these limitations, we propose a novel membrane-potential driven aggregate-label learning algorithm, namely MPD-AL. With this algorithm, the easiest modifiable time instant is identified from membrane potential traces of the neuron, and guild the synaptic adaptation based on the presynaptic neurons’ contribution at this time instant. The experimental results demonstrate that the proposed algorithm enables the neurons to generate the desired number of spikes, and to detect useful clues embedded within unrelated spiking activities and background noise with a better learning efficiency over the state-of-the-art TDP1 and Multi-Spike Tempotron algorithms. Furthermore, we propose a data-driven dynamic decoding scheme for practical classification tasks, of which the aggregate labels are hard to define. This scheme effectively improves the classification accuracy of the aggregate-label learning algorithms as demonstrated on a speech recognition task.