Deep neural networks are over-parameterized and easily overfit to and memorize the datasets that they train on. In the extreme case, it has been shown that networks can memorize a randomly labeled dataset. In this paper, we propose using the curvature of the loss function around each training sample, averaged over training epochs, as a measure of memorization of a sample. We show that this curvature metric effectively captures memorization statistics, both qualitatively and quantitatively in popular image datasets. We provide quantitative validation of the proposed metric against memorization scores released by Feldman & Zhang (2020). Further, experiments on mislabeled data detection show that corrupted samples are learned with high curvature and using curvature for identifying mislabelled examples outperforms existing approaches. Qualitatively, we find that high curvature samples correspond to long-tailed, mislabeled, or conflicting instances, indicating a likelihood of memorization. Notably, this analysis helps us find, to the best of our knowledge, a novel failure mode on the CIFAR100 and ImageNet datasets: that of duplicated images with differing labels.

In this paper, we study the second order properties of the loss of trained deep neural networks with respect to the training data points to understand the curvature of the loss surface in the vicinity of these points. We find that there is an unexpected concentration of samples with very low curvature. We note that these low curvature samples are largely consistent across completely different architectures, and identifiable in the early epochs of training. We show that the curvature relates to the ‘cleanliness’ of the data points, with low curvatures samples corresponding to clean, higher clarity samples, representative of their category. Alternatively, high curvature samples are often occluded, have conflicting features and visually atypical of their category. Armed with this insight, we introduce SLo-Curves, a novel coreset identification and training algorithm. SLo-curves identifies the samples with low curvatures as being more data-efficient and trains on them with an additional regularizer that penalizes high curvature of the loss surface in their vicinity. We demonstrate the efficacy of SLo-Curves on CIFAR-10 and CIFAR-100 datasets, where it outperforms state of the art coreset selection methods at small coreset sizes by up to 9%. The identified coresets generalize across architectures, and hence can be pre-computed to generate condensed versions of datasets for use in downstream tasks. Code is available at https://github.com/ishagarg/SLo-Curves.

Spiking Neural Networks (SNNs) offer a promising alternative to traditional deep learning, since they provide higher computational efficiency due to event-driven information processing. SNNs distribute the analog values of pixel intensities into binary spikes over time. However, the most widely used input coding schemes, such as Poisson based rate-coding, do not leverage the additional temporal learning capability of SNNs effectively. Moreover, these SNNs suffer from high inference latency which is a major bottleneck to their deployment. To overcome this, we propose a time-based encoding scheme that utilizes Discrete Cosine Transform (DCT) to reduce the number of timesteps required for inference (DCT-SNN). DCT decomposes an image into a weighted sum of sinusoidal basis images. At each time step, a single frequency base, taken in order and modulated by its corresponding DCT coefficient, is input to an accumulator that generates spikes upon crossing a threshold. We use the proposed scheme to train DCT-SNN, a low-latency deep SNN with leaky-integrate-and-fire neurons using surrogate gradient descent based backpropagation. We achieve top-1 accuracy of 89.94%, 68.30% and 52.43% on CIFAR10, CIFAR-100 and TinyImageNet, respectively using VGG architectures. Notably, DCT-SNN performs inference with 2-14X reduced latency compared to other state-of-the-art SNNs, while achieving comparable accuracy to their standard deep learning counterparts. The dimension of the transform allows us to control the number of timesteps required for inference. Additionally, we can trade-off accuracy with latency in a principled manner by dropping the highest frequency components during inference. The code is publicly available.1

Spiking Neural Networks (SNNs) are a promising alternative to traditional deep learning methods since they perform event-driven information processing. However, a major drawback of SNNs is high inference latency. The efficiency of SNNs could be enhanced using compression methods such as pruning and quantization. Notably, SNNs, unlike their non-spiking counterparts, consist of a temporal dimension, the compression of which can lead to latency reduction. In this paper, we propose spatial and temporal pruning of SNNs. First, structured spatial pruning is performed by determining the layer-wise significant dimensions using principal component analysis of the average accumulated membrane potential of the neurons. This step leads to 10-14X model compression. Additionally, it enables inference with lower latency and decreases the spike count per inference. To further reduce latency, temporal pruning is performed by gradually reducing the timesteps while training. The networks are trained using surrogate gradient descent based backpropagation and we validate the results on CIFAR10 and CIFAR100, using VGG architectures. The spatiotemporally pruned SNNs achieve 89.04% and 66.4% accuracy on CIFAR10 and CIFAR100, respectively, while performing inference with 3-30X reduced latency compared to state-of-the-art SNNs. Moreover, they require 8-14X lesser compute energy compared to their unpruned standard deep learning counterparts. The energy numbers are obtained by multiplying the number of operations with energy per operation. These SNNs also provide 1–4% higher robustness against Gaussian noise corrupted inputs. Furthermore, we perform weight quantization and find that performance remains reasonably stable up to 5-bit quantization.