Continual learning (CL) has attracted increasing attention in the recent past. It aims to mimic the human ability to learn new concepts without catastrophic forgetting. While existing CL methods accomplish this to some extent, they are still prone to semantic drift of the learned feature space. Foundation models, which are endowed with a robust feature representation, learned from very large datasets, provide an interesting substrate for the solution of the CL problem. Recent work has also shown that they can be adapted to specific tasks by prompt tuning techniques that leave the generality of the representation mostly unscathed. An open question is, however, how to learn both prompts that are task specific and prompts that are global, i.e. capture cross-task information. In this work, we propose the Prompt Of Prompts (POP) model, which addresses this goal by progressively learning a group of task-specified prompts and a group of global prompts, denoted as POP, to integrate information from the former. We show that a foundation model equipped with POP learning is able to outperform classic CL methods by a significant margin. Moreover, as prompt tuning only requires a small set of training samples, POP is able to perform CL in the few-shot setting, while still outperforming competing methods trained on the entire dataset.

The problem of class incremental learning (CIL) is considered. State-of-the-art approaches use a dynamic architecture based on network expansion (NE), in which a task expert is added per task. While effective from a computational standpoint, these methods lead to models that grow quickly with the number of tasks. A new NE method, dense network expansion (DNE), is proposed to achieve a better trade-off between accuracy and model complexity. This is accomplished by the introduction of dense connections between the intermediate layers of the task expert networks, that enable the transfer of knowledge from old to new tasks via feature sharing and reusing. This sharing is implemented with a cross-task attention mechanism, based on a new task attention block (TAB), that fuses information across tasks. Unlike traditional attention mechanisms, TAB operates at the level of the feature mixing and is decoupled with spatial attentions. This is shown more effective than a joint spatial-and-task attention for CIL. The proposed DNE approach can strictly maintain the feature space of old classes while growing the network and feature scale at a much slower rate than previous methods. In result, it outperforms the previous SOTA methods by a margin of 4\% in terms of accuracy, with similar or even smaller model scale.

We study channel number reduction in combination with weight binarization (1-bit weight precision) to trim a convolutional neural network for a keyword spotting (classification) task. We adopt a group-wise splitting method based on the group Lasso penalty to achieve over 50 % channel sparsity while maintaining the network performance within 0.25 % accuracy loss. We show an effective three-stage procedure to balance accuracy and sparsity in network training. Keywords: Convolutional Neural Network · Channel Pruning · Weight Binarization · Classification. 1 Introduction Reducing complexity of neural networks while maintaining their performance is both fundamental and practical for resource limited platforms such as mobile phones. In this paper, we integrate two methods, namely channel pruning and weight quantization, to trim down the number of parameters for a keyword spotting convolutional neural network (CNN, [4]).

Training activation quantized neural networks involves minimizing a piecewise constant function whose gradient vanishes almost everywhere, which is undesirable for the standard back-propagation or chain rule. An empirical way around this issue is to use a straight-through estimator (STE) (Bengio et al., 2013) in the backward pass, so that the "gradient" through the modified chain rule becomes non-trivial. Since this unusual "gradient" is certainly not the gradient of loss function, the following question arises: why searching in its negative direction minimizes the training loss? In this paper, we provide the theoretical justification of the concept of STE by answering this question. We consider the problem of learning a two-linear-layer network with binarized ReLU activation and Gaussian input data. We shall refer to the unusual "gradient" given by the STE-modifed chain rule as coarse gradient. The choice of STE is not unique. We prove that if the STE is properly chosen, the expected coarse gradient correlates positively with the population gradient (not available for the training), and its negation is a descent direction for minimizing the population loss. We further show the associated coarse gradient descent algorithm converges to a critical point of the population loss minimization problem. Moreover, we show that a poor choice of STE leads to instability of the training algorithm near certain local minima, which is verified with CIFAR-10 experiments.

ShuffleNet is a state-of-the-art light weight convolutional neural network architecture. Its basic operations include group, channel-wise convolution and channel shuffling. However, channel shuffling is manually designed empirically. Mathematically, shuffling is a multiplication by a permutation matrix. In this paper, we propose to automate channel shuffling by learning permutation matrices in network training. We introduce an exact Lipschitz continuous non-convex penalty so that it can be incorporated in the stochastic gradient descent to approximate permutation at high precision. Exact permutations are obtained by simple rounding at the end of training and are used in inference. The resulting network, referred to as AutoShuffleNet, achieved improved classification accuracies on CIFAR-10 and ImageNet data sets. In addition, we found experimentally that the standard convex relaxation of permutation matrices into stochastic matrices leads to poor performance. We prove theoretically the exactness (error bounds) in recovering permutation matrices when our penalty function is zero (very small). We present examples of permutation optimization through graph matching and two-layer neural network models where the loss functions are calculated in closed analytical form. In the examples, convex relaxation failed to capture permutations whereas our penalty succeeded.

Quantized deep neural networks (QDNNs) are attractive due to their much lower memory storage and faster inference speed than their regular full precision counterparts. To maintain the same performance level especially at low bit-widths, QDNNs must be retrained. Their training involves piecewise constant activation functions and discrete weights, hence mathematical challenges arise. We introduce the notion of coarse derivative and propose the blended coarse gradient descent (BCGD) algorithm, for training fully quantized neural networks. Coarse gradient is generally not a gradient of any function but an artificial ascent direction. The weight update of BCGD goes by coarse gradient correction of a weighted average of the full precision weights and their quantization (the so-called blending), which yields sufficient descent in the objective value and thus accelerates the training. Our experiments demonstrate that this simple blending technique is very effective for quantization at extremely low bit-width such as binarization. In full quantization of ResNet-18 for ImageNet classification task, BCGD gives 64.36% top-1 accuracy with binary weights across all layers and 4-bit adaptive activation. If the weights in the first and last layers are kept in full precision, this number increases to 65.46%. As theoretical justification, we provide the convergence analysis of coarse gradient descent for a two-layer neural network model with Gaussian input data, and prove that the expected coarse gradient correlates positively with the underlying true gradient.