Optimizing for In-memory Deep Learning with Emerging Memory Technology

In-memory deep learning computes neural network models where they are stored, thus avoiding long distance communication between memory and computation units, resulting in considerable savings in energy and time. In-memory deep learning has already demonstrated orders of magnitude higher performance density and energy efficiency. The use of emerging memory technology promises to increase the gains in density, energy, and performance even further. However, emerging memory technology is intrinsically unstable, resulting in random fluctuations of data reads. This can translate to non-negligible accuracy loss, potentially nullifying the gains. In this paper, we propose three optimization techniques that can mathematically overcome the instability problem of emerging memory technology. They can improve the accuracy of the in-memory deep learning model while maximizing its energy efficiency. Experiments show that our solution can fully recover most models' state-of-the-art accuracy, and achieves at least an order of magnitude higher energy efficiency than the state-of-the-art.

Embedding Principle: a hierarchical structure of loss landscape of deep neural networks

We prove a general Embedding Principle of loss landscape of deep neural networks (NNs) that unravels a hierarchical structure of the loss landscape of NNs, i.e., loss landscape of an NN contains all critical points of all the narrower NNs. This result is obtained by constructing a class of critical embeddings which map any critical point of a narrower NN to a critical point of the target NN with the same output function. By discovering a wide class of general compatible critical embeddings, we provide a gross estimate of the dimension of critical submanifolds embedded from critical points of narrower NNs. We further prove an irreversiblility property of any critical embedding that the number of negative/zero/positive eigenvalues of the Hessian matrix of a critical point may increase but never decrease as an NN becomes wider through the embedding. Using a special realization of general compatible critical embedding, we prove a stringent necessary condition for being a "truly-bad" critical point that never becomes a strict-saddle point through any critical embedding. This result implies the commonplace of strict-saddle points in wide NNs, which may be an important reason underlying the easy optimization of wide NNs widely observed in practice.

E3NE: An End-to-End Framework for Accelerating Spiking Neural Networks with Emerging Neural Encoding on FPGAs

Compiler frameworks are crucial for the widespread use of FPGA-based deep learning accelerators. They allow researchers and developers, who are not familiar with hardware engineering, to harness the performance attained by domain-specific logic. There exists a variety of frameworks for conventional artificial neural networks. However, not much research effort has been put into the creation of frameworks optimized for spiking neural networks (SNNs). This new generation of neural networks becomes increasingly interesting for the deployment of AI on edge devices, which have tight power and resource constraints. Our end-to-end framework E3NE automates the generation of efficient SNN inference logic for FPGAs. Based on a PyTorch model and user parameters, it applies various optimizations and assesses trade-offs inherent to spike-based accelerators. Multiple levels of parallelism and the use of an emerging neural encoding scheme result in an efficiency superior to previous SNN hardware implementations. For a similar model, E3NE uses less than 50% of hardware resources and 20% less power, while reducing the latency by an order of magnitude. Furthermore, scalability and generality allowed the deployment of the large-scale SNN models AlexNet and VGG.

MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs

In this paper, we propose a model-operator-data network (MOD-Net) for solving PDEs. A MOD-Net is driven by a model to solve PDEs based on operator representation with regularization from data. In this work, we use a deep neural network to parameterize the Green's function. The empirical risk consists of the mean square of the governing equation, boundary conditions, and a few labels, which are numerically computed by traditional schemes on coarse grid points with cheap computation cost. With only the labeled dataset or only the model constraints, it is insufficient to accurately train a MOD-Net for complicate problems. Intuitively, the labeled dataset works as a regularization in addition to the model constraints. The MOD-Net is much efficient than original neural operator because the MOD-Net also uses the information of governing equation and the boundary conditions of the PDE rather than purely the expensive labels. Since the MOD-Net learns the Green's function of a PDE, it solves a type of PDEs but not a specific case. We numerically show MOD-Net is very efficient in solving Poisson equation and one-dimensional Boltzmann equation. For non-linear PDEs, where the concept of the Green's function does not apply, the non-linear MOD-Net can be similarly used as an ansatz for solving non-linear PDEs.

Privacy Budget Scheduling

Machine learning (ML) models trained on personal data have been shown to leak information about users. Differential privacy (DP) enables model training with a guaranteed bound on this leakage. Each new model trained with DP increases the bound on data leakage and can be seen as consuming part of a global privacy budget that should not be exceeded. This budget is a scarce resource that must be carefully managed to maximize the number of successfully trained models. We describe PrivateKube, an extension to the popular Kubernetes datacenter orchestrator that adds privacy as a new type of resource to be managed alongside other traditional compute resources, such as CPU, GPU, and memory. The abstractions we design for the privacy resource mirror those defined by Kubernetes for traditional resources, but there are also major differences. For example, traditional compute resources are replenishable while privacy is not: a CPU can be regained after a model finishes execution while privacy budget cannot. This distinction forces a re-design of the scheduler. We present DPF (Dominant Private Block Fairness) -- a variant of the popular Dominant Resource Fairness (DRF) algorithm -- that is geared toward the non-replenishable privacy resource but enjoys similar theoretical properties as DRF. We evaluate PrivateKube and DPF on microbenchmarks and an ML workload on Amazon Reviews data. Compared to existing baselines, DPF allows training more models under the same global privacy guarantee. This is especially true for DPF over R\'enyi DP, a highly composable form of DP.

An Upper Limit of Decaying Rate with Respect to Frequency in Deep Neural Network

Deep neural network (DNN) usually learns the target function from low to high frequency, which is called frequency principle or spectral bias. This frequency principle sheds light on a high-frequency curse of DNNs -- difficult to learn high-frequency information. Inspired by the frequency principle, a series of works are devoted to develop algorithms for overcoming the high-frequency curse. A natural question arises: what is the upper limit of the decaying rate w.r.t. frequency when one trains a DNN? In this work, our theory, confirmed by numerical experiments, suggests that there is a critical decaying rate w.r.t. frequency in DNN training. Below the upper limit of the decaying rate, the DNN interpolates the training data by a function with a certain regularity. However, above the upper limit, the DNN interpolates the training data by a trivial function, i.e., a function is only non-zero at training data points. Our results indicate a better way to overcome the high-frequency curse is to design a proper pre-condition approach to shift high-frequency information to low-frequency one, which coincides with several previous developed algorithms for fast learning high-frequency information. More importantly, this work rigorously proves that the high-frequency curse is an intrinsic difficulty of DNNs.

Embedding Principle of Loss Landscape of Deep Neural Networks

Understanding the structure of loss landscape of deep neural networks (DNNs)is obviously important. In this work, we prove an embedding principle that the loss landscape of a DNN "contains" all the critical points of all the narrower DNNs. More precisely, we propose a critical embedding such that any critical point, e.g., local or global minima, of a narrower DNN can be embedded to a critical point/hyperplane of the target DNN with higher degeneracy and preserving the DNN output function. The embedding structure of critical points is independent of loss function and training data, showing a stark difference from other nonconvex problems such as protein-folding. Empirically, we find that a wide DNN is often attracted by highly-degenerate critical points that are embedded from narrow DNNs. The embedding principle provides an explanation for the general easy optimization of wide DNNs and unravels a potential implicit low-complexity regularization during the training. Overall, our work provides a skeleton for the study of loss landscape of DNNs and its implication, by which a more exact and comprehensive understanding can be anticipated in the near

Towards Understanding the Condensation of Two-layer Neural Networks at Initial Training

It is important to study what implicit regularization is imposed on the loss function during the training that leads over-parameterized neural networks (NNs) to good performance on real dataset. Empirically, existing works have shown that weights of NNs condense on isolated orientations with small initialization. The condensation implies that the NN learns features from the training data and is effectively a much smaller network. In this work, we show that the singularity of the activation function at original point is a key factor to understanding the condensation at initial training stage. Our experiments suggest that the maximal number of condensed orientations is twice of the singularity order. Our theoretical analysis confirms experiments for two cases, one is for the first-order singularity activation function and the other is for the one-dimensional input. This work takes a step towards understanding how small initialization implicitly leads NNs to condensation at initial training, which is crucial to understand the training and the learning of deep NNs.

DTNN: Energy-efficient Inference with Dendrite Tree Inspired Neural Networks for Edge Vision Applications

Deep neural networks (DNN) have achieved remarkable success in computer vision (CV). However, training and inference of DNN models are both memory and computation intensive, incurring significant overhead in terms of energy consumption and silicon area. In particular, inference is much more cost-sensitive than training because training can be done offline with powerful platforms, while inference may have to be done on battery powered devices with constrained form factors, especially for mobile or edge vision applications. In order to accelerate DNN inference, model quantization was proposed. However previous works only focus on the quantization rate without considering the efficiency of operations. In this paper, we propose Dendrite-Tree based Neural Network (DTNN) for energy-efficient inference with table lookup operations enabled by activation quantization. In DTNN both costly weight access and arithmetic computations are eliminated for inference. We conducted experiments on various kinds of DNN models such as LeNet-5, MobileNet, VGG, and ResNet with different datasets, including MNIST, Cifar10/Cifar100, SVHN, and ImageNet. DTNN achieved significant energy saving (19.4X and 64.9X improvement on ResNet-18 and VGG-11 with ImageNet, respectively) with negligible loss of accuracy. To further validate the effectiveness of DTNN and compare with state-of-the-art low energy implementation for edge vision, we design and implement DTNN based MLP image classifiers using off-the-shelf FPGAs. The results show that DTNN on the FPGA, with higher accuracy, could achieve orders of magnitude better energy consumption and latency compared with the state-of-the-art low energy approaches reported that use ASIC chips.