Current artificial neural networks are trained with parameters encoded as floating point numbers that occupy lots of memory space at inference time. Due to the increase in the size of deep learning models, it is becoming very difficult to consider training and using artificial neural networks on edge devices. Binary neural networks promise to reduce the size of deep neural network models, as well as to increase inference speed while decreasing energy consumption. Thus, they may allow the deployment of more powerful models on edge devices. However, binary neural networks are still proven to be difficult to train using the backpropagation-based gradient descent scheme. This paper extends the work of \cite{crulis2023alternatives}, which proposed adapting to binary neural networks two promising alternatives to backpropagation originally designed for continuous neural networks, and experimented with them on simple image classification datasets. This paper proposes new experiments on the ImageNette dataset, compares three different model architectures for image classification, and adds two additional alternatives to backpropagation.
The backpropagation algorithm, which had been originally introduced in the 1970s, is the workhorse of learning in neural networks. This backpropagation algorithm makes use of the famous machine learning algorithm known as Gradient Descent, which is a first-order iterative optimization algorithm for finding the minimum of a function. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient (or of the approximate gradient) of the function at the current point. In this paper, we develop an alternative to the backpropagation without…
Cerebras；Tesla（特斯拉）；Cerebras Systems, Inc（Cerebras Systems 公司）；Google（谷歌）
New hardware can substantially increase the speed and efficiency of deep neural network training. To guide the development of future hardware architectures, it is pertinent to explore the hardware and machine learning properties of alternative training algorithms. In this work we evaluate the use of small batch, fine-grained Pipelined Backpropagation, an asynchronous pipeline parallel training algorithm that has significant hardware advantages. We introduce two methods, Spike Compensation and Linear Weight Prediction, that effectively mitigate the downsides caused by the asynchronicity of Pipe…
We introduce the HSIC (Hilbert-Schmidt independence criterion) bottleneck for training deep neural networks. The HSIC bottleneck is an alternative to the conventional cross-entropy loss and backpropagation that has a number of distinct advantages. It mitigates exploding and vanishing gradients, resulting in the ability to learn very deep networks without skip connections. There is no requirement for symmetric feedback or update locking. We find that the HSIC bottleneck provides performance on MNIST/FashionMNIST/CIFAR10 classification comparable to backpropagation with a cross-entropy target, e…
Delhi Technological University（德里理工大学）；CHRIST (Deemed to be University)（克里斯大学（被视为大学））
There are numerous models of quantum neural networks that have been applied to variegated problems such as image classification, pattern recognition etc.Quantum inspired algorithms have been relevant for quite awhile. More recently, in the NISQ era, hybrid quantum classical models have shown promising results. Multi-feature regression is common problem in classical machine learning. Hence we present a comparative analysis of continuous variable quantum neural networks (Variational circuits) and quantum backpropagating multi layer perceptron (QBMLP). We have chosen the contemporary problem of p…
Recent advances in deep neural networks (DNNs) owe their success to training algorithms that use backpropagation and gradient-descent. Backpropagation, while highly effective on von Neumann architectures, becomes inefficient when scaling to large networks. Commonly referred to as the weight transport problem, each neuron's dependence on the weights and errors located deeper in the network require exhaustive data movement which presents a key problem in enhancing the performance and energy-efficiency of machine-learning hardware. In this work, we propose a bio-plausible alternative to backpropa…
The de facto algorithm for training the back pass of a feedforward neural network is backpropagation (BP). The use of almost-everywhere differentiable activation functions made it efficient and effective to propagate the gradient backwards through layers of deep neural networks. However, in recent years, there has been much research in alternatives to backpropagation. This analysis has largely focused on reaching state-of-the-art accuracy in multilayer perceptrons (MLPs) and convolutional neural networks (CNNs). In this paper, we analyze the stability and similarity of predictions and neurons …
Louisiana State University（路易斯安那州立大学）；Georgia Institute of Technology（佐治亚理工学院）
K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization methods have been proposed to address this problem. In this paper, we first present an overview of these methods with an emphasis on their computational efficiency. We then compare eight commonly used linear time complexity initialization methods on a large and diverse collection of data sets using various performance criteria. Finally, we analyze the experimen…
Sichuan University（四川大学）；China University of Petroleum（中国石油大学）
This paper offers a novel mathematical approach, the modified Fractional-order Steepest Descent Method (FSDM) for training BackPropagation Neural Networks (BPNNs); this differs from the majority of the previous approaches and as such. A promising mathematical method, fractional calculus, has the potential to assume a prominent role in the applications of neural networks and cybernetics because of its inherent strengths such as long-term memory, nonlocality, and weak singularity. Therefore, to improve the optimization performance of classic first-order BPNNs, in this paper we study whether it c…
Since its inception, deep learning has been overwhelmingly reliant on backpropagation and gradient-based optimization algorithms in order to learn weight and bias parameter values. Tractable Approximate Gaussian Inference (TAGI) algorithm was shown to be a viable and scalable alternative to backpropagation for shallow fully-connected neural networks. In this paper, we are demonstrating how TAGI matches or exceeds the performance of backpropagation, for training classic deep neural network architectures. Although TAGI's computational efficiency is still below that of deterministic approaches re…
HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation
the Faculty of Electrical Engineering, Czestochowa University of Technology（捷斯托霍瓦技术大学电子工程系）；the Faculty of Mathematics and Computer Science, University of Lodz（罗兹大学数学与计算机科学系）；the Centre for Data Analysis, Modelling and Computational Sciences (CAMINO), University of Lodz（罗兹大学数据分析、建模与计算科学中心）
Alternatives to backpropagation have long been studied to better understand how biological brains may learn. Recently, they have also garnered interest as a way to train neural networks more efficiently. By relaxing constraints inherent to backpropagation (e.g., symmetric feedforward and feedback weights, sequential updates), these methods enable promising prospects, such as local learning. However, the tradeoffs between different methods in terms of final task performance, convergence speed, and ultimately compute and data requirements are rarely outlined. In this work, we use scaling laws to…
Local learning for stable backpropagation-free neural network training towards physical learning
Department of Materials Science and Engineering, Delft University of Technology（材料科学与工程系，代尔夫特理工大学）；Department of Precision and Microsystems Engineering, Delft University of Technology（精密与微系统工程系，代尔夫特理工大学）；Department of Intelligent Systems, Delft University of Technology（智能系统系，代尔夫特理工大学）
This tutorial paper surveys provably optimal alternatives to end-to-end backpropagation (E2EBP) -- the de facto standard for training deep architectures. Modular training refers to strictly local training without both the forward and the backward pass, i.e., dividing a deep architecture into several nonoverlapping modules and training them separately without any end-to-end operation. Between the fully global E2EBP and the strictly local modular training, there are weakly modular hybrids performing training without the backward pass only. These alternatives can match or surpass the performance …
Donders Institute for Brain, Cognition and Behaviour（唐德斯大脑、认知与行为研究所）；Radboud University（拉德堡德大学）
Traditional backpropagation of error, though a highly successful algorithm for learning in artificial neural network models, includes features which are biologically implausible for learning in real neural circuits. An alternative called target propagation proposes to solve this implausibility by using a top-down model of neural activity to convert an error at the output of a neural network into layer-wise and plausible 'targets' for every unit. These targets can then be used to produce weight updates for network training. However, thus far, target propagation has been heuristically proposed w…
Orthogonal Weight Modification Enhances Learning Scalability and Convergence Efficiency without Gradient Backpropagation
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Future Technology, University of Chinese Academy of Sciences（中国科学院大学未来技术学院）；Key Laboratory of Brain Cognition and Brain-inspired Intelligence Technology, Chinese Academy of Sciences（中国科学院脑认知与类脑智能技术重点实验室）
University of Oxford（牛津大学）；MRC Brain Network Dynamics Unit（医学研究理事会脑网络动力学单元）；Hebei University of Technology（河北工业大学）
Predictive coding networks (PCNs) are an influential model for information processing in the brain. They have appealing theoretical interpretations and offer a single mechanism that accounts for diverse perceptual phenomena of the brain. On the other hand, backpropagation (BP) is commonly regarded to be the most successful learning method in modern machine learning. Thus, it is exciting that recent work formulates inference learning (IL) that trains PCNs to approximate BP. However, there are several remaining critical issues: (i) IL is an approximation to BP with unrealistic/non-trivial requir…
School of Computer and Communication Sciences（计算机与通信科学学院）；EPFL（洛桑联邦理工学院）
Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matrices. While this can be mitigated by partitioning the data in small and arbitrary groups, doing so has no theoretical basis and makes its impossible to exploit the power of ED to the full. In this paper, we introduce a numerically stable and differentiable approach to leveraging eigenvectors in deep networks. It can handle large matrices witho…
Heidelberg University（海德堡大学）；Özyeğin University（厄兹耶因大学）；Bosch Center for Artificial Intelligence（博世人工智能中心）
We propose a new Bayesian Neural Net formulation that affords variational inference for which the evidence lower bound is analytically tractable subject to a tight approximation. We achieve this tractability by (i) decomposing ReLU nonlinearities into the product of an identity and a Heaviside step function, (ii) introducing a separate path that decomposes the neural net expectation from its variance. We demonstrate formally that introducing separate latent binary variables to the activations allows representing the neural network likelihood as a chain of linear operations. Performing variatio…
Centrale Marseille（马赛中央理工学院）；Aix Marseille Univ（艾克斯-马赛大学）；CNRS（法国国家科学研究中心）；LIS（信息科学与系统实验室）；Institute of Advanced Research on Artificial Intelligence (IARAI)（人工智能高级研究院（IARAI））
We propose Sideways, an approximate backpropagation scheme for training video models. In standard backpropagation, the gradients and activations at every computation step through the model are temporally synchronized. The forward activations need to be stored until the backward pass is executed, preventing inter-layer (depth) parallelization. However, can we leverage smooth, redundant input streams such as videos to develop a more efficient training scheme? Here, we explore an alternative to backpropagation; we overwrite network activations whenever new ones, i.e., from new frames, become avai…
University of Maryland（马里兰大学）；Department of Computer Science（计算机科学系）；Department of Physics（物理系）；Institute for Adv. Computer Studies（高级计算机研究所）
In many real-world applications, fully-differentiable RNNs such as LSTMs and GRUs have been widely deployed to solve time series learning tasks. These networks train via Backpropagation Through Time, which can work well in practice but involves a biologically unrealistic unrolling of the network in time for gradient updates, are computationally expensive, and can be hard to tune. A second paradigm, Reservoir Computing, keeps the recurrent weight matrix fixed and random. Here, we propose a novel hybrid network, which we call Hybrid Backpropagation Parallel Echo State Network (HBP-ESN) which com…
We propose a new learning framework, signal propagation (sigprop), for propagating a learning signal and updating neural network parameters via a forward pass, as an alternative to backpropagation. In sigprop, there is only the forward path for inference and learning. So, there are no structural or computational constraints necessary for learning to take place, beyond the inference model itself, such as feedback connectivity, weight transport, or a backward pass, which exist under backpropagation based approaches. That is, sigprop enables global supervised learning with only a forward path. Th…
University of Geneva（日内瓦大学）；UCL Centre for Artificial Intelligence（伦敦大学学院人工智能中心）
We present the Graph Forward-Forward (GFF) algorithm, an extension of the Forward-Forward procedure to graphs, able to handle features distributed over a graph's nodes. This allows training graph neural networks with forward passes only, without backpropagation. Our method is agnostic to the message-passing scheme, and provides a more biologically plausible learning scheme than backpropagation, while also carrying computational advantages. With GFF, graph neural networks are trained greedily layer by layer, using both positive and negative samples. We run experiments on 11 standard graph prope…
Softmax function is widely used in artificial neural networks for multiclass classification, multilabel classification, attention mechanisms, etc. However, its efficacy is often questioned in literature. The log-softmax loss has been shown to belong to a more generic class of loss functions, called spherical family, and its member log-Taylor softmax loss is arguably the best alternative in this class. In another approach which tries to enhance the discriminative nature of the softmax function, soft-margin softmax (SM-softmax) has been proposed to be the most suitable alternative. In this work,…
School of Applied and Engineering Physics, Cornell University（康奈尔大学应用与工程物理系）；NTT Physics and Informatics Laboratories, NTT Research, Inc.（NTT Research公司NTT物理与信息学实验室）；School of Electrical and Computer Engineering, Cornell University（康奈尔大学电气与计算机工程学院）
Deep neural networks have become a pervasive tool in science and engineering. However, modern deep neural networks' growing energy requirements now increasingly limit their scaling and broader use. We propose a radical alternative for implementing deep neural network models: Physical Neural Networks. We introduce a hybrid physical-digital algorithm called Physics-Aware Training to efficiently train sequences of controllable physical systems to act as deep neural networks. This method automatically trains the functionality of any sequence of real physical systems, directly, using backpropagatio…
School of Microelectronics, Xidian University（西安电子科技大学微电子学院）；Guangzhou Institute of Technology, Xidian University（西安电子科技大学广州研究院）
Spiking neural networks (SNNs) can utilize spatio-temporal information and have a nature of energy efficiency which is a good alternative to deep neural networks(DNNs). The event-driven information processing makes SNNs can reduce the expensive computation of DNNs and save a lot of energy consumption. However, high training and inference latency is a limitation of the development of deeper SNNs. SNNs usually need tens or even hundreds of time steps during the training and inference process which causes not only the increase of latency but also the waste of energy consumption. To overcome this …
The scaling hypothesis motivates the expansion of models past trillions of parameters as a path towards better performance. Recent significant developments, such as GPT-3, have been driven by this conjecture. However, as models scale-up, training them efficiently with backpropagation becomes difficult. Because model, pipeline, and data parallelism distribute parameters and gradients over compute nodes, communication is challenging to orchestrate: this is a bottleneck to further scaling. In this work, we argue that alternative training methods can mitigate these issues, and can inform the desig…
An artificial neural network can be trained by uniformly broadcasting a reward signal to units that implement a REINFORCE learning rule. Though this presents a biologically plausible alternative to backpropagation in training a network, the high variance associated with it renders it impractical to train deep networks. The high variance arises from the inefficient structural credit assignment since a single reward signal is used to evaluate the collective action of all units. To facilitate structural credit assignment, we propose replacing the reward signal to hidden units with the change in t…
This work designs an image restoration deep network relying on unfolded Chambolle-Pock primal-dual iterations. Each layer of our network is built from Chambolle-Pock iterations when specified for minimizing a sum of a $\ell_2$-norm data-term and an analysis sparse prior. The parameters of our network are the step-sizes of the Chambolle-Pock scheme and the linear operator involved in sparsity-based penalization, including implicitly the regularization parameter. A backpropagation procedure is fully described. Preliminary experiments illustrate the good behavior of such a deep primal-dual networ…
