The paper proposes a new algorithm called SymBa that aims to achieve more biologically plausible learning than Back-Propagation (BP). The algorithm is based on the Forward-Forward (FF) algorithm, which is a BP-free method for training neural networks. SymBa improves the FF algorithm's convergence behavior by addressing the problem of asymmetric gradients caused by conflicting converging directions for positive and negative samples. The algorithm balances positive and negative losses to enhance performance and convergence speed. Furthermore, it modifies the FF algorithm by adding Intrinsic Class Pattern (ICP) containing class information to prevent the loss of class information during training. The proposed algorithm has the potential to improve our understanding of how the brain learns and processes information and to develop more effective and efficient artificial intelligence systems. The paper presents experimental results that demonstrate the effectiveness of SymBa algorithm compared to the FF algorithm and BP.

We present multiplexed gradient descent (MGD), a gradient descent framework designed to easily train analog or digital neural networks in hardware. MGD utilizes zero-order optimization techniques for online training of hardware neural networks. We demonstrate its ability to train neural networks on modern machine learning datasets, including CIFAR-10 and Fashion-MNIST, and compare its performance to backpropagation. Assuming realistic timescales and hardware parameters, our results indicate that these optimization techniques can train a network on emerging hardware platforms orders of magnitude faster than the wall-clock time of training via backpropagation on a standard GPU, even in the presence of imperfect weight updates or device-to-device variations in the hardware. We additionally describe how it can be applied to existing hardware as part of chip-in-the-loop training, or integrated directly at the hardware level. Crucially, the MGD framework is highly flexible, and its gradient descent process can be optimized to compensate for specific hardware limitations such as slow parameter-update speeds or limited input bandwidth.

We provide a new efficient version of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

A physical self-learning machine can be defined as a nonlinear dynamical system that can be trained on data (similar to artificial neural networks), but where the update of the internal degrees of freedom that serve as learnable parameters happens autonomously. In this way, neither external processing and feedback nor knowledge of (and control of) these internal degrees of freedom is required. We introduce a general scheme for self-learning in any time-reversible Hamiltonian system. We illustrate the training of such a self-learning machine numerically for the case of coupled nonlinear wave fields.

Dynamical networks are versatile models that can describe a variety of behaviours such as synchronisation and feedback. However, applying these models in real world contexts is difficult as prior information pertaining to the connectivity structure or local dynamics is often unknown and must be inferred from time series observations of network states. Additionally, the influence of coupling interactions between nodes further complicates the isolation of local node dynamics. Given the architectural similarities between dynamical networks and recurrent neural networks (RNN), we propose a network inference method based on the backpropagation through time (BPTT) algorithm commonly used to train recurrent neural networks. This method aims to simultaneously infer both the connectivity structure and local node dynamics purely from observation of node states. An approximation of local node dynamics is first constructed using a neural network. This is alternated with an adapted BPTT algorithm to regress corresponding network weights by minimising prediction errors of the dynamical network based on the previously constructed local models until convergence is achieved. This method was found to be succesful in identifying the connectivity structure for coupled networks of Lorenz, Chua and FitzHugh-Nagumo oscillators. Freerun prediction performance with the resulting local models and weights was found to be comparable to the true system with noisy initial conditions. The method is also extended to non-conventional network couplings such as asymmetric negative coupling.

PCANet and its variants provided good accuracy results for classification tasks. However, despite the importance of network depth in achieving good classification accuracy, these networks were trained with a maximum of nine layers. In this paper, we introduce a residual compensation convolutional network, which is the first PCANet-like network trained with hundreds of layers while improving classification accuracy. The design of the proposed network consists of several convolutional layers, each followed by post-processing steps and a classifier. To correct the classification errors and significantly increase the network's depth, we train each layer with new labels derived from the residual information of all its preceding layers. This learning mechanism is accomplished by traversing the network's layers in a single forward pass without backpropagation or gradient computations. Our experiments on four distinct classification benchmarks (MNIST, CIFAR-10, CIFAR-100, and TinyImageNet) show that our deep network outperforms all existing PCANet-like networks and is competitive with several traditional gradient-based models.

Quaternion valued neural networks experienced rising popularity and interest from researchers in the last years, whereby the derivatives with respect to quaternions needed for optimization are calculated as the sum of the partial derivatives with respect to the real and imaginary parts. However, we can show that product- and chain-rule does not hold with this approach. We solve this by employing the GHRCalculus and derive quaternion backpropagation based on this. Furthermore, we experimentally prove the functionality of the derived quaternion backpropagation.

We propose a novel backpropagation algorithm for training spiking neural networks (SNNs) that encodes information in the relative multiple spike timing of individual neurons without single-spike restrictions. The proposed algorithm inherits the advantages of conventional timing-based methods in that it computes accurate gradients with respect to spike timing, which promotes ideal temporal coding. Unlike conventional methods where each neuron fires at most once, the proposed algorithm allows each neuron to fire multiple times. This extension naturally improves the computational capacity of SNNs. Our SNN model outperformed comparable SNN models and achieved as high accuracy as non-convolutional artificial neural networks. The spike count property of our networks was altered depending on the time constant of the postsynaptic current and the membrane potential. Moreover, we found that there existed the optimal time constant with the maximum test accuracy. That was not seen in conventional SNNs with single-spike restrictions on time-to-fast-spike (TTFS) coding. This result demonstrates the computational properties of SNNs that biologically encode information into the multi-spike timing of individual neurons. Our code would be publicly available.

Backpropagation neural network is used to improve the accuracy of neural network and make them capable of self-learning. Backpropagation means "backward propagation of errors". Here error is spread into the reverse direction in order to achieve better performance. Backpropagation is an algorithm for supervised learning of artificial neural networks that uses the gradient descent method to minimize the cost function. It searches for optimal weights that optimize the mean-squared distance between the predicted and actual labels.

Backpropagation is a process involved in training a neural network. It involves taking the error rate of a forward propagation and feeding this loss backward through the neural network layers to fine-tune the weights.