Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often required to alleviate prohibitive workloads on hardware. Despite the remarkable success of backpropagation, the algorithm itself is not capable of considering such constraints unless additional algorithms are applied simultaneously. To address this issue, we propose the constrained backpropagation (CBP) algorithm based on a pseudo-Lagrange multiplier method to obtain the optimal set of weights that satisfy a given set of constraints. The defining characteristic of the proposed CBP algorithm is the utilization of a Lagrangian function (loss function plus constraint function) as its objective function. We considered various types of constraints--binary, ternary, one-bit shift, and two-bit shift weight constraints. As a post-training method, CBP applied to AlexNet, ResNet-18, ResNet-50, and GoogLeNet on ImageNet, which were pre-trained using the conventional backpropagation. For all cases, the proposed algorithm outperforms the state-of-the-art methods on ImageNet, e.g., 66.6%, 74.4%, and 64.0% top-1 accuracy for ResNet-18, ResNet-50, and GoogLeNet with binary weights, respectively. This highlights CBP as a learning algorithm to address diverse constraints with the minimal performance loss by employing appropriate constraint functions.

Bloodstock shortages and its uncertain demand has become a major problem for all countries worldwide. Therefore, this study aims to provide solution to the issues of blood distribution during the Covid-19 Pandemic at Bengkulu, Indonesia. The Backpropagation algorithm was used to improve the possibility of discovering available and potential donors. Furthermore, the distances, age, and length of donation were measured to obtain the right person to donate blood when it needed. The Backpropagation uses three input layers to classify eligible donors, namely age, body, weight, and bias. In addition, the system through its query automatically counts the variables via the Fuzzy Tahani and simultaneously access the vast database.

Since OpenAI released CLIP, trained on internet pictures and their nearby text, people have been using it to generate images. In all these methods - CLIP Dall-E, CLIP BigGAN, CLIP FFT, CLIP VQGAN, CLIP diffusion - you come up with a text prompt, some algorithm presents its images to CLIP, and CLIP's role is to judge how well the images match the prompt. With CLIP's judgements for feedback, the algorithm can self-adjust to make its images match the prompt. But we also do the reverse and set up an app where you give CLIP an image, and then CLIP judges how well text matches the image. One such app is CLIP backpropagation.

A neuron is a container that contains a mathematical function which is known as an activation function, inputs (x1 and x2 here), a vector of weights(w1,w2 here) and a bias(b). A neuron first computes the weighted sum of the inputs. The activation function is simply a mathematical function that takes in an input and produces an output. Think of the activation function as a mathematical operation that normalizes the input and produces an output. The output is then passed forward onto the neurons on the subsequent layer.

In the above image, it has 3 features. This could be for example the height(1.75 Note that we only input one sample (one human in our example) into the neuron at once. It is a prediction the neuron makes according to one input sample. We can choose ourselfs what our neuron should predict.

Backpropagation (BP) is a core component of the contemporary deep learning incarnation of neural networks. Briefly, BP is an algorithm that exploits the computational architecture of neural networks to efficiently evaluate the gradient of a cost function during neural network parameter optimization. The validity of BP rests on the application of a multivariate chain rule to the computational architecture of neural networks and their associated objective functions. Introductions to deep learning theory commonly present the computational architecture of neural networks in matrix form, but eschew a parallel formulation and justification of BP in the framework of matrix differential calculus. This entails several drawbacks for the theory and didactics of deep learning. In this work, we overcome these limitations by providing a full induction proof of the BP algorithm in matrix notation. Specifically, we situate the BP algorithm in the framework of matrix differential calculus, encompass affine-linear potential functions, prove the validity of the BP algorithm in inductive form, and exemplify the implementation of the matrix form BP algorithm in computer code.

In theory, the choice of ReLU'(0) in [0, 1] for a neural network has a negligible influence both on backpropagation and training. Yet, in the real world, 32 bits default precision combined with the size of deep learning problems makes it a hyperparameter of training methods. We investigate the importance of the value of ReLU'(0) for several precision levels (16, 32, 64 bits), on various networks (fully connected, VGG, ResNet) and datasets (MNIST, CIFAR10, SVHN). We observe considerable variations of backpropagation outputs which occur around half of the time in 32 bits precision. The effect disappears with double precision, while it is systematic at 16 bits. For vanilla SGD training, the choice ReLU'(0) = 0 seems to be the most efficient. We also evidence that reconditioning approaches as batch-norm or ADAM tend to buffer the influence of ReLU'(0)'s value. Overall, the message we want to convey is that algorithmic differentiation of nonsmooth problems potentially hides parameters that could be tuned advantageously.

There is particular interest in Spike-based learning in plastic neuronal networks is deep learning, which is a central tool in modern machine playing increasingly key roles in both theoretical neuroscience learning. Deep learning relies on a layered, feedforward and neuromorphic computing. The brain learns network similar to the early layers of the visual cortex, in part by modifying the synaptic strengths between neurons with threshold nonlinearities at each layer that resemble and neuronal populations. While specific synaptic mean-field approximations of neuronal integrate-and-fire plasticity or neuromodulatory mechanisms may vary in models. While feedforward networks are readily translated different brain regions, it is becoming clear that a significant to neuromorphic hardware [6-8], the far more computationally level of dynamical coordination between disparate intensive training of these networks'on chip' neuronal populations must exist, even within an individual has proven elusive as the structure of backpropagation neural circuit [1]. Classically, backpropagation (BP, makes the algorithm notoriously difficult to implement and other learning algorithms) has been essential for supervised in a neural circuit [9, 10]. A feasible neural implementation learning in artificial neural networks (ANNs). of the backpropagation algorithm has gained renewed Although the question of whether or not BP operates in scrutiny with the rise of new neuromorphic computational the brain is still an outstanding issue [2], BP does solve architectures that feature local synaptic plasticity the problem of how a global objective function can be [5, 11-13]. Because of the well-known difficulties, neuromorphic related to local synaptic modification in a network.

Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities. For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors at spike times in order to compute the exact gradient in an event-based, temporally and spatially sparse fashion. We use gradients computed via EventProp to train networks on the Yin-Yang and MNIST datasets using either a spike time or voltage based loss function and report competitive performance. Our work supports the rigorous study of gradient-based learning algorithms in spiking neural networks and provides insights toward their implementation in novel brain-inspired hardware.

The dictionary learning problem, representing data as a combination of few atoms, has long stood as a popular method for learning representations in statistics and signal processing. The most popular dictionary learning algorithm alternates between sparse coding and dictionary update steps, and a rich literature has studied its theoretical convergence. The growing popularity of neurally plausible unfolded sparse coding networks has led to the empirical finding that backpropagation through such networks performs dictionary learning. This paper offers the first theoretical proof for these empirical results through PUDLE, a Provable Unfolded Dictionary LEarning method. We highlight the impact of loss, unfolding, and backpropagation on convergence. We discover an implicit acceleration: as a function of unfolding, the backpropagated gradient converges faster and is more accurate than the gradient from alternating minimization. We complement our findings through synthetic and image denoising experiments. The findings support the use of accelerated deep learning optimizers and unfolded networks for dictionary learning.