Article presents QR and LQ decomposition algorithms for various matrix sizes and ranks.
problem Solving least squares problems in machine learning and computer vision.
method Developed novel matrix backpropagation algorithms for QR and LQ decompositions of different matrix sizes and ranks.
result Numerical stability and computational efficiency of the proposed methods.
Study proposes memory-efficient backpropagation for linear layers in neural networks.
problem Significant memory usage in backpropagation through linear layers in neural networks.
method Randomized matrix multiplications to reduce memory usage with a moderate decrease in test accuracy.
result Demonstrated benefits of the proposed method on fine-tuning pre-trained models.
We provide a proof of backpropagation algorithm in matrix notation.
problem The lack of a full induction proof of backpropagation algorithm in matrix notation.
method We provide a full induction proof of the BP algorithm in matrix notation, situating it in the framework of matrix differential calculus.
result We prove the validity of the backpropagation algorithm in inductive form.
Teaches matrix calculus for machine learning and optimization.
problem Computing derivatives of functions involving matrices.
method Extends differential calculus to vector spaces, focusing on practical applications in machine learning.
result Introduction of adjoint and reverse-mode differentiation for efficient computation.
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 neur…
The backpropagation algorithm for calculating gradients has been widely used in computation of weights for deep neural networks (DNNs). This method requires derivatives of objective functions and has some difficulties finding appropriate parameters such as learning rate. In this paper, we propose a novel approach for c…
Boosts linear neurons for faster convergence in neural networks.
problem Optimizing neural networks' neurons in function space.
method Reparameterizing network to whiten neuron features using Boosted Backpropagation.
result Equivalent to preconditioned gradient descent, leading to faster convergence.
SnAp approximates RTRL for online training of sparse recurrent networks.
problem Training large sparse recurrent networks online is computationally expensive.
method Sparse n-step Approximation (SnAp) of the RTRL influence matrix.
result SnAp with n=2 remains tractable for highly sparse networks and outperforms backpropagation through time.
Belief propagation recovers backpropagation results.
problem Connection between backpropagation and belief propagation poorly understood.
method Converted backpropagation input to belief propagation input and showed results.
result Backpropagation is a special case of belief propagation.
We investigate the use of regularized Newton methods with adaptive norms for optimizing neural networks. This approach can be seen as a second-order counterpart of adaptive gradient methods, which we here show to be interpretable as first-order trust region methods with ellipsoidal constraints. In particular, we prove …
Neural NMF discovers hierarchical topics in multilayer data.
problem Detecting latent hierarchical structure in multilayer data.
method Recursive application of nonnegative matrix factorization (NMF) in layers with backpropagation optimization.
result Neural NMF outperforms other hierarchical NMF methods in synthetic and real-world datasets.
Paper proposes DAG-DB for learning discrete DAGs via backpropagation.
problem Learning Directed Acyclic Graphs (DAGs) from data.
method DAG-DB uses Discrete Backpropagation with I-MLE and Straight-Through Estimation.
result DAG-DB learns DAGs effectively using probabilistic sampling and backpropagation.
GAIT-prop derives a biologically plausible learning rule from backpropagation.
problem Biological implausibility in traditional backpropagation for neural networks.
method GAIT-prop uses a top-down model to convert output error into plausible targets for weight updates.
result GAIT-prop and backpropagation give identical weight updates under certain conditions.
New theory for local parameterization of deep ReLU networks.
problem Determining local parameters of deep ReLU neural networks.
method Introducing local lifting operators and charts of a manifold, deriving necessary and sufficient conditions for local identifiability.
result Sharp and testable conditions for local identifiability of deep ReLU networks.
This work shows synthetic gradients can outperform backpropagation in sample efficiency.
problem The efficiency of backpropagation in training neural networks.
method Unified vectorized feedback framework for loss-based and reward-based learning, introducing synthetic gradients.
result Synthetic gradients can achieve lower gradient-estimation mean squared error than backpropagation under certain conditions.
A new method reduces deep learning training costs by 92%.
problem High computational cost of backpropagation in deep neural networks.
method Dithered backprop with non-subtractive dither quantization.
result 92% sparsity with minimal accuracy loss.
A new method computes gradients without backpropagation.
problem Optimization of machine learning models.
method Forward mode automatic differentiation to compute gradients.
result Forward gradient is an unbiased estimate of the gradient, eliminating the need for backpropagation.
A method learns matrix factorization from diverse matrices and applies the knowledge to unseen matrices.
problem Matrix factorization without shared rows or columns.
method Neural network meta-learned to minimize expected imputation error using MAP estimation.
result The method can impute missing values from unseen matrices efficiently.
New algorithm shows neural networks can learn without full backpropagation.
problem Stochastic gradient descent with backpropagation is non-biologically plausible.
method Random and fixed backpropagation weights in a feedback alignment algorithm.
result Error converges to zero exponentially fast in overparameterized networks.
Neural network learning is usually time-consuming since backpropagation needs to compute full gradients and backpropagate them across multiple layers. Despite its success of existing works in accelerating propagation through sparseness, the relevant theoretical characteristics remain under-researched and empirical stud…
Skip connections improve biologically-inspired learning rules.
problem Biologically-inspired learning rules often underperform compared to backpropagation.
method Introduced skip connections between intermediate layers in biologically-motivated learning rules.
result Skip connections can match the performance of backpropagation and are robust to hyper-parameters.
A new method for learning Bayesian neural networks using layerwise inference.
problem Learning Bayesian neural networks efficiently and accurately.
method Bayesian layerwise inference, treating neural networks as stacked Bayesian linear models, with pseudo-targets defined by backpropagated gradients.
result The method converges quickly and performs well on various benchmarks.
Pipelined Backpropagation trains large models without batches efficiently.
problem Training large models efficiently on hardware with limited batch sizes.
method Fine-grained Pipelined Backpropagation with Spike Compensation and Linear Weight Prediction.
result Fine-grained Pipelined Backpropagation with a batch size of one matches the accuracy of SGD for multiple networks.
ZORB speeds up neural network training without sacrificing accuracy.
problem Slow and strenuous training of neural networks using gradient descent.
method Uses pseudoinverse of targets instead of gradients for backpropagation.
result ZORB converges 300 times faster than Adam on MNIST without hyperparameter tuning.
Backpropagation algorithm is indispensable for the training of feedforward neural networks. It requires propagating error gradients sequentially from the output layer all the way back to the input layer. The backward locking in backpropagation algorithm constrains us from updating network layers in parallel and fully l…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to deep architectures has remained a major challenge. Recent results connected dee…
We propose a modular extension of backpropagation for the computation of block-diagonal approximations to various curvature matrices of the training objective (in particular, the Hessian, generalized Gauss-Newton, and positive-curvature Hessian). The approach reduces the otherwise tedious manual derivation of these mat…
Mean field theory explains gradient backpropagation in deep dropout networks.
problem Understanding gradient backpropagation in deep dropout networks.
method Applied mean field theory to dropout networks, considering realistic training conditions.
result Gradient backpropagation length is limited by depth scales, not just independence assumption.
Backpropagation-free RL method trains layers using local signals.
problem Vanishing or exploding gradients in backpropagation-based RL.
method Local pairwise distance matching for layer-wise training without backpropagation.
result Backpropagation-free method achieves competitive performance and stability.
In real-world scenarios, it is appealing to learn a model carrying out stochastic operations internally, known as stochastic computation graphs (SCGs), rather than learning a deterministic mapping. However, standard backpropagation is not applicable to SCGs. We attempt to address this issue from the angle of cost propa…
VSML unifies meta learning concepts and enables simple backpropagation.
problem Improving and unifying meta learning concepts for neural networks.
method Unified approach using variable shared meta learning and simple weight-sharing.
result Simple backpropagation can be implemented and meta learned without gradient calculation.
Sideways trains video models by overwriting activations as new frames arrive, potentially improving generalization.
problem Training deep video models synchronously slows down and requires storing activations, limiting parallelism.
method Sideways trains video models by overwriting activations as new frames arrive, breaking the precise correspondence between gradients and activations.
result Sideways training can converge and potentially generalize better than standard synchronized backpropagation.
Study shows Direct Feedback Alignment fails to offer more efficient scaling than backpropagation.
problem Understanding and optimizing training methods for neural networks.
method Use of scaling laws to compare Direct Feedback Alignment (DFA) and backpropagation.
result DFA fails to offer more efficient scaling than backpropagation.
Proposes TAGI for efficient Gaussian inference in Bayesian neural networks.
problem Efficient inference in Bayesian neural networks with complex architectures.
method Analytical method for tractable approximate Gaussian inference (TAGI).
result Matches performance of gradient-based methods with O(n) computational complexity. A faster, more stable method for optimizing topological functions.
problem Optimizing topological functions is computationally expensive and unstable.
method Introduces a novel backpropagation scheme for faster and more robust optimization.
result Produces more robust optima and stable visualizations.
New learning rules for wide neural networks without backpropagation.
problem Training wide neural networks efficiently and without backpropagation.
method Input-weight alignment driven by gradient descent in the NTK regime.
result Biologically-motivated learning rules equivalent to backpropagation in wide networks.
In order to integrate uncertainty estimates into deep time-series modelling, Kalman Filters (KFs) (Kalman et al., 1960) have been integrated with deep learning models, however, such approaches typically rely on approximate inference techniques such as variational inference which makes learning more complex and often le…
We introduce the chi-square test neural network: a single hidden layer backpropagation neural network using chi-square test theorem to redefine the cost function and the error function. The weights and thresholds are modified using standard backpropagation algorithm. The proposed approach has the advantage of making co…
Most successful machine intelligence systems rely on gradient-based learning, which is made possible by backpropagation. Some systems are designed to aid us in interpreting data when explicit goals cannot be provided. These unsupervised systems are commonly trained by backpropagating through a likelihood function. We i…
Backpropagation-free trunk training improves model performance on various benchmarks.
problem Memory inefficiency and noisy gradient estimates in deep network training.
method Split Forward Gradient (Split-FG) method that splits network into trunk and head, estimating only trunk gradient.
result Split-FG achieves better performance than pure forward-gradient training and backpropagation on various benchmarks.
We consider time-domain digital backpropagation with chromatic dispersion filters jointly optimized and quantized using machine-learning techniques. Compared to the baseline implementations, we show improved BER performance and >40% power dissipation reductions in 28-nm CMOS.
New method reduces deep learning training costs by approximating vector-jacobian products.
problem Efficiently training deep neural networks with reduced computational and memory costs.
method Randomized, unbiased approximations of vector-jacobian products during backpropagation.
result Validated potential for reducing deep learning training costs through unbiased estimates.
Second-order optimization methods such as natural gradient descent have the potential to speed up training of neural networks by correcting for the curvature of the loss function. Unfortunately, the exact natural gradient is impractical to compute for large models, and most approximations either require an expensive it…
We propose a low-complexity sub-banded DSP architecture for digital backpropagation where the walk-off effect is compensated using simple delay elements. For a simulated 96-Gbaud signal and 2500 km optical link, our method achieves a 2.8 dB SNR improvement over linear equalization.
Arguably the biggest challenge in applying neural networks is tuning the hyperparameters, in particular the learning rate. The sensitivity to the learning rate is due to the reliance on backpropagation to train the network. In this paper we present the first application of Implicit Stochastic Gradient Descent (ISGD) to…
Forward gradients improve neural network training without backpropagation issues.
problem Training neural networks without backpropagation's locking and memorization problems.
method Using directional derivatives in forward differentiation mode, with biased guesses based on feedback from small auxiliary networks.
result Using gradients from a local loss as a candidate direction improves Forward Gradient methods.
A major drawback of backpropagation through time (BPTT) is the difficulty of learning long-term dependencies, coming from having to propagate credit information backwards through every single step of the forward computation. This makes BPTT both computationally impractical and biologically implausible. For this reason,…
Large multilayer neural networks trained with backpropagation have recently achieved state-of-the-art results in a wide range of problems. However, using backprop for neural net learning still has some disadvantages, e.g., having to tune a large number of hyperparameters to the data, lack of calibrated probabilistic pr…