Training deep neural networks typically relies on backpropagating high dimensional error signals a computationally intensive process with little evidence supporting its implementation in the brain. However, since most tasks involve low-dimensional outputs, we propose that low-dimensional error signals may suffice for effective learning. To test this hypothesis, we introduce a novel local learning rule based on Feedback Alignment that leverages indirect, low-dimensional error feedback to train large networks. Our method decouples the backward pass from the forward pass, enabling precise control over error signal dimensionality while maintaining high-dimensional representations. We begin with a detailed theoretical derivation for linear networks, which forms the foundation of our learning framework, and extend our approach to nonlinear, convolutional, and transformer architectures. Remarkably, we demonstrate that even minimal error dimensionality on the order of the task dimensionality can achieve performance matching that of traditional backpropagation. Furthermore, our rule enables efficient training of convolutional networks, which have previously been resistant to Feedback Alignment methods, with minimal error. This breakthrough not only paves the way toward more biologically accurate models of learning but also challenges the conventional reliance on high-dimensional gradient signals in neural network training. Our findings suggest that low-dimensional error signals can be as effective as high-dimensional ones, prompting a reevaluation of gradient-based learning in high-dimensional systems. Ultimately, our work offers a fresh perspective on neural network optimization and contributes to understanding learning mechanisms in both artificial and biological systems.

Over the past few decades, extensive research has been devoted to the design of artificial reverberation algorithms aimed at emulating the room acoustics of physical environments. Despite significant advancements, automatic parameter tuning of delay-network models remains an open challenge. We introduce a novel method for finding the parameters of a Feedback Delay Network (FDN) such that its output renders target attributes of a measured room impulse response. The proposed approach involves the implementation of a differentiable FDN with trainable delay lines, which, for the first time, allows us to simultaneously learn each and every delay-network parameter via backpropagation. The iterative optimization process seeks to minimize a perceptually-motivated time-domain loss function incorporating differentiable terms accounting for energy decay and echo density. Through experimental validation, we show that the proposed method yields time-invariant frequency-independent FDNs capable of closely matching the desired acoustical characteristics, and outperforms existing methods based on genetic algorithms and analytical FDN design.

A key challenge in solving the deterministic inverse reinforcement learning (IRL) problem online and in real-time is the existence of multiple solutions. Nonuniqueness necessitates the study of the notion of equivalent solutions, i.e., solutions that result in a different cost functional but same feedback matrix, and convergence to such solutions. While offline algorithms that result in convergence to equivalent solutions have been developed in the literature, online, real-time techniques that address nonuniqueness are not available. In this paper, a regularized history stack observer that converges to approximately equivalent solutions of the IRL problem is developed. Novel data-richness conditions are developed to facilitate the analysis and simulation results are provided to demonstrate the effectiveness of the developed technique.

Feedback alignment algorithms are an alternative to backpropagation to train neural networks, whereby some of the partial derivatives that are required to compute the gradient are replaced by random terms. This essentially transforms the update rule into a random walk in weight space. Surprisingly, learning still works with those algorithms, including training of deep neural networks. This is generally attributed to an alignment of the update of the random walker with the true gradient - the eponymous gradient alignment -- which drives an approximate gradient descend. The mechanism that leads to this alignment remains unclear, however. In this paper, we use mathematical reasoning and simulations to investigate gradient alignment. We observe that the feedback alignment update rule has fixed points, which correspond to extrema of the loss function. We show that gradient alignment is a stability criterion for those fixed points. It is only a necessary criterion for algorithm performance. Experimentally, we demonstrate that high levels of gradient alignment can lead to poor algorithm performance and that the alignment is not always driving the gradient descend.

In the quest to enhance the efficiency and bio-plausibility of training deep neural networks, Feedback Alignment (FA), which replaces the backward pass weights with random matrices in the training process, has emerged as an alternative to traditional backpropagation. While the appeal of FA lies in its circumvention of computational challenges and its plausible biological alignment, the theoretical understanding of this learning rule remains partial. This paper uncovers a set of conservation laws underpinning the learning dynamics of FA, revealing intriguing parallels between FA and Gradient Descent (GD). Our analysis reveals that FA harbors implicit biases akin to those exhibited by GD, challenging the prevailing narrative that these learning algorithms are fundamentally different. Moreover, we demonstrate that these conservation laws elucidate sufficient conditions for layer-wise alignment with feedback matrices in ReLU networks. We further show that this implies over-parameterized two-layer linear networks trained with FA converge to minimum-norm solutions. The implications of our findings offer avenues for developing more efficient and biologically plausible alternatives to backpropagation through an understanding of the principles governing learning dynamics in deep networks.

We present DeepCSI, a novel approach to Wi-Fi radio fingerprinting (RFP) which leverages standard-compliant beamforming feedback matrices to authenticate MU-MIMO Wi-Fi devices on the move. By capturing unique imperfections in off-the-shelf radio circuitry, RFP techniques can identify wireless devices directly at the physical layer, allowing low-latency low-energy cryptography-free authentication. However, existing Wi-Fi RFP techniques are based on software-defined radio (SDRs), which may ultimately prevent their widespread adoption. Moreover, it is unclear whether existing strategies can work in the presence of MU-MIMO transmitters - a key technology in modern Wi-Fi standards. Conversely from prior work, DeepCSI does not require SDR technologies and can be run on any low-cost Wi-Fi device to authenticate MU-MIMO transmitters. Our key intuition is that imperfections in the transmitter's radio circuitry percolate onto the beamforming feedback matrix, and thus RFP can be performed without explicit channel state information (CSI) computation. DeepCSI is robust to inter-stream and inter-user interference being the beamforming feedback not affected by those phenomena. We extensively evaluate the performance of DeepCSI through a massive data collection campaign performed in the wild with off-the-shelf equipment, where 10 MU-MIMO Wi-Fi radios emit signals in different positions. Experimental results indicate that DeepCSI correctly identifies the transmitter with an accuracy of up to 98%. The identification accuracy remains above 82% when the device moves within the environment. To allow replicability and provide a performance benchmark, we pledge to share the 800 GB datasets - collected in static and, for the first time, dynamic conditions - and the code database with the community.

Gradient descent and backpropagation have enabled neural networks to achieve remarkable results in many real-world applications. Despite ongoing success, training a neural network with gradient descent can be a slow and strenuous affair. We present a simple yet faster training algorithm called Zeroth-Order Relaxed Backpropagation (ZORB). Instead of calculating gradients, ZORB uses the pseudoinverse of targets to backpropagate information. ZORB is designed to reduce the time required to train deep neural networks without penalizing performance. To illustrate the speed up, we trained a feed-forward neural network with 11 layers on MNIST and observed that ZORB converged 300 times faster than Adam while achieving a comparable error rate, without any hyperparameter tuning. We also broaden the scope of ZORB to convolutional neural networks, and apply it to subsamples of the CIFAR-10 dataset. Experiments on standard classification and regression benchmarks demonstrate ZORB's advantage over traditional backpropagation with Gradient Descent.

The backpropagation algorithm has long been the canonical training method for neural networks. Modern paradigms are implicitly optimized for it, and numerous guidelines exist to ensure its proper use. Recently, synthetic gradients methods - where the error gradient is only roughly approximated - have garnered interest. These methods not only better portray how biological brains are learning, but also open new computational possibilities, such as updating layers asynchronously. Even so, they have failed to scale past simple tasks like MNIST or CIFAR-10. This is in part due to a lack of standards, leading to ill-suited models and practices forbidding such methods from performing to the best of their abilities. In this work, we focus on direct feedback alignment and present a set of best practices justified by observations of the alignment angles. We characterize a bottleneck effect that prevents alignment in narrow layers, and hypothesize it may explain why feedback alignment methods have yet to scale to large convolutional networks.

Recent advances in deep neural networks (DNNs) owe their success to training algorithms that use backpropagation and gradientdescent. 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 backpropagation drawing from advances in feedback alignment algorithms in which the error computation at a single synapse reduces to the product of three scalar values, satisfying the three factor rule. Using a sparse feedback matrix, we show that a neuron needs only a fraction of the information previously used by the feedback alignment algorithms to yield results which are competitive with backpropagation. Consequently, memory and compute can be partitioned and distributed whichever way produces the most efficient forward pass so long as a single error can be delivered to each neuron. We evaluate our algorithm using standard data sets, including ImageNet, to address the concern of scaling to challenging problems. Our results show orders of magnitude improvement in data movement and 2 improvement in multiply-and-accumulate operations over backpropagation. All the code and results are available under https://github.com/bcrafton/ssdfa. I. INTRODUCTION The demise of Dennard scaling [11] and decline of Moores Law [27] have exposed the fundamental scaling limitations of the von Neumann models of computing. This transition is accompanied by the realization that in a fast evolving, socially interconnected world, we are observing a seismic shift in the amount of unstructured data that need to be processed in real-time [25] which has heralded the third wave of Artificial Intelligence and the exponential growth of Machine Learning in data-analytics, real-time control, computer vision, robotics and so on. We expect that intelligent systems of the future will be limited by the energy growth of data movement rather than compute.