Forward-mode AD that are closer estimations of the true gradients.

An empirical study on how training with forward gradients navigates in the loss landscape is further explored.

Continuously adapting pre-trained models to local data on resource constrained edge devices is the $\emph{last mile}$ for model deployment. However, as models increase in size and depth, backpropagation requires a large amount of memory, which becomes prohibitive for edge devices. In addition, most existing low power neural processing engines (e.g., NPUs, DSPs, MCUs, etc.) are designed as fixed-point inference accelerators, without training capabilities. Forward gradients, solely based on directional derivatives computed from two forward calls, have been recently used for model training, with substantial savings in computation and memory. However, the performance of quantized training with fixed-point forward gradients remains unclear. In this paper, we investigate the feasibility of on-device training using fixed-point forward gradients, by conducting comprehensive experiments across a variety of deep learning benchmark tasks in both vision and audio domains. We propose a series of algorithm enhancements that further reduce the memory footprint, and the accuracy gap compared to backpropagation. An empirical study on how training with forward gradients navigates in the loss landscape is further explored. Our results demonstrate that on the last mile of model customization on edge devices, training with fixed-point forward gradients is a feasible and practical approach.

The gradients used to train neural networks are typically computed using backpropagation. While an efficient way to obtain exact gradients, backpropagation is computationally expensive, hinders parallelization, and is biologically implausible. Forward gradients are an approach to approximate the gradients from directional derivatives along random tangents computed by forward-mode automatic differentiation. So far, research has focused on using a single tangent per step. This paper provides an in-depth analysis of multi-tangent forward gradients and introduces an improved approach to combining the forward gradients from multiple tangents based on orthogonal projections. We demonstrate that increasing the number of tangents improves both approximation quality and optimization performance across various tasks.

Finetuning large language models (LLMs) in federated learning (FL) settings has become important as it allows resource-constrained devices to finetune a model using private data. However, finetuning LLMs using backpropagation requires excessive memory (especially from intermediate activations) for resource-constrained devices. While Forward-mode Auto-Differentiation (AD) can reduce memory footprint from activations, we observe that directly applying it to LLM finetuning results in slow convergence and poor accuracy. This work introduces Spry, an FL algorithm that splits trainable weights of an LLM among participating clients, such that each client computes gradients using Forward-mode AD that are closer estimates of the true gradients. Spry achieves a low memory footprint, high accuracy, and fast convergence. We theoretically show that the global gradients in Spry are unbiased estimates of true global gradients for homogeneous data distributions across clients, while heterogeneity increases bias of the estimates. We also derive Spry's convergence rate, showing that the gradients decrease inversely proportional to the number of FL rounds, indicating the convergence up to the limits of heterogeneity. Empirically, Spry reduces the memory footprint during training by 1.4-7.1$\times$ in contrast to backpropagation, while reaching comparable accuracy, across a wide range of language tasks, models, and FL settings. Spry reduces the convergence time by 1.2-20.3$\times$ and achieves 5.2-13.5\% higher accuracy against state-of-the-art zero-order methods. When finetuning Llama2-7B with LoRA, compared to the peak memory usage of 33.9GB of backpropagation, Spry only consumes 6.2GB of peak memory. For OPT13B, the reduction is from 76.5GB to 10.8GB. Spry makes feasible previously impossible FL deployments on commodity mobile and edge devices. Source code is available at https://github.com/Astuary/Spry.

Scientific computing is an essential tool for scientific discovery and engineering design, and its computational cost is always a main concern in practice. To accelerate scientific computing, it is a promising approach to use machine learning (especially meta-learning) techniques for selecting hyperparameters of traditional numerical methods. There have been numerous proposals to this direction, but many of them require automatic-differentiable numerical methods. However, in reality, many practical applications still depend on well-established but non-automatic-differentiable legacy codes, which prevents practitioners from applying the state-of-the-art research to their own problems. To resolve this problem, we propose a non-intrusive methodology with a novel gradient estimation technique to combine machine learning and legacy numerical codes without any modification. We theoretically and numerically show the advantage of the proposed method over other baselines and present applications of accelerating established non-automatic-differentiable numerical solvers implemented in PETSc, a widely used open-source numerical software library.

Training a deep neural network using gradient-based methods necessitates the calculation of gradients at each level. However, using backpropagation or reverse mode differentiation, to calculate the gradients necessities significant memory consumption, rendering backpropagation an inefficient method for computing gradients. This paper focuses on analyzing the performance of the well-known Frank-Wolfe algorithm, a.k.a. conditional gradient algorithm by having access to the forward mode of automatic differentiation to compute gradients. We provide in-depth technical details that show the proposed Algorithm does converge to the optimal solution with a sub-linear rate of convergence by having access to the noisy estimate of the true gradient obtained in the forward mode of automated differentiation, referred to as the Projected Forward Gradient. In contrast, the standard Frank-Wolfe algorithm, when provided with access to the Projected Forward Gradient, fails to converge to the optimal solution. We demonstrate the convergence attributes of our proposed algorithms using a numerical example.

Computational Fluid Dynamics (CFD) is used in the design and optimization of gas turbines and many other industrial/ scientific applications. However, the practical use is often limited by the high computational cost, and the accurate resolution of near-wall flow is a significant contributor to this cost. Machine learning (ML) and other data-driven methods can complement existing wall models. Nevertheless, training these models is bottlenecked by the large computational effort and memory footprint demanded by back-propagation. Recent work has presented alternatives for computing gradients of neural networks where a separate forward and backward sweep is not needed and storage of intermediate results between sweeps is not required because an unbiased estimator for the gradient is computed in a single forward sweep. In this paper, we discuss the application of this approach for training a subgrid wall model that could potentially be used as a surrogate in wall-bounded flow CFD simulations to reduce the computational overhead while preserving predictive accuracy.