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Gradients without Backpropagation
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Using backpropagation to compute gradients of objective functions for optimization has remained a mainstay of machine learning. Backpropagation, or reverse-mode differentiation, is a special case within the general family of automatic differentiation algorithms that also includes the forward mode. We present a method to compute gradients based solely on the directional derivative that one can compute exactly and efficiently via the forward mode. We call this formulation the forward gradient, an unbiased estimate of the gradient that can be evaluated in a single forward run of the function, entirely eliminating the need for backpropagation in gradient descent. We demonstrate forward gradient descent in a range of problems, showing substantial savings in computation and enabling training up to twice as fast in some cases.
Forward citations
Cited by 9 Pith papers
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The Program Hypergraph: Multi-Way Relational Structure for Geometric Algebra, Spatial Compute, and Physics-Aware Compilation
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Dimensional types that persist through MLIR lowering jointly drive numeric representation selection and deterministic memory allocation as coeffects on a single program semantic graph.
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Reconstructing Backpropagation from Forward Fluctuations in Noise-modulated Neural Networks
In a noise-modulated neural network, backpropagation's transposed-weight multiplications can be replaced by covariance estimates from forward fluctuations, matching backpropagation accuracy on small tasks.
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Adaptive Domain Models: Bayesian Evolution, Warm Rotation, and Principled Training for Geometric and Neuromorphic AI
The paper claims that composing the Dimensional Type System, Program Hypergraph, and b-posit 2026 standard yields depth-independent training memory at ~2x inference, grade-preserving updates, Bayesian distillation for...
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Forward-Only Continual Learning
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TITAN-Guide: Taming Inference-Time AligNment for Guided Text-to-Video Diffusion Models
A training-free guidance method that uses forward gradients instead of backpropagation to steer text-to-video diffusion latents with lower GPU memory.
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Memory Savings at What Cost? A Study of Alternatives to Backpropagation
Checkpointed backpropagation beats forward-mode AD and zero-order optimization in accuracy, convergence speed, and compute for LLM fine-tuning, undermining claims that the alternatives are practical memory savers.
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MobiEdit: Resource-efficient Knowledge Editing for Personalized On-device LLMs
MobiEdit performs on-device LLM knowledge editing by estimating gradients through forward passes only, combined with mixed-precision quantization, early stopping, and prefix caching.
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