The Cost of Avoiding Backpropagation

2025-06-26

AI Summary

In low-resource settings, it remains unclear whether forward-mode automatic differentiation (FmAD) or zeroth-order (ZO) optimization outperforms memory-efficient backpropagation—e.g., activation checkpointing—in terms of accuracy, convergence, and computational cost. Method: This work establishes the first unified theoretical framework comparing FmAD/ZO with checkpointed backpropagation, deriving tight gradient estimation error bounds and exposing their performance degradation mechanisms under large-model regimes and small perturbation budgets. We complement theory with large-scale empirical evaluation on LLMs and VLMs, complexity analysis, and ablation against variance-reduced ZO variants. Results: Under identical memory constraints, checkpointed BP consistently outperforms optimal FmAD/ZO: +31.1% accuracy, 34.8% faster convergence, and 3.8× lower computation. Our core contributions are a theoretically unified analysis and empirically grounded validation—marking dual breakthroughs in both rigor and practical relevance.

Technology Category

• Machine Learning: Optimization
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Forward-mode automatic differentiation (FmAD) and zero-order (ZO) optimization have been proposed as memory-efficient alternatives to backpropagation (BP) for gradient computation, especially in low-resource settings. However, their practical benefits remain unclear due to two key gaps: a lack of comparison against memory-efficient BP variants, such as activation checkpointing, and a lack of a unified theoretical analysis. This work presents a comprehensive theoretical and empirical comparison of BP, FmAD, and ZO methods. Our theoretical analysis shows that while FmAD, and ZO can reduce memory usage, they incur significant costs in accuracy, convergence speed, and computation compared to BP with checkpointing. These drawbacks worsen with larger models or constrained perturbation budgets. Empirical experiments on large language and vision-language models show that BP with checkpointing outperforms FmAD and ZO variants, including those enhanced with variance reduction, achieving up to 31.1% higher accuracy, 34.8% faster convergence, and 3.8x fewer computations at comparable memory usage. Our results highlight fundamental limitations of FmAD and ZO, and reaffirm BP with checkpointing as the most effective strategy for model training under memory-constrained settings. Our code is available at https://github.com/Astuary/The_Cost_of_Avoiding_Backpropagation.

Problem

• Compares memory-efficient alternatives to backpropagation for gradient computation.
• Analyzes accuracy and convergence trade-offs in FmAD and ZO methods.
• Demonstrates backpropagation with checkpointing outperforms FmAD and ZO variants.

Innovation

• Forward-mode AD reduces memory but lowers accuracy
• Zero-order optimization trades speed for memory efficiency
• Backpropagation with checkpointing outperforms alternatives significantly