Memory-Efficient Activation Checkpointing with Sliding Window and Hirschberg's Algorithm for 0/1 Knapsack Solving in PyTorch
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Computer Science > Machine Learning
Title:Memory-Efficient Activation Checkpointing with Sliding Window and Hirschberg's Algorithm for 0/1 Knapsack Solving in PyTorch
Abstract:Activation checkpointing minimizes the runtime of neural networks under a given memory budget, by selecting which intermediate tensors to store and which to recompute. PyTorch solves this as a 0/1 knapsack problem, where operations from a joint forward-backward computation graph are items with a memory cost (weight) and a runtime saving (value). The default solver, dp_knapsack, allocates a full dynamic programming (DP) table of shape $(n+1) \times (W+1)$, where $n$ is the number of operations and $W$ is the quantized memory budget. This method is resource-hungry and crashes at $n = 100$ items on a machine with 64 GB RAM.
In this paper, we introduce dp_knapsack_sliding_hirschberg, which combines the sliding window trick and Hirschberg's algorithm to reduce peak memory from $O(nW)$ to $O(W)$ while preserving the exact optimal solution. Our experiments show successful knapsack execution at $n = 2000$, where dp_knapsack fails at $n = 100$, a 20$\times$ increase in computable problem size. In addition, our benchmarks show a consistent 25-28\% runtime speedup over dp_knapsack.
The implementation is merged into PyTorch and released in version 2.10.
| Comments: | Accepted to COLM 2026 Workshop on Efficient Reasoning |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2608.08740 [cs.LG] |
| (or arXiv:2608.08740v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.08740
arXiv-issued DOI via DataCite (pending registration)
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