Large Language Model training is increasingly constrained by memory capacity. Activation Checkpointing reduces activation memory by avoiding storing selected activations during the forward pass and rematerializing them during backpropagation, thereby trading memory savings for additional computation. Although this technique is essential for scaling model training, rematerialization can be prohibitively expensive, particularly for Transformer linear layers. Approximate computation could reduce this overhead, but conventional approaches either introduce errors that accumulate over the backward pass or fail to exploit information available from the initial forward pass. We introduce a novel approximate rematerialization method that can yield unbiased gradient estimates: using information collected during the initial forward pass, the method selectively recomputes only the most important layer components, either through greedy selection or randomized sketching. Ablation studies show that the resulting gradients closely match the exact gradients. When applied to feed-forward layers, attention layers, or both, our method can recompute only two-thirds of the layer components in a Llama-488M model, while increasing perplexity by just 1.7%, 1.2%, and 2.5%, respectively.

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