Gradient Accumulation for Large Batches | Generated by AI
Andrej Karpathy’s Explanation of Gradient Accumulation Steps
In his YouTube video “Let’s build GPT: from scratch, in code, spelled out” (a detailed tutorial on implementing and training a GPT-like model from the ground up), Andrej Karpathy discusses gradient accumulation around the 2:51:40 mark. He uses it primarily as a practical workaround for training large language models on hardware with limited GPU memory, while still simulating the large effective batch sizes (e.g., 0.5 million tokens) described in the original GPT-2 and GPT-3 papers. Here’s a breakdown of his key points:
Why Use Gradient Accumulation?
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Hardware Limitations: Modern GPUs (like consumer-grade ones) can’t fit massive batch sizes in memory due to the computational demands of transformer models. For instance, Karpathy targets a batch size of ~0.5M tokens to match research setups, but a single GPU might only handle micro-batches of 4-8 samples. Without accumulation, you’d be stuck with tiny batches, leading to noisy gradients and slower convergence.
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Better Training Stability and Performance: Larger effective batch sizes (achieved via accumulation) reduce gradient variance, making updates more reliable and speeding up training. Karpathy emphasizes this for reproducibility—sticking close to the GPT papers’ hyperparams (e.g., paired with specific learning rate schedules) yields better results than naive small-batch training.
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Quote from Karpathy (around 2:51:40): “So we want to use a batch size of .5 million roughly but the question is how do we use .5 million if we only have a small GPU? Well, for that we need to use what’s called gradient accumulation… so we’re going to turn to that next and it allows us to simulate in a serial way any arbitrary batch size that we set.”
In essence, it’s a “serial simulation” of parallelism: you process data in smaller chunks but accumulate the gradients as if it were one big batch, enabling scalable training without needing a data center.
How It Works (in His Implementation)
Karpathy implements it explicitly in PyTorch:
- Set a small micro-batch size (e.g., 4-8 samples) that fits in GPU memory.
- Run forward and backward passes for
accumulation_stepsiterations (e.g., 32 steps), summing gradients element-wise each time without updating weights. - After all steps, perform one optimizer step with the accumulated gradients.
- Scale the loss by
1/accumulation_stepsto normalize.
This ensures the effective batch size is micro_batch_size × accumulation_steps × sequence_length. He combines it with tricks like mixed-precision training, FlashAttention, and torch.compile for efficiency.
Bonus: Implicit Accumulation via Weight Tying
Karpathy also ties this to weight tying (sharing the token embedding matrix wte with the output head in GPT-2 style). During backprop, gradients from both the input embeddings and output logits “naturally accumulate” into the same tensor—saving ~30% parameters and adding an inductive bias that input/output representations should align. Quote: “In the backward pass we’ll get gradient contributions from both branches… these gradients will add up on the wte tensor.”
Overall, these techniques let you train GPT-scale models on a single GPU while faithfully replicating paper results. For the full context, watch from ~2:50:00 onward in the video.
Let’s build GPT: from scratch, in code, spelled out