RTX 4070 VRAM Usage Explained | Generated by AI

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Why ~6.5 GB Memory Usage?

The RTX 4070 has 12 GB VRAM (12288 MiB, shown as 12282 MiB likely due to rounding/reserved space). Your training process is using 6582 MiB (~6.4 GB) total, with the Python process accounting for 4464 MiB (~4.4 GB); the difference includes CUDA context overhead, temporary kernels, and caches from torch.compile (noted in the log: “compiling the model…”). This is high for a small 30M-parameter model because GPU memory during transformer training is dominated by activations (intermediate computations in forward/backward passes), not just parameters. Parameters alone would use only ~0.5 GB, but activations scale aggressively with your config’s batch_size, block_size, n_embd, and n_layer. PyTorch’s autograd keeps forward-pass outputs in memory for backpropagation (no gradient checkpointing in default nanoGPT), and features like AMP (mixed precision), fused AdamW, and model compilation add overhead.

Key reasons for this level of usage:

• Activations dominate (4–5 GB here): Each forward pass through the transformer layers generates large intermediate tensors (e.g., query/key/value projections in attention, feed-forward hidden states). Backward pass doubles this by allocating gradient temporaries. Attention also has O(batch_size × num_heads × block_size²) memory for score matrices (e.g., ~50 MB per layer before release), though nanoGPT’s implementation reuses buffers where possible.
• No optimizations for memory: nanoGPT defaults to full activation storage without checkpointing (which trades compute for memory by recomputing fwd during bwd). Torch.compile fuses operations but can increase peak allocation during graph capture and execution.
• Mixed precision overhead: Model/grads in FP16 (2 bytes/param), but AdamW optimizer states in FP32 (8 bytes each for momentum/variance, ~2× params). Input batches (FP16 tokens) are small (~16 KB), but temporaries aren’t.
• Runtime factors: Gradient accumulation (steps=4) processes batch_size=16 per step but doesn’t multiply memory (grads accumulate in place); however, eval phases (eval_iters=200) temporarily spike usage. Your log shows steady training at iter 1300, so this is baseline.

In short, it’s “so high” relative to the model size because small models like this still incur full transformer overhead per token, and your config (batch=16, block=512) processes ~8K tokens per step—enough to fill VRAM significantly without aggressive optimization.

How to Estimate ~6.5 GB from the Config

You can’t predict exactly without profiling (e.g., via torch.utils.bottleneck or NVIDIA Nsight), as it depends on PyTorch version, CUDA, and exact impl details. But you can approximate using standard formulas for transformer training memory. These break VRAM into components: parameters/optimizer (~10–20% of total), activations (~70–80%), and overhead (~10%). All calcs below assume FP16 training (dtype=’float16’ from log’s GradScaler) with AdamW.

1. Parameter Memory (Easy to Estimate: ~0.06 GB)

• Formula: num_params × bytes_per_param (model in FP16).
• From log: 29.94M params.
• FP16: 29.94M × 2 bytes = 59.88 MB (~0.06 GB).
• How to compute params from config (nanoGPT formula): ≈ 12 × n_layer × n_embd² (transformer blocks) + n_embd × vocab_size (embed + LM head).
  • 12 × 6 × 384² = 12 × 6 × 147,456 ≈ 10.6M
  • 384 × 50,304 ≈ 19.3M
  • Total: ~29.9M (matches log; small extras like biases/LN ignored).

2. Gradients + Optimizer Memory (~0.3–0.6 GB)

• Gradients: Same as params (FP16): another ~0.06 GB.
• Optimizer (fused AdamW, log confirms): 2 states (momentum, variance) per decayed param, typically FP32.
  • Decayed params: 30.13M (log: 26 tensors, 30,130,176 params).
  • Formula: decayed_params × 2 × 4 bytes (FP32) = 30.13M × 8 ≈ 241 MB.
  • Non-decayed (biases/LN): Small, ~5K params, negligible.
• Total core: params + grads + opt ≈ (2 + 8) bytes/param = 10 bytes/param × 30M ≈ 300 MB.
  • Range: 12–20 bytes/param if including FP32 master weights or extras (common in mixed precision).
• From config: Scales directly with n_layer, n_embd (bigger = more params). Your small sizes keep this low.

3. Activations Memory (Hardest/Trickiest: ~4–5 GB)

• This is the bulk and varies by impl. It’s O(batch_size × block_size × n_embd × n_layer) for linear parts, plus O(batch_size × n_head × block_size²) for attention scores.
• Basic Formula (from transformer training estimators):

  activations_bytes ≈ batch_size × block_size × n_embd × n_layer × multiplier × 2 (FP16 bytes)
  

  • Multiplier: Empirical 16–34 for fwd (embed + per-layer attn/FFN buffers) + bwd (2–3× fwd). Common value: 24 (12 for fwd, 12 for bwd; accounts for ~4–6 tensors/layer like Q/K/V/out in attn, up/down in FFN with 4× intermediate dim).
  • Your config: batch_size=16, block_size=512, n_embd=384, n_layer=6.
  • Base: 16 × 512 × 384 × 6 = 18.87M “elements”.
  • × 24 × 2 bytes = 18.87M × 48 ≈ 906 MB (underestimate).
• Attention-Specific Spike (O(seq²), significant at block_size=512):
  • Per layer: batch_size × n_head × block_size² × 2 bytes (for QK^T scores matrix).
  • 16 × 6 × 512 × 512 × 2 ≈ 50.3 MB/layer.
  • × n_layer=6, but sequential (not all at once): ~50–100 MB peak per layer during fwd, plus bwd temps. Total adds ~0.3–0.5 GB across passes.
• Adjusted Empirical Total for Your Config: The basic formula underestimates by 4–5× due to PyTorch temps (e.g., GEMM buffers in FFN/attn, no release until bwd end) and nanoGPT’s loop-based layers storing all fwd outputs (~ L × 4–6 × batch × seq × embd bytes). Real-world: ~ batch_size × block_size × n_embd × n_layer × 160 × 2 bytes ≈ 18.87M × 320 ≈ 6 GB (tuned to match your 6.5 GB total; aligns with similar small-GPT reports).
  • Why 160? Includes full bwd (no checkpointing), FFN intermediate (4× n_embd), residuals/LN caches, and ~20–30% PyTorch overhead per tensor.
• From config: Scales linearly with batch_size/block_size (token throughput), quadratically with block_size (attn), and with n_embd/n_layer (depth/width). Your values are moderate but compound: e.g., halving batch_size to 8 would cut activations ~50%, saving ~2–3 GB.

4. Overhead and Misc (~1 GB)

• CUDA/PyTorch: Context (~500 MB), kernel launches, allocator fragmentation.
• Torch.compile: Graph captures + fused ops add 0.5–1 GB (log shows compilation; can be profiled with torch._dynamo.config).
• Data: Batch tokens (negligible), but if eval is running, eval_iters=200 adds temporary batches.
• Total: Core (0.4 GB) + activations (4.5 GB) + overhead (1.5 GB) ≈ 6.4 GB.

Validation Against Similar Setups

• NanoGPT/GPT-2 small (124M params, embd=768=2× yours, layers=12=2×, batch~8–16, seq=1024=2×) typically uses 6–10 GB in FP16 training. Your model is ~1/4 params but similar token volume (16×512 vs. 16×1024 /2 for scaling), so ~half would be 3–5 GB base—your extra comes from no checkpointing and compilation.
• Tools for better prediction:
  • Run python -m torch.utils.bottleneck during training for breakdown.
  • Use Hugging Face’s estimate_memory() or libraries like modelscope for LLM estimators (adapt for nanoGPT).
  • Online calculators (e.g., from search results) input your params/batch/seq for ~5–7 GB estimate.

To reduce to <4 GB: Set batch_size=8 (or use gradient_accumulation_steps=8 for same effective batch=64), block_size=256, or add gradient checkpointing (modify model.forward to use torch.utils.checkpoint). Your setup fits comfortably in 12 GB, but monitor with nvidia-smi -l 1 for spikes.

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