Save FP8 tensors in autograd ctx instead of full-precision inputs

Store quantized input/weight and their inverse scales in _Float8Matmul ctx to avoid re-quantization in backward and reduce saved-activation memory without changing numerics.

nanochat/fp8.py

@@ -123,19 +123,16 @@ def _to_col_major(x):
 class _Float8Matmul(torch.autograd.Function):
     """Custom autograd for the three FP8 GEMMs of a Linear layer.
 
-    The forward saves input and weight in their original precision for the
-    backward pass. Each GEMM independently re-quantizes its operands to FP8.
-    (We don't reuse the forward's FP8 tensors in backward — the backward might
-    want different precision, and saving FP8 would lose information.)
+    The forward quantizes input and weight to FP8 and saves 
+    the quantized tensors + scales for backward.
     """
 
     @staticmethod
     def forward(ctx, input_2d, weight):
-        ctx.save_for_backward(input_2d, weight)
-
         # Quantize both operands to e4m3 (higher precision format)
         input_fp8, input_inv = _to_fp8(input_2d, torch.float8_e4m3fn)
         weight_fp8, weight_inv = _to_fp8(weight, torch.float8_e4m3fn)
+        ctx.save_for_backward(input_fp8, input_inv, weight_fp8, weight_inv)
 
         # output = input @ weight.T
         # input_fp8 is [B, K] contiguous = row-major (good for first arg)
@@ -156,13 +153,12 @@ class _Float8Matmul(torch.autograd.Function):
 
     @staticmethod
     def backward(ctx, grad_output):
-        input_2d, weight = ctx.saved_tensors
+        in_fp8, in_inv, w_fp8, w_inv = ctx.saved_tensors
 
         # === GEMM 1: grad_input = grad_output @ weight ===
         # Shapes: [B, N] @ [N, K] -> [B, K]
         # Gradients use e5m2 (wider range), weights use e4m3 (higher precision)
         go_fp8, go_inv = _to_fp8(grad_output, torch.float8_e5m2)
-        w_fp8, w_inv = _to_fp8(weight, torch.float8_e4m3fn)
         # go_fp8 is [B, N] contiguous = row-major, good for first arg
         # w_fp8 is [N, K] contiguous = row-major, need column-major for second arg
         w_col = _to_col_major(w_fp8)
@@ -178,7 +174,6 @@ class _Float8Matmul(torch.autograd.Function):
         # === GEMM 2: grad_weight = grad_output.T @ input ===
         # Shapes: [N, B] @ [B, K] -> [N, K]
         go_fp8_2, go_inv_2 = _to_fp8(grad_output, torch.float8_e5m2)
-        in_fp8, in_inv = _to_fp8(input_2d, torch.float8_e4m3fn)
         # go_fp8_2 is [B, N] contiguous, we need go.T = [N, B] as first arg.
         # Transposing gives column-major, but first arg needs row-major,
         # so we must call .contiguous() to physically rearrange the memory.