fix(loss): compute causal-LM cross-entropy in float32

[le1nux]

The problem

CLMCrossEntropyLoss passes the model's logits straight into CrossEntropyLoss:

loss = self.loss_fun(shift_logits.view(-1, shift_logits.size(-1)), shift_labels.view(-1))

Under mixed precision those logits are bfloat16, and nothing promotes them. FSDP2's
MixedPrecisionPolicy casts parameters; it does not install torch.autocast, so the
operator-level float32 autocast list — which normally covers log_softmax / cross_entropy —
never applies.

This is about tensor precision, not accumulation. PyTorch's kernels already accumulate in
float32 for half-precision inputs. What is lost without the cast is the precision of the stored
tensors: the log-softmax output, the tensors its backward reads, and the returned loss scalar.
The scalar dominates — at a loss magnitude of ~36 the bfloat16 grid is 0.25 wide, and the measured
error before the cast is exactly that quantum.

What the reference implementations do

Both up-cast at exactly this point, unconditionally:

• TorchTitan — every one of its cross-entropy paths (torchtitan/components/loss.py):

  return torch.nn.functional.cross_entropy(
      pred.flatten(0, 1).float(), labels.flatten(0, 1), reduction="sum", ignore_index=IGNORE_INDEX
  )

  It does not trade this away for memory either: the chunked path still does
  logits.float().reshape(B * L, V) and accumulates through GradAccumulator(..., dtype=torch.float32).
  Memory is solved by chunking the sequence, not by dropping the up-cast.
• HF transformers — ForCausalLMLoss opens with logits = logits.float()
  (transformers/loss/loss_utils.py).

The fix

One .float() on the logits, plus a comment recording why it must not be removed.

Measured

Against an independent float64 evaluation of identical bfloat16-quantized logits, vocab 131072:

variant	error vs float64	what it is
bfloat16 logits, loss returned in bfloat16 (before)	4.89e-2	the bfloat16 quantum at loss ≈ 36
bfloat16 logits, per-token losses summed in float32	2.98e-3	residual from bfloat16-stored log-probs
float32 logits (after)	2.36e-6

Reproduced on an A100: 3.18e-2 → 1.78e-7, and the 3.18e-2 is again exactly the bfloat16 quantum at
that magnitude — confirming the error is stored-tensor precision rather than an accumulator artefact.

On a real 8B checkpoint over 262,144 held-out tokens, the gradient into lm_head differs by
0.19% between the two paths, and the up-cast recovers about 1.8× of it. The remainder is
imposed by the bfloat16 logit boundary itself and is not reachable from the loss — stated so nobody
expects this to be exact.

After the change the loss and its gradient are bit-identical to TorchTitan's formulation
(max |diff| = 0.0) for bfloat16, float16 and float32 inputs at vocab 1024 and 131072.

Tests

Three new tests, each of which fails without the fix:

1. the returned loss dtype is float32 for half-precision logits;
2. the loss is within 1e-4 of a float64 reference (it was ~5e-2 off; it is now 2.4e-6). The reference
   is computed directly via F.cross_entropy, not by calling the loss with a float64 tensor —
   the implementation casts its input to float32, so that would silently compare the fix with itself;
3. it matches TorchTitan's sum-reduction-over-valid-tokens formulation, including IGNORE_INDEX
   handling. The reference is inlined so the test carries no dependency on torchtitan.

tests/test_loss_functions.py passes (7 tests); 5 of them go red with the .float() removed. The
pinned pre-commit gate (isort 5.11.5 / black 23.9.1 / ruff 0.0.278) passes.
tests/instruction_tuning/test_e2e_instruction_tuning.py fails on this branch and on clean
main — pre-existing and unrelated. The full 545-test suite has not been run end-to-end here.

Memory note for large-vocabulary training

Casting a [2, 8192, 131072] logit tensor materialises 8 GiB in float32, alongside the other
loss buffers. On a configuration already near its memory ceiling, either chunk the loss or reduce the
micro-batch. TorchTitan's chunked path is the reference approach.

Note for the in-flight refactor

nano_expert_parallelism refactors this into two free functions, clm_cross_entropy_loss and
clm_cross_entropy_loss_sum; both need the same .float(). Worth carrying over, not least
because ChunkedCLMCrossEntropyLoss's docstring already promises "the float32 up-cast inside
cross-entropy" — a claim that only becomes true once this lands.

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