Add `xtrain_autodiff::checkpoint::checkpoint(segment_fn, input, params)`, a
higher-order autograd node (à la torch.utils.checkpoint) for activation
recomputation (Phase T13 / KI-3):
- forward: run `segment_fn` on detached leaves so its internal ops are NOT
recorded on the outer tape; keep only the output value (the local sub-tape —
and thus the segment's intermediate activations — drops immediately). The
checkpoint node's parents are [input, ..params].
- backward: re-run `segment_fn` from the saved input + (unchanged) param values
into a fresh local tape, seed the recomputed output with the upstream grad,
backprop, then push the recovered input/param grads to the real parents. Local
tape drops at the end → recomputed activations freed.
Exact by construction (same deterministic kernels, same inputs) → grads match
the non-checkpointed path. Composes with bf16 (T12, same path on recompute) and
DDP (T8, per-rank).
Supporting change: `Var::backward_seeded(seed)` — backward from an explicit
non-scalar upstream grad (the segment output is generally not a scalar);
`backward()` is now the scalar wrapper that seeds ones.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Var = Rc<RefCell<VarNode>> on a define-by-run tape: value + optional grad +
parents + backward closure. backward() seeds a scalar loss, walks reverse
topo order, and pushes grads to parents. push_grad always SUMs into the grad
slot — the fan-out accumulation path T3 lacked. Per-crate build.rs emits the
no_cuda cfg (does not propagate); engine gated, grad_check stays host-only.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
New xtrain-autodiff crate with a reusable central finite-difference
gradient check: grad_check(x, shape, f, analytic_grad, cfg) compares an
analytic gradient against (f(x+ε)-f(x-ε))/2ε per element with a relative
tolerance. Host-only (no CUDA): the loss closure owns any GPU work, so
T4's per-op backward checks can reuse it directly. Includes host unit
tests (sum(x²) grad 2x passes; a wrong grad is rejected).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
