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Add the Aida optimizer - #551

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shaneraphel:add-aida-optimizer

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@shaneraphel shaneraphel commented Sep 25, 2026 •

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Summary

Adds Aida, which exploits layerwise gradient statistics through mutual vector projections of the gradient and its running average, from https://arxiv.org/abs/2203.13273.

The port follows https://github.com/guoqiang-zhang-x/Aida-Optimizer with three modernizations:

  • the reference add_(scalar, tensor) calls use the pre-1.5 torch signature and fail on current torch; the port uses add_(tensor, alpha=...) / addcmul_
  • the reference adds eps into exp_avg_var in place, so eps accumulates into the state every step; the port computes the denom out of place
  • K and xi move from instance attributes into the group defaults (with validation and __setstate__ fallbacks), so checkpoints round-trip; the dead amsgrad group key is dropped

Fixes #538.

Test plan

  • pytest tests/test_aida.py: 4 passed — two steps match a hand-computed reference for K in {1, 2, 3}, exp_avg_var after one step is exactly (1-b2)*residual^2 with no eps, reset() clears state, invalid K/xi rejected
  • pytest tests/test_optimizer_with_nn.py -k Aida: 1 passed
  • pytest tests/test_param_validation.py -k Aida: 2 passed
  • tests/test_optimizer.py -k Aida: 7 failures in the state-dict round-trip assertion, the same pre-existing torch-2.11 harness issue documented in Add the Sophia optimizer #550 (verified identical on Lion, Apollo, Adahessian without any change)

Prepared with an AI assistant. I reviewed the diff and ran the tests on CPU.

get_trace averaged the Hessian diagonal over the spatial dims only for
4D kernels. Conv1d (3D) and Conv3d (5D) weights left tmp_output
unbound. Average over dims 2..ndim-1 instead; 4D is unchanged.
Each mode factor of an order-k tensor enters to the power -1/(2k):
-1/4 per side for matrices. The code used -1/k, twice the published
exponent. The 7 pre-existing test_optimizer Shampoo failures are a
state-dict precision issue on this torch version and fail identically
without this change.
warmup_rate (default 1e-6) replaces the hard-coded warm-up slope and
min_step_size (default 1e-2) the floor. Old checkpoints without the new
group keys fall back to the old values. The 7 pre-existing
test_optimizer Adafactor failures are a state-dict precision issue on
this torch version and fail identically without this change.
Second-order optimizer with a diagonal Hessian estimate (SophiaG).
Follows the reference update, including update_hessian refresh,
maximize flag, and sparse-gradient rejection. CUDA-graph capturable
execution is not ported. Wired into the test harness lists and README.
Layerwise-gradient-statistics optimizer with K mutual projections of
the gradient and its running average. Modernizes the reference
in-place add_ calls, keeps eps out of the state, and holds K/xi in the
group defaults. Wired into the test harness lists and README.

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[Feature Request] Aida optimizer

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