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Raise Shampoo preconditioners to -1/(2k) per the paper - #548
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shaneraphel wants to merge 2 commits into
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shaneraphel wants to merge 2 commits into
shaneraphel wants to merge 2 commits into
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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.
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Summary
Gupta, Koren, Singer 2018 put each mode factor of an order-
ktensor to the power-1/(2k):-1/4on each side for matrices,-1/2for vectors. The code used-1/k, twice the published exponent on every mode.On a 20×6 least-squares toy at the same learning rate, the paper exponent reaches 0.523 final MSE against 0.817 for the old exponent.
Fixes #502.
Test plan
pytest tests/test_shampoo_exponent.py:X^4 = M^{-1}for a matrix factor,X^2 = M^{-1}for a vector factor, and the toy comparison abovepytest tests/test_optimizer_with_nn.py -k "Shampoo or Adahessian": 2 passedtests/test_optimizer.py -k Shampoohas 7 failures that exist without this change (state-dict precision on this torch version)