[SYSTEMDS-3926] add test nn optimizers#2538
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Add previously-missing invariant checks flagged in code review: adam.dml - inline lr_eff for the 1xN shape case (stop piggy-backing on lr_eff1 from the 2x3 case; a shape bug would have silently passed) - sign / direction sanity: at X=0 with m=v=0 the step is opposite to dX - state independence from X: m,v depend only on dX and prior state - textbook vs compact bias-correction equivalence at t=2 (1e-4 slack for the epsilon-placement difference) - lr=0 no-op (parameters must not move) - large-gradient (1e10) finiteness and step-magnitude bound - no-stall check on the convergence loop (loss at step 400 < loss at 200) adamw.dml - lambda=0 reduces AdamW to Adam (X within 1e-4 for eps placement, m/v exactly to 1e-12) — the strongest single decoupling invariant - sign / direction sanity (lambda=0 pins the adaptive term's sign) - state independence from X - lr=0 no-op with lambda>0 (both terms scale with lr; X must be pinned) - large-gradient finiteness with a decay-inclusive bound - decay-heavy convergence run (lambda=0.1) — the existing lambda=0.001 run was basically Adam - clarify the t=1 collapse in the mixed-gradient analytic comment adagrad.dml - replace magic min(cache)<10 threshold with an anchored 2x growth check over the observed step-1 cache - non-negativity of cache (single- and multi-step) - mixed-sign accumulation: c += dX^2 must not depend on sign of dX - sign / direction sanity - lr=0 no-op (parameters pinned, cache still accumulates) - large-gradient finiteness and step ~lr bound Mutation-tested: a sign flip in adam.dml, a cache-reset and a cache+=|dX| mutation in adagrad.dml, and dropping *X from AdamW's decay term or using beta*t instead of beta^t all now surface as ERROR: lines from the new assertions above.
test: close review gaps in adam/adamw/adagrad optimizer tests
Darius3001
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