[tschm]

Fixes #244.

The variable is the tolerance, not the SCS version

scs >= 3.3.0 broke three gradcheck tests. It turns out neither SCS nor the implicit derivative is wrong — both sides of the gradcheck comparison were only accurate to ~1e-4, which is the atol being asserted.

Measured against the closed-form Jacobian of test_dual_gradcheck_vector_equality:

solver tolerance	analytic gradient error
SCS default	1.25e-02
eps=1e-10	7.0e-10

Same story for test_sdp: the layer's analytic Jacobian is off by 3.05e-04 at default tolerance and 2.4e-08 at eps=1e-8. So cvxpylayers' derivative machinery is correct, and its accuracy is capped by the forward solve.

The finite difference is worse. At default tolerance its error is pinned at ~3.4e-04 for every step size from 1e-6 to 1e-3 — that is solver noise, not curvature — and only starts scaling with h once the solve is tight:

solver tolerance	h=1e-6	h=1e-5	h=1e-4
default	3.35e-04	3.50e-04	3.50e-04
eps=1e-10	8.16e-05	8.24e-06	7.26e-07

3.3.x broke nothing. It stopped over-delivering on the requested tolerance, so the two noise realizations stopped cancelling. The 1.4x margin on 3.2.11 reported in the issue was the noise floor rather than a margin.

The fix

Of the three directions in #244 this is (3): fix the accuracy, don't hide the symptom. No assertion is loosened and no scs bound is added.

• GRADCHECK_SOLVER_ARGS = {"eps": 1e-10}, passed at layer construction in all 14 diffcp-backed gradcheck tests — not just the three that failed, since every one of them had the same latent exposure.
• test_sdp additionally takes eps=1e-4 for the finite-difference step. Its optimum is the rank-one projector onto the smallest eigenvector of C, so most entries of dX/dC are near zero and are compared against atol alone; a tight solve alone leaves those sitting exactly at the finite-difference floor.
• The solver="MOREAU" gradcheck tests are left alone: eps is a diffcp/SCS key and those tests are unaffected.

Margins

From a harness that shrinks atol on each gradcheck test until it fails:

	before	after, 3.3.1	after, 3.2.11
test_sdp	fails	1000x	1000x
test_dual_gradcheck_inequality	fails	10,000x	100,000x
test_dual_gradcheck_vector_equality	fails	>10⁶x	>10⁶x
tightest of all 18 gradcheck tests	~1x	1000x	1000x

Verification

• 87 passed / 40 skipped on both scs==3.3.1 and scs==3.2.11 (baseline: 3 failed / 84 passed on 3.3.1)
• ruff@0.12.7 check clean on both touched files; ruff format --diff is byte-identical before and after, so the change is format-neutral (tests/test_torch.py is CRLF and already fails format --check on master, along with two other test files — left as-is rather than dragging in ~2700 lines of reformatting)

This should turn test_cvxpylayers in cvxpy's extensions.yml green again.

Upstream

Diagnosis confirmed independently by SCS upstream in cvxgrp/scs#464, which closed with exactly this prescription: "gradcheck tests should pass tight solver tolerances via solver_args, and the SDP check needs either a larger finite-difference step or a comparison against a closed-form derivative." cvxgrp/scs#463 investigated 3.3.0's b-dependent equilibration as the mechanism and ruled it out.

🤖 Generated with Claude Code

[tschm]

@PTNobel please have a look. This seems to be an annoying problem for cvxpy at the moment

[SteveDiamond]

The tighter forward solves and larger SDP finite-difference step are a reasonable fix for solver-noise-sensitive gradchecks. Assertions are preserved and production code is unchanged. Reviewed the diff; I did not rerun the reported local tests, and the historical failing CI job details are no longer available.