[AHMETHAKANBEZIR1]

SciPy evaluates Dirichlet densities for a matrix whose columns are samples, but the reverse-mode rules broadcast the concentration vector against the sample axis and do not reduce concentration gradients across samples. For example, differentiating a summed logpdf with three components and two samples raises a broadcasting error even though density evaluation succeeds.

Compute the local derivatives in sample-major order, restore the original coordinate layout, and use the existing unbroadcast_f helper to accumulate gradients for shared concentrations. This covers batches with all simplex components supplied; support for SciPy's abbreviated last-component input is unchanged.

Validation:

• Six new weighted batch cases (one, two, and three samples; PDF and log-PDF), checking both arguments through second-order reverse-mode differentiation: all six fail on unchanged master and pass with the patch. Four existing single-sample controls pass throughout.
• Full test suite: python -m pytest -n 2 — 651 passed, 14 warnings on Python 3.12.14, NumPy 2.5.4, SciPy 1.18.1.
• Configured pre-commit hooks and git diff --check pass. Forward-mode support is unchanged.

AI disclosure: OpenAI Codex autonomously prepared the code, tests, and this description. Validation and an additional AI review were performed; there has been no independent human review.