[M-Colley]

The default LinearOperator._bilinear_derivative detaches every representation tensor and calls autograd.grad without create_graph. Operators that inherit this fallback consequently lose representation-input higher derivatives. For example, kron(Diag(ones(4)), Root(a) + Diag(0.06 * ones(2))).to_dense().sin().sum() has the correct first derivative with respect to a, but that derivative is detached despite create_graph=True. The equivalent dense torch.kron expression has a nonzero Hessian. Correlated multitask likelihood covariance materialization is one affected use case.

This repair retains the existing detached ordinary-backward path. When the caller requests a derivative graph, it builds independent view nodes for differentiable representation tensors and requests graph construction from the nested autograd call. The views are important: simply reusing the original tensors would include unwanted paths through dependent left/right vectors or through another representation tensor when computing a partial derivative. The resulting partial derivatives remain connected to all original tensors for subsequent backward passes.

Tests include:

• A nonlinear fallback operator with dependent representations and vectors, checked against explicit analytic partials and mixed higher derivatives.
• Kronecker Root-plus-Diagonal covariance compositions against independent dense algebra through third derivatives, including batches/broadcasting and CPU/CUDA.
• Gradcheck/gradgradcheck and an ordinary-backward control.

The unmodified source fails eight new CPU/CUDA subcases. The repaired representative operator suites (Kronecker, concatenation, triangular, added-diagonal, sum and the new fallback regressions) pass 968 tests and ten subcases on Torch 2.13 CPU/CUDA, and 968 tests and five subcases on Torch 2.14.1 CPU. Formatting, Flake8 and git diff --check pass.

Related analytic specializations are proposed separately in #152 and #153. This change fixes the remaining general fallback and does not depend on either PR. Prepared with assistance from OpenAI Codex; the source reproductions and validation described above were executed locally.