Semantic port of mar-yan24's mark/autodifferentiation2 (131 commits
behind) onto the rebased autodiff branch. Preserves the design intact:

- solver_implicit_adjoint: tape-backward hook solving H v = adj_qacc
  with the retained Newton Hessian, writing adj_qacc_smooth = M v
- GPU tile-Cholesky adjoint paths (small-nv single tile, blocked
  solve-only with stored factor, blocked full factorize+solve)
- Data.solver_h / solver_hfactor / solver_Jaref retained state,
  allocated in make_data/put_data, aliased by the solver context

Adaptations to current main:
- create_blocked_cholesky_func no longer exists upstream (replaced by
  fused create_blocked_cholesky_factorize_solve_func in 083e5ef);
  _adjoint_cholesky_full_blocked uses the fused func
- dropped his update_constraint_gauss_cost kernel (belonged to the
  pre-google-deepmind#1301 solver context which carried ctx.cost; current main computes
  gauss cost inside the linesearch tiles)
- dropped his support.py next_act removal (current main's derivative.py
  imports it)
- solver retained fields placed at the end of Data (types_test enforces
  warp-only fields after MuJoCo fields, with matching docstring order)
- test_solver_retained_state used an undefined SPARSE_CONSTRAINT_JACOBIAN
  global; replaced with m.is_sparse

Verification: full suite 1078 passed / 23 skipped, including his 4
GradSolverAdjointTest cases. Cross-validated independently: the GPU
adjoint mapped to force space (M^-1 M H^-1 g) matches central finite
differences through the full GPU solver to 8e-5 max relative error on
a persistent-contact scene.

Signed-off-by: johnnynunez <johnnynuca14@gmail.com>

Co-authored-by: Mark Yang <markyang2005@gmail.com>

Semantic port of mar-yan24's mark/autodifferentiation3 (123 commits
behind) onto the 2/3 port. Preserves the design intact:

- collision_smooth.py: smooth analytic distance functions overwrite
  discrete contact geometry (dist/pos/frame) during taped forwards;
  differentiable constraint assembly (smooth_contact_to_efc) recomputes
  efc.J/efc.pos on an AD-visible path. Plane-sphere, sphere-sphere,
  sphere-capsule, capsule-capsule, plane-capsule supported; other geom
  pairs pass through with zero gradient.
- adjoint.py: efc-level adjoint kernels (_efc_J_grad_kernel,
  _efc_pos_grad_kernel) connecting the phase-2 KKT adjoint to contact
  geometry; smooth/surrogate friction adjoint variants.
- forward.py: tape-aware Phase 3 hooks after collision and
  make_constraint; _record_solver_adjoint/_record_fwd_accel_adjoint/
  _record_euler_damp_adjoint tape callbacks; _isolate_intermediates_for_ad
  per-substep array isolation; freejoint zerograd fix (is_free flag
  instead of continue) was already present upstream.
- grad.py: COLLISION_GRAD_FIELDS registry + dotted-path _resolve_field.

Adaptations to current main:
- _record_euler_damp_adjoint captures damp_deriv (polynomial damping,
  computed from the substep's qvel at record time) instead of the old
  constant dof_damping, matching the forward euler solve; sparse kernel
  call updated to the M_rownnz/M_rowadr signature
- _qfrc_smooth factory kernel re-enabled for backward (pure elementwise
  sum; main had enable_backward=False which severed the qfrc_smooth ->
  qfrc_actuator/ctrl gradient chain)
- jac_dof calls updated for the body_isdofancestor parameter
- _solve_LD_sparse: kept main's fused fast path for non-grad solves,
  adopted the nograd-copy + manual-adjoint design for grad solves
- warmstart copy uses d.qacc (solver solution) not integrator-local qacc,
  restoring upstream/sleep semantics; sleep.wake retained in forward()
- step-level xpos-loss tests refresh kinematics inside the tape (step()
  does not recompute xpos post-integration; FD agrees it would otherwise
  be identically zero) and the nonzero-gradient guard is scaled by the
  FD norm (single-step dL/dctrl ~ dt^2 ~ 2e-7 < the old 1e-6 threshold)
- d.qM -> d.M renames; dropped stale pre-google-deepmind#1301 hunks (gauss_cost kernel,
  old next_act relocation, old collision_flex/passive/types drift)

Verification: full suite 1093 passed / 23 skipped, including all 29
grad tests (solver adjoint, euler damp stress, smooth contact, friction
surrogate, freejoint kinematics).

Signed-off-by: johnnynunez <johnnynuca14@gmail.com>

…signment

Semantic re-implementation of mar-yan24's count->scan->emit pipeline
(google-deepmind#1300) on top of the post-a23500c constraint
kernels, since the original branch predates the efc_contact rewrite and
95 other upstream commits and cannot be rebased mechanically.

When opt.deterministic=True, the racy wp.atomic_add(nefc/efc_nnz) slot
allocation in every constraint family is replaced with: a count kernel
that writes per-thread row/nnz counts, a per-world exclusive scan that
converts counts to offsets and bumps the totals, and emit kernels that
read base+offset instead of atomic results. Constraint rows therefore
land at identical positions on every run of the same input.

Differences from the original google-deepmind#1300 branch:
- Contact families use a single _efc_contact_count kernel mirroring the
  unified _efc_contact_init (upstream a23500c replaced the per-cone
  _contact_pyramidal/_contact_elliptic kernels this no longer touches).
- _equality_flex_count honors eq_active (upstream 80bbba7).
- All new kernel factories are wrapped in @cache_kernel (upstream
  f0e2d81) so repeated step() calls do not recreate kernels.
- Host-side overflow validation is skipped while a CUDA graph capture is
  active, making opt.deterministic capture-safe (the original branch
  documented capture as unsupported).
- Ports the expanded determinism regression tests, minus the benchmark
  coverage that targeted the pre-google-deepmind#1301 benchmark API.

Verified: full suite 1101 passed / 23 skipped; constraint rows (nefc,
efc.type/id, sparse J structure and values) bitwise stable across
same-process trials with CUDA graph capture; ~9% overhead at 1 world,
~24% at 256 worlds on RTX PRO 6000 Blackwell.

Signed-off-by: johnnynunez <johnnynuca14@gmail.com>

Co-authored-by: Mark Yang <markyang2005@gmail.com>

Semantic port of mar-yan24's mark/autodifferentiation3 (123 commits
behind) onto the 2/3 port. Preserves the design intact:

- collision_smooth.py: smooth analytic distance functions overwrite
  discrete contact geometry (dist/pos/frame) during taped forwards;
  differentiable constraint assembly (smooth_contact_to_efc) recomputes
  efc.J/efc.pos on an AD-visible path. Plane-sphere, sphere-sphere,
  sphere-capsule, capsule-capsule, plane-capsule supported; other geom
  pairs pass through with zero gradient.
- adjoint.py: efc-level adjoint kernels (_efc_J_grad_kernel,
  _efc_pos_grad_kernel) connecting the phase-2 KKT adjoint to contact
  geometry; smooth/surrogate friction adjoint variants.
- forward.py: tape-aware Phase 3 hooks after collision and
  make_constraint; _record_solver_adjoint/_record_fwd_accel_adjoint/
  _record_euler_damp_adjoint tape callbacks; _isolate_intermediates_for_ad
  per-substep array isolation; freejoint zerograd fix (is_free flag
  instead of continue) was already present upstream.
- grad.py: COLLISION_GRAD_FIELDS registry + dotted-path _resolve_field.

Adaptations to current main:
- _record_euler_damp_adjoint captures damp_deriv (polynomial damping,
  computed from the substep's qvel at record time) instead of the old
  constant dof_damping, matching the forward euler solve; sparse kernel
  call updated to the M_rownnz/M_rowadr signature
- _qfrc_smooth factory kernel re-enabled for backward (pure elementwise
  sum; main had enable_backward=False which severed the qfrc_smooth ->
  qfrc_actuator/ctrl gradient chain)
- jac_dof calls updated for the body_isdofancestor parameter
- _solve_LD_sparse: kept main's fused fast path for non-grad solves,
  adopted the nograd-copy + manual-adjoint design for grad solves
- warmstart copy uses d.qacc (solver solution) not integrator-local qacc,
  restoring upstream/sleep semantics; sleep.wake retained in forward()
- step-level xpos-loss tests refresh kinematics inside the tape (step()
  does not recompute xpos post-integration; FD agrees it would otherwise
  be identically zero) and the nonzero-gradient guard is scaled by the
  FD norm (single-step dL/dctrl ~ dt^2 ~ 2e-7 < the old 1e-6 threshold)
- d.qM -> d.M renames; dropped stale pre-google-deepmind#1301 hunks (gauss_cost kernel,
  old next_act relocation, old collision_flex/passive/types drift)

Verification: full suite 1093 passed / 23 skipped, including all 29
grad tests (solver adjoint, euler damp stress, smooth contact, friction
surrogate, freejoint kinematics).

Signed-off-by: johnnynunez <johnnynuca14@gmail.com>

Co-authored-by: Mark Yang <markyang2005@gmail.com>