Execution Capability Matrix

The executable source of truth is tide.core.backends.backend_capabilities(). The table below mirrors the current rows. A new combination is supported only after code, capability selection, numerical tests, and public documentation agree.

Operation vocabulary

Operation	Meaning
forward	Nonlinear propagation $F(m)$
jvp	Tangent action $J(m)v$
vjp	Adjoint action $J(m)^\top r$
second_vjp	Nonlinear second-order action $(DJ(m)[v])^\top r$

forward and vjp share capability rows because standard reverse-mode differentiation begins with the stored or recomputed forward trajectory.

Stable rows

All rows support CPU and CUDA devices, float32 and float64 dtypes, subject to native library availability on the selected machine.

Backend	Dimension	Operations	Storage modes	Gradient targets	Callbacks	Reusable background
Reference	TM2D	forward, vjp	auto, device, CPU, disk, none	epsilon, sigma, mu, perturbation, source, state	yes	no
Reference	TM2D	jvp	auto, device, CPU, disk, none	epsilon, sigma, mu, perturbation, source, state	no	no
Reference	TM2D	second_vjp	device, CPU, disk	epsilon, sigma, mu, perturbation, source, state	no	no
Reference	EM3D	forward, vjp	auto, device, CPU, disk, none	epsilon, sigma, mu, perturbation, source, state	yes	no
Reference	EM3D	jvp	device, none	epsilon, sigma, mu, perturbation, source, state	no	no
Reference	EM3D	second_vjp	device	epsilon, sigma, mu, perturbation, source, state	no	no
Native	TM2D	forward, vjp	auto, device, CPU, disk, none	epsilon, sigma, source	yes	no
Native	TM2D	jvp	auto, device, CPU, disk, none	epsilon, sigma, perturbation	no	yes
Native	TM2D	second_vjp	device, CPU, disk	epsilon, sigma	no	no
Native	EM3D	forward, vjp	auto, device, CPU, disk, none	epsilon, sigma, source	yes	no
Native	EM3D	jvp	device, none	epsilon, sigma, perturbation	no	no
Native	EM3D	second_vjp	device	epsilon, sigma	no	no

Gradient targets

• epsilon, sigma, and mu refer to background material tensors.
• perturbation refers to EMDirection fields used by JVP and differentiated tangent workflows.
• source refers to source-amplitude samples.
• state refers to initial field or derivative-state tensors.

A capability row lists the largest target set that the backend family can accept. Individual physics adapters may impose a narrower operation-specific rule. For example, TM2D JVP does not currently accept a mu direction.

Storage interpretation

Storage cells describe accepted public policy for that operation:

• auto resolves from configured device and host byte limits.
• device stores eligible trajectory state on the compute device.
• cpu stores on the host.
• disk stores below the configured path.
• none avoids snapshot allocation where the operation permits it.

Native EM3D JVP accepts device or no snapshot storage. Native EM3D second VJP requires device storage. Reference capability is not universally broader: it intentionally follows the same EM3D derivative storage boundaries for operations that lack another implemented path.

Fallback behavior

Backend selection evaluates the complete plan. A request can be rejected because of operation, gradient target, storage, callbacks, device, dtype, dispersion, batched-model layout, or native availability.

• FallbackPolicy.ERROR raises with the unsupported reason.
• FallbackPolicy.REFERENCE selects the reference backend only if a reference row covers the full request.
• BackendPreference.NATIVE combined with error fallback is the appropriate choice when benchmarking native execution.

No solver adapter should invent a fallback after the central decision.

Runtime-only checks

The matrix captures stable declarative capability. Some conditions remain dependent on the loaded binary or runtime object:

• Required native ABI symbol exists.
• CUDA architecture is compatible with the built library.
• Tensor layout is contiguous where the ABI requires it.
• Dispersion and snapshot representation are compatible.
• torch.func transform state can use the selected adapter.

These checks must honor the same fallback policy and report a descriptive reason.

Querying the live matrix

import tide
from tide.core.backends import backend_capabilities

for preference in (
    tide.BackendPreference.REFERENCE,
    tide.BackendPreference.NATIVE,
):
    print(preference.value)
    for row in backend_capabilities(preference).matrix:
        print(row)

When this output and the rendered table disagree, treat the Python output as authoritative and update the documentation in the same change.