Native hooks for Fourier transforms and diagonal scans

CPU execution declines these hooks before recording anything, allowing the generic differentiable program to run on its ordinary operations. CUDA execution validates reference identities, selects the corresponding backend capsule, and records a native node. This keeps provider selection and cross-session checks on the same path as the other eager operations.

def Runtime.Autograd.Torch.Internal.EagerSession.spectralNative? {α : Type} [TorchLean.Storage α] {shape : Spec.Shape} (s : EagerSession α) (op : NN.Backend.BackendOp) (refs : Array (Option RefIdentity)) (record : Cuda.Tape → Result (Cuda.Tape × ℕ)) : IO (Option (TensorRef α shape))

Run a native tape constructor only for a CUDA session, preserving its reference identity.

def Runtime.Autograd.Torch.Internal.EagerSession.rfft1dNative? {α : Type} [TorchLean.Storage α] (s : EagerSession α) {batch n : ℕ} (x : TensorRef α [batch, n]) : IO (Option (TensorRef α [batch, n / 2 + 1, 2]))

Native real-transform hook; CPU interpreters use the generic matrix reference.

def Runtime.Autograd.Torch.Internal.EagerSession.irfft1dNative? {α : Type} [TorchLean.Storage α] (s : EagerSession α) {batch n : ℕ} (x : TensorRef α [batch, n / 2 + 1, 2]) : IO (Option (TensorRef α [batch, n]))

Native normalized inverse hook with explicit output length.

def Runtime.Autograd.Torch.Internal.EagerSession.selectiveScanDiagNative? {α : Type} [TorchLean.Storage α] (s : EagerSession α) {seqLen state : ℕ} (a b : TensorRef α [state]) (x : TensorRef α [seqLen, state]) (initial : TensorRef α [state]) : IO (Option (TensorRef α [seqLen, state]))

Native shared-coefficient scan hook with gradients for coefficients, input, and state.

def Runtime.Autograd.Torch.Internal.EagerSession.selectiveScanDiagVarNative? {α : Type} [TorchLean.Storage α] (s : EagerSession α) {seqLen state : ℕ} (a b x : TensorRef α [seqLen, state]) (initial : TensorRef α [state]) : IO (Option (TensorRef α [seqLen, state]))

Native token-dependent scan hook, including coefficient and continuation-state gradients.

def Runtime.Autograd.Torch.Internal.EagerSession.spectralConv1dRfftNative? {α : Type} [TorchLean.Storage α] (s : EagerSession α) {grid width modes : ℕ} (x : TensorRef α [grid, width]) (realWeight imagWeight : TensorRef α [modes, width, width]) : IO (Option (TensorRef α [grid, width]))

Native one-sided spectral convolution with the same parameter layout as its reference.