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ecc81b3 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 | """The kernel family: per-axis attention contracted across the lattice.
Where :class:`~torch_dimensions.AxialScan` sweeps a 1-D mixer along one axis
per layer, this builds an explicit ``(A, A)`` operator per axis and contracts
them all every layer — the factorized joint operator is a Kronecker product,
which is what keeps cost quadratic in axial size rather than in cell count.
Two variants, differing in where the kernel comes from:
- **axial attention** (``per_line=True``): scores are computed per line, so
every row of the fold gets its own attention pattern.
- **CaFA** (``per_line=False``): features are pooled over the *other* spatial
axes first, giving one kernel per axis per (batch, timestep) — the
factorized-attention construction, cheaper and more structured.
The hybrid form: on a lattice with a time axis, the kernels own the spatial
axes and the model's 1-D mixer runs along time, each layer. This is why
``td.LSTM(nd_method=td.cafa)`` is meaningful — CaFA never consumes the LSTM,
it handles the axes the LSTM does not. Pooling (CaFA) deliberately keeps the
time dimension unpooled so the kernel at time ``t`` sees only time ``t``:
causality along time is the mixer's property and must not leak away through a
pooled kernel.
Scores carry a learnable relative-position bias per axis (spatial axes have
static sizes, so the table is well-defined); gating is ``"softmax"`` or
``"leaky_relu"`` (the CaFA paper's default). Sparse lattices are handled by
:func:`~torch_dimensions.axial_contract`'s per-line renormalization — for a
softmax kernel that renormalization *is* masked softmax, and for a signed
gate the relative cancellation guard applies.
"""
from __future__ import annotations
import math
from collections.abc import Callable
import torch
import torch.nn as nn
import torch.nn.functional as F
from torch_dimensions.compose.kernel import axial_contract
from torch_dimensions.compose.scan import axial_apply
from torch_dimensions.lattice import Lattice
from torch_dimensions.plan import ScanPlan
__all__ = ["AxialKernel"]
_GATES = ("softmax", "leaky_relu")
class AxialKernel(nn.Module):
"""Kernel-family block: per-axis attention over the lattice, optional
mixer along time. See the module docstring.
Args:
mixer: zero-arg factory (or module) for the per-layer *time* mixer.
Requires the lattice to have a time axis — on a purely spatial
lattice the kernels are the whole model and a mixer would be
silently dead weight, which is refused rather than allowed.
Pass ``None`` for a kernel-only block.
plan: depth and axis coverage. Each layer contracts every *spatial*
axis the plan mentions, in the plan's first-appearance order;
an axis the plan never names is never contracted (and
``plan.resolve`` warns, same as the scan family).
per_line: per-line scores (axial attention) vs pooled per-axis
kernels (CaFA).
gate: ``"softmax"`` or ``"leaky_relu"``.
qk_norm: RMS-normalize the query and key before their product. Costs
nothing and stops the scores' scale drifting with feature norm,
which is why the CaFA reference implementation offers it.
kernel_residual: add a learnable ``gamma * I`` to the kernel *before*
the gate, so a contraction starts near "keep your own value" and
has to learn to mix. Taken from CaFA's ``LowRankKernel``, where it
is on by default; here it is off by default so existing models are
unchanged. ``gamma`` initializes to ``1/sqrt(d_model)``, as theirs
does.
Two options CaFA has that this does *not* copy: rotary position embedding
on the query and key (this uses a learned relative-position bias table
instead) and their spherical quadrature weights, which are a property of
the sphere rather than of the method.
"""
def __init__(
self,
mixer: Callable[[], nn.Module] | nn.Module | None,
plan: ScanPlan,
lattice: Lattice,
d_model: int,
*,
per_line: bool = True,
gate: str = "softmax",
qk_norm: bool = False,
kernel_residual: bool = False,
dropout: float = 0.0,
norm: bool = True,
residual: bool = True,
chunk: int | None = None,
) -> None:
super().__init__()
if gate not in _GATES:
raise ValueError(f"gate must be one of {_GATES}; got {gate!r}")
self.lattice = lattice
self.plan = plan.resolve(lattice)
self.d_model = d_model
self.per_line = per_line
self.gate = gate
self.qk_norm = qk_norm
self.kernel_residual = kernel_residual
self.residual = residual
self.chunk = chunk
time_index = 0 if lattice.time else None
self.spatial_axes = [int(a) for a in self.plan.axes if a != time_index]
if not self.spatial_axes:
raise ValueError("the kernel family needs at least one spatial axis in the plan")
n = len(self.plan)
h = d_model
# Flat (layer, axis) indexing — layer * n_axes + j — keeps every
# per-axis module addressable without nested ModuleLists.
n_ax = len(self.spatial_axes)
self.q = nn.ModuleList(nn.Linear(h, h, bias=False) for _ in range(n * n_ax))
self.k = nn.ModuleList(nn.Linear(h, h, bias=False) for _ in range(n * n_ax))
sizes = [lattice.axis_size(a) for a in self.spatial_axes]
self.bias = nn.ParameterList(
nn.Parameter(torch.zeros(a, a)) for _ in range(n) for a in sizes
)
# One gamma per (layer, axis), like the per-axis kernels it scales.
# Initialized to 1/sqrt(d_model) — CaFA's value.
self.gamma = (
nn.ParameterList(nn.Parameter(torch.tensor(h**-0.5)) for _ in range(n * n_ax))
if kernel_residual
else None
)
self.out = nn.ModuleList(nn.Linear(h, h) for _ in range(n))
self.norms = nn.ModuleList(nn.LayerNorm(h) for _ in range(n)) if norm else None
self.drop = nn.Dropout(dropout)
if lattice.time:
if mixer is None:
self.mixers = None
elif isinstance(mixer, nn.Module):
self.mixers = nn.ModuleList([mixer] * n) # shared, as in AxialScan
else:
self.mixers = nn.ModuleList([mixer() for _ in range(n)])
self.time_norms = (
nn.ModuleList(nn.LayerNorm(h) for _ in range(n))
if norm and self.mixers is not None
else None
)
else:
if mixer is not None:
raise ValueError(
"a mixer was given but the lattice has no time axis for it to sweep; "
"the kernel family owns every spatial axis, so the mixer would be dead "
"weight. Use a lattice with time=True (the hybrid form) or mixer=None."
)
self.mixers = None
self.time_norms = None
if not lattice.is_dense:
self.register_buffer("cell_mask", lattice.mask(torch.bool), persistent=False)
else:
self.cell_mask = None
def _masked(self, x: torch.Tensor) -> torch.Tensor:
if self.cell_mask is None:
return x
return x * self.cell_mask.to(x.dtype)
def _qk_norm(self, x: torch.Tensor) -> torch.Tensor:
"""RMS-normalize the last dimension, or pass through.
No learnable scale: the score already has one in `scale`, and a second
would be the same parameter twice.
"""
if not self.qk_norm:
return x
return x * torch.rsqrt(x.pow(2).mean(-1, keepdim=True) + 1e-6)
def _kernel(self, layer: int, j: int, axis: int, h: torch.Tensor) -> torch.Tensor:
"""Build the ``(M, A, A)`` operator for one axis of one layer."""
lat = self.lattice
scale = 1.0 / math.sqrt(self.d_model)
idx = layer * len(self.spatial_axes) + j
bias = self.bias[idx]
if self.per_line:
seq, _ = lat.to_sequence(h, axis) # (M, A, H)
q = self._qk_norm(self.q[idx](seq))
k = self._qk_norm(self.k[idx](seq))
scores = q @ k.transpose(1, 2) * scale + bias
else:
# Pool over the *other spatial* axes only. Batch stays batch, and
# time deliberately stays unpooled: a kernel at time t built from
# future timesteps would leak the future into a "causal" model.
d = lat.tensor_dim(axis)
keep = {0, d, h.ndim - 1}
if lat.time:
keep.add(1)
reduce_dims = tuple(i for i in range(h.ndim) if i not in keep)
counts = lat.valid_counts(axis).to(h.dtype).to(h.device)
pooled = h.sum(reduce_dims) if reduce_dims else h # (B, [T,] A, H)
pooled = pooled / counts.unsqueeze(-1)
q = self._qk_norm(self.q[idx](pooled))
k = self._qk_norm(self.k[idx](pooled))
scores = q @ k.transpose(-1, -2) * scale + bias # (B, [T,] A, A)
a = scores.shape[-1]
# Expand to one kernel per folded line. The fold orders leading
# dims as (B, [T,] *others), batch-major, so lines sharing a
# (batch, timestep) are contiguous.
lines_per = 1
for i in range(1, h.ndim - 1):
if i != d:
lines_per *= h.shape[i]
if lat.time:
lines_per //= h.shape[1]
scores = scores.reshape(-1, 1, a, a).expand(-1, lines_per, a, a)
else:
scores = scores.reshape(-1, 1, a, a).expand(-1, lines_per, a, a)
scores = scores.reshape(-1, a, a)
if self.gamma is not None:
# `gamma * I`, added before the gate exactly as CaFA does — after
# the gate it would be a different model, since softmax is not
# additive. A contraction therefore starts near the identity and
# has to learn to mix, rather than starting fully mixed.
eye = torch.eye(scores.shape[-1], device=scores.device, dtype=scores.dtype)
scores = scores + self.gamma[idx] * eye
if self.gate == "softmax":
return F.softmax(scores, dim=-1)
return F.leaky_relu(scores)
def forward(self, x: torch.Tensor) -> torch.Tensor:
if x.shape[-1] != self.d_model:
raise ValueError(f"expected {self.d_model} features, got {x.shape[-1]}")
x = self._masked(x)
valid = None if self.cell_mask is None else self.cell_mask.to(x.dtype)
for i in range(len(self.plan)):
h = self.norms[i](x) if self.norms is not None else x
for j, axis in enumerate(self.spatial_axes):
kernel = self._kernel(i, j, axis, h)
h = axial_contract(h, self.lattice, axis, kernel, valid=valid)
h = self.out[i](h)
x = x + self.drop(h) if self.residual else self.drop(h)
x = self._masked(x)
if self.mixers is not None:
h = self.time_norms[i](x) if self.time_norms is not None else x
h = axial_apply(h, self.lattice, 0, self.mixers[i], chunk=self.chunk)
x = x + self.drop(h)
x = self._masked(x)
return x
def extra_repr(self) -> str:
kind = "per-line" if self.per_line else "pooled (CaFA)"
return f"d_model={self.d_model}, {kind}, gate={self.gate}, lattice={self.lattice}"
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