Cortex-M backend: lower quantized GELU via the activation LUT (pytorch#21025)

### Summary
Extend the existing sigmoid/tanh/silu activation-LUT path to GELU: add
an exact (erf) _gelu to _ACTIVATION_FNS, register aten.gelu in the
quantizer's ACTIVATION_OP_PATTERNS (the generic CortexMActivationCheck
needs no change), and add aten.gelu to the quantized_activation dialect
substitution. Unlike silu, aten.gelu is a core-aten op that survives
to_edge unchanged, so no to_edge preservation is required.
build_activation_lut only sees the op target, so the table is always the
exact/erf GELU regardless of the approximate kwarg.

### Test plan
Verified test-first (RED->GREEN) with five nn.GELU() dialect cases (ramp
/ saturating / asymmetric-zp / zero) whose numerics are validated
against the reference (qtol=1); the full cortex_m op dialect suite still
passes (177 passed).

Authored with Claude Code.

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

Author: rascani

backends/cortex_m/passes/aten_to_cortex_m_pass.py

@@ -304,6 +304,7 @@ def _has_qparams(node: Node) -> bool:
 @AtenToCortexMPass.register_dialect_substitution(exir_ops.edge.aten.sigmoid.default)
 @AtenToCortexMPass.register_dialect_substitution(exir_ops.edge.aten.tanh.default)
 @AtenToCortexMPass.register_dialect_substitution(exir_ops.edge.aten.silu.default)
+@AtenToCortexMPass.register_dialect_substitution(exir_ops.edge.aten.gelu.default)
 def _get_activation_replacement(
     node: Node, dialect_pass: AtenToDialectPass
 ) -> DialectNodeSpec | None:

backends/cortex_m/passes/passes_utils.py

@@ -204,10 +204,15 @@ def _stable_silu(x: float) -> float:
     return x * _stable_sigmoid(x)
 
 
+def _gelu(x: float) -> float:
+    return 0.5 * x * (1.0 + math.erf(x / math.sqrt(2.0)))
+
+
 _ACTIVATION_FNS = {
     exir_ops.edge.aten.sigmoid.default: _stable_sigmoid,
     exir_ops.edge.aten.tanh.default: math.tanh,
     exir_ops.edge.aten.silu.default: _stable_silu,
+    exir_ops.edge.aten.gelu.default: _gelu,
 }
 
 

backends/cortex_m/quantizer/quantizer_support.py

@@ -124,6 +124,7 @@
     (torch.ops.aten.sigmoid.default,): CortexMActivationCheck,
     (torch.ops.aten.tanh.default,): CortexMActivationCheck,
     (torch.ops.aten.silu.default,): CortexMActivationCheck,
+    (torch.ops.aten.gelu.default,): CortexMActivationCheck,
 }
 
 POOL_OP_PATTERNS = {

backends/cortex_m/test/ops/test_activation_quant.py

@@ -61,6 +61,24 @@ def forward(self, x):
         return torch.nn.functional.silu(x)
 
 
+class _GELU(torch.nn.Module):
+    ops_before_transforms = {
+        **_OPS_BEFORE,
+        "executorch_exir_dialects_edge__ops_aten_gelu_default": 1,
+    }
+    ops_after_transforms = {
+        **_OPS_AFTER,
+        "executorch_exir_dialects_edge__ops_aten_gelu_default": 0,
+    }
+
+    def __init__(self):
+        super().__init__()
+        self.gelu = torch.nn.GELU()  # default: exact / erf
+
+    def forward(self, x):
+        return self.gelu(x)
+
+
 import torch as _torch
 
 
@@ -133,6 +151,26 @@ def _zero_input(shape):
         model=_SiLU(),
         example_inputs=(_zero_input((16,)),),
     ),
+    "gelu_rank1": McuTestCase(
+        model=_GELU(),
+        example_inputs=(ramp_tensor(-6, 6, (16,)),),
+    ),
+    "gelu_rank4": McuTestCase(
+        model=_GELU(),
+        example_inputs=(ramp_tensor(-4, 4, (1, 8, 4, 4)),),
+    ),
+    "gelu_saturating": McuTestCase(
+        model=_GELU(),
+        example_inputs=(ramp_tensor(-50, 50, (32,)),),
+    ),
+    "gelu_asymmetric_zp": McuTestCase(
+        model=_GELU(),
+        example_inputs=(ramp_tensor(-1, 9, (16,)),),
+    ),
+    "gelu_zero": McuTestCase(
+        model=_GELU(),
+        example_inputs=(_zero_input((16,)),),
+    ),
 }