[quant] Implement forward and backward autograd functions for fake quantize (#81438)

### Summary:
This PR implements custom autograd functions for forward and backward to be used in APoT fake quantization. The implementation follows this doc about custom autograd functions: https://pytorch.org/tutorials/beginner/examples_autograd/polynomial_custom_function.html

### Test Plan:
Run tests with: `python test/quantization/core/experimental/test_fake_quantize.py`
Pull Request resolved: https://github.com/pytorch/pytorch/pull/81438
Approved by: https://github.com/jerryzh168

mypy.ini

@@ -70,6 +70,9 @@ ignore_missing_imports = True
 [mypy-torch.ao.quantization.experimental.APoT_tensor]
 ignore_missing_imports = True
 
+[mypy-torch.ao.quantization.experimental.fake_quantize_function]
+ignore_missing_imports = True
+
 #
 # Files with various errors. Mostly real errors, possibly some false
 # positives as well.

test/quantization/core/experimental/test_fake_quantize.py

@@ -5,6 +5,10 @@ import unittest
 from torch.ao.quantization.experimental.observer import APoTObserver
 from torch.ao.quantization.experimental.quantizer import quantize_APoT, dequantize_APoT
 from torch.ao.quantization.experimental.fake_quantize import APoTFakeQuantize
+from torch.ao.quantization.experimental.fake_quantize_function import fake_quantize_function
+forward_helper = fake_quantize_function.forward
+backward = fake_quantize_function.backward
+from torch.autograd import gradcheck
 
 class TestFakeQuantize(unittest.TestCase):
     r""" Tests fake quantize calculate_qparams() method
@@ -72,5 +76,17 @@ class TestFakeQuantize(unittest.TestCase):
         with self.assertRaises(Exception):
             apot_fake.forward(torch.clone(X), False)
 
+    r""" Tests fake quantize helper backward() method
+         using torch.autograd.gradcheck function.
+    """
+    def test_backward(self):
+        input = torch.randn(20, dtype=torch.double, requires_grad=True)
+
+        observer = APoTObserver(b=4, k=2)
+        observer(input)
+        alpha, gamma, quantization_levels, level_indices = observer.calculate_qparams(signed=False)
+
+        test = gradcheck(fake_quantize_function.apply, (input, alpha, gamma, quantization_levels, level_indices), atol=1e-4)
+
 if __name__ == '__main__':
     unittest.main()

torch/ao/quantization/experimental/fake_quantize.py

@@ -1,8 +1,8 @@
 import torch
 from torch import Tensor
 from torch.ao.quantization.experimental.observer import APoTObserver
-from torch.ao.quantization.experimental.quantizer import quantize_APoT, dequantize_APoT
 from torch.ao.quantization.fake_quantize import FakeQuantizeBase
+from torch.ao.quantization.experimental.fake_quantize_function import fake_quantize_function
 
 class APoTFakeQuantize(FakeQuantizeBase):
     alpha: Tensor
@@ -28,7 +28,6 @@ class APoTFakeQuantize(FakeQuantizeBase):
                     and self.quantization_levels is not None
                     and self.level_indices is not None), "Must set qparams for fake quant"
 
-            X = quantize_APoT(X, self.alpha, self.gamma, self.quantization_levels, self.level_indices)
-            X = dequantize_APoT(X)
+            X = fake_quantize_function.apply(X, self.alpha, self.gamma, self.quantization_levels, self.level_indices)
 
         return X

torch/ao/quantization/experimental/fake_quantize_function.py

@@ -0,0 +1,27 @@
+import torch
+from torch import Tensor
+from torch.ao.quantization.experimental.quantizer import quantize_APoT, dequantize_APoT
+
+class fake_quantize_function(torch.autograd.Function):
+    @staticmethod
+    def forward(ctx,  # type: ignore[override]
+                x: Tensor,
+                alpha: Tensor,
+                gamma: Tensor,
+                quantization_levels: Tensor,
+                level_indices: Tensor) -> Tensor:
+        quantized_result = quantize_APoT(x, alpha, gamma, quantization_levels, level_indices)
+
+        # calculate mask tensor
+        mask = x.detach().apply_(lambda x: (x <= alpha and x >= -alpha))
+
+        result = dequantize_APoT(quantized_result)
+
+        ctx.save_for_backward(mask)
+
+        return result
+
+    @staticmethod
+    def backward(ctx, grad_output: Tensor) -> Tensor:  # type: ignore[override]
+        mask = ctx.saved_tensors
+        return grad_output * mask

torch/ao/quantization/experimental/quantizer.py

@@ -1,5 +1,6 @@
 import torch
 from torch import Tensor
+import numpy as np
 from torch.ao.quantization.experimental.apot_utils import float_to_apot, apot_to_float
 
 # class to store APoT quantizer and
@@ -33,10 +34,13 @@ class APoTQuantizer():
         result = torch.tensor([])
 
         # map float_to_apot over tensor2quantize elements
-        tensor2quantize = tensor2quantize.apply_(lambda x: float_to_apot(x,
-                                                                         self.quantization_levels,
-                                                                         self.level_indices,
-                                                                         self.alpha))
+        tensor2quantize = tensor2quantize.detach().apply_(lambda x: float_to_apot(x,
+                                                                                  self.quantization_levels,
+                                                                                  self.level_indices,
+                                                                                  self.alpha))
+
+        # convert to APoT int representation for dtype
+        tensor2quantize = tensor2quantize.int()
 
         from torch.ao.quantization.experimental.APoT_tensor import TensorAPoT
 
@@ -56,7 +60,12 @@ class APoTQuantizer():
         apot_tensor_data = apot_tensor.data
 
         # map apot_to_float over tensor2quantize elements
-        result = apot_tensor_data.apply_(lambda x: float(apot_to_float(x, self.quantization_levels, self.level_indices)))
+        result_temp = np.empty(apot_tensor_data.size())
+        for ele in apot_tensor_data:
+            new_ele = apot_to_float(ele, self.quantization_levels, self.level_indices)
+            np.append(result_temp, new_ele)
+
+        result = torch.from_numpy(result_temp).int()
 
         return result