4-bit subtractor threshold circuit, magnitude 88

README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- arithmetic
+---
+
+# threshold-subtractor4bit
+
+4-bit subtractor. Computes A - B (modulo 16) with borrow output.
+
+## Function
+
+subtractor4bit(A, B) = (A - B) mod 16, borrow_out
+
+## Truth Table (selected rows)
+
+| A | B | Diff | Borrow |
+|---|---|------|--------|
+| 7 | 3 | 4 | 0 |
+| 5 | 5 | 0 | 0 |
+| 3 | 7 | 12 | 1 |
+| 0 | 1 | 15 | 1 |
+
+## Architecture
+
+Ripple-borrow subtractor using full subtractor units.
+
+For each bit i:
+- diff_i = a_i XOR b_i XOR borrow_{i-1}
+- borrow_i = majority(NOT(a_i), b_i, borrow_{i-1})
+
+The borrow signal indicates A < B (unsigned comparison).
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 8 (a3-a0, b3-b0) |
+| Outputs | 5 (d3-d0, bout) |
+| Neurons | 25 |
+| Layers | 8 |
+| Parameters | 86 |
+| Magnitude | 88 |
+
+## Usage
+
+```python
+from safetensors.torch import load_file
+# See model.py for full implementation
+
+# 7 - 3 = 4
+# subtractor4(0,1,1,1, 0,0,1,1) = [0,1,0,0, 0]
+
+# 3 - 7 = 12 (wraps), borrow=1
+# subtractor4(0,0,1,1, 0,1,1,1) = [1,1,0,0, 1]
+```
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-subtractor4bit",
+  "description": "4-bit subtractor (A - B mod 16)",
+  "inputs": 8,
+  "outputs": 5,
+  "neurons": 25,
+  "layers": 8,
+  "parameters": 88
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# 4-bit subtractor: A - B (mod 16)
+# Input: [a3, a2, a1, a0, b3, b2, b1, b0]
+# Output: [d3, d2, d1, d0, bout] where bout is final borrow
+
+# For each bit i:
+#   diff_i = a_i XOR b_i XOR bout_{i-1}
+#   bout_i = majority(NOT(a_i), b_i, bout_{i-1}) = (b_i + bout_{i-1} > a_i)
+#          = threshold with weights [-1, 1, 1] on [a_i, b_i, bout_{i-1}], bias -1
+
+# Bit 0 (no borrow in):
+#   d0 = a0 XOR b0
+#   bout0 = NOT(a0) AND b0 = threshold([-1, 1], -1) on [a0, b0]
+
+# XOR components for d0: OR and NAND on [a0, b0]
+weights['d0_or.weight'] = torch.tensor([[0., 0., 0., 1., 0., 0., 0., 1.]], dtype=torch.float32)
+weights['d0_or.bias'] = torch.tensor([-1.], dtype=torch.float32)
+weights['d0_nand.weight'] = torch.tensor([[0., 0., 0., -1., 0., 0., 0., -1.]], dtype=torch.float32)
+weights['d0_nand.bias'] = torch.tensor([1.], dtype=torch.float32)
+
+# bout0 = NOT(a0) AND b0
+weights['bout0.weight'] = torch.tensor([[0., 0., 0., -1., 0., 0., 0., 1.]], dtype=torch.float32)
+weights['bout0.bias'] = torch.tensor([-1.], dtype=torch.float32)
+
+# d0 = AND(d0_or, d0_nand)
+weights['d0.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['d0.bias'] = torch.tensor([-2.], dtype=torch.float32)
+
+# Bit 1: d1 = XOR3(a1, b1, bout0), bout1 = majority(NOT(a1), b1, bout0)
+# Using flat XOR3 architecture: 3 hidden neurons + 1 output
+# But we need to handle the cascading borrow... Let's use a simpler cascade approach
+
+# For bits 1-3, we use XOR(XOR(ai, bi), bout_{i-1})
+# This needs 2 XOR2 gates per bit = 6 neurons per bit for diff
+# Plus 1 neuron for borrow = 7 neurons per bit
+
+# Bit 1:
+# First XOR: a1 XOR b1
+weights['xor1_or.weight'] = torch.tensor([[0., 0., 1., 0., 0., 0., 1., 0.]], dtype=torch.float32)
+weights['xor1_or.bias'] = torch.tensor([-1.], dtype=torch.float32)
+weights['xor1_nand.weight'] = torch.tensor([[0., 0., -1., 0., 0., 0., -1., 0.]], dtype=torch.float32)
+weights['xor1_nand.bias'] = torch.tensor([1.], dtype=torch.float32)
+weights['xor1.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['xor1.bias'] = torch.tensor([-2.], dtype=torch.float32)
+
+# Second XOR for d1: (a1 XOR b1) XOR bout0 - needs bout0 from layer 1
+# d1_or takes [xor1, bout0], d1_nand takes [xor1, bout0]
+weights['d1_or.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['d1_or.bias'] = torch.tensor([-1.], dtype=torch.float32)
+weights['d1_nand.weight'] = torch.tensor([[-1., -1.]], dtype=torch.float32)
+weights['d1_nand.bias'] = torch.tensor([1.], dtype=torch.float32)
+weights['d1.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['d1.bias'] = torch.tensor([-2.], dtype=torch.float32)
+
+# bout1 = majority(NOT(a1), b1, bout0) - threshold with [-1, 1, 1] bias -1
+# But we need to include bout0 in the input... This will be computed in forward pass
+weights['bout1.weight'] = torch.tensor([[1., 1., 1.]], dtype=torch.float32)  # [NOT(a1), b1, bout0]
+weights['bout1.bias'] = torch.tensor([-2.], dtype=torch.float32)  # fires when 2+ are true
+
+# Similar for bits 2 and 3
+weights['xor2_or.weight'] = torch.tensor([[0., 1., 0., 0., 0., 1., 0., 0.]], dtype=torch.float32)
+weights['xor2_or.bias'] = torch.tensor([-1.], dtype=torch.float32)
+weights['xor2_nand.weight'] = torch.tensor([[0., -1., 0., 0., 0., -1., 0., 0.]], dtype=torch.float32)
+weights['xor2_nand.bias'] = torch.tensor([1.], dtype=torch.float32)
+weights['xor2.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['xor2.bias'] = torch.tensor([-2.], dtype=torch.float32)
+
+weights['d2_or.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['d2_or.bias'] = torch.tensor([-1.], dtype=torch.float32)
+weights['d2_nand.weight'] = torch.tensor([[-1., -1.]], dtype=torch.float32)
+weights['d2_nand.bias'] = torch.tensor([1.], dtype=torch.float32)
+weights['d2.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['d2.bias'] = torch.tensor([-2.], dtype=torch.float32)
+
+weights['bout2.weight'] = torch.tensor([[1., 1., 1.]], dtype=torch.float32)
+weights['bout2.bias'] = torch.tensor([-2.], dtype=torch.float32)
+
+weights['xor3_or.weight'] = torch.tensor([[1., 0., 0., 0., 1., 0., 0., 0.]], dtype=torch.float32)
+weights['xor3_or.bias'] = torch.tensor([-1.], dtype=torch.float32)
+weights['xor3_nand.weight'] = torch.tensor([[-1., 0., 0., 0., -1., 0., 0., 0.]], dtype=torch.float32)
+weights['xor3_nand.bias'] = torch.tensor([1.], dtype=torch.float32)
+weights['xor3.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['xor3.bias'] = torch.tensor([-2.], dtype=torch.float32)
+
+weights['d3_or.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['d3_or.bias'] = torch.tensor([-1.], dtype=torch.float32)
+weights['d3_nand.weight'] = torch.tensor([[-1., -1.]], dtype=torch.float32)
+weights['d3_nand.bias'] = torch.tensor([1.], dtype=torch.float32)
+weights['d3.weight'] = torch.tensor([[1., 1.]], dtype=torch.float32)
+weights['d3.bias'] = torch.tensor([-2.], dtype=torch.float32)
+
+weights['bout3.weight'] = torch.tensor([[1., 1., 1.]], dtype=torch.float32)
+weights['bout3.bias'] = torch.tensor([-2.], dtype=torch.float32)
+
+save_file(weights, 'model.safetensors')
+
+# Verify with direct computation
+def subtractor4(a3, a2, a1, a0, b3, b2, b1, b0):
+    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0),
+                        float(b3), float(b2), float(b1), float(b0)])
+
+    # Bit 0
+    d0_or = int((inp @ weights['d0_or.weight'].T + weights['d0_or.bias'] >= 0).item())
+    d0_nand = int((inp @ weights['d0_nand.weight'].T + weights['d0_nand.bias'] >= 0).item())
+    d0 = int((torch.tensor([float(d0_or), float(d0_nand)]) @ weights['d0.weight'].T + weights['d0.bias'] >= 0).item())
+    bout0 = int((inp @ weights['bout0.weight'].T + weights['bout0.bias'] >= 0).item())
+
+    # Bit 1
+    xor1_or = int((inp @ weights['xor1_or.weight'].T + weights['xor1_or.bias'] >= 0).item())
+    xor1_nand = int((inp @ weights['xor1_nand.weight'].T + weights['xor1_nand.bias'] >= 0).item())
+    xor1 = int((torch.tensor([float(xor1_or), float(xor1_nand)]) @ weights['xor1.weight'].T + weights['xor1.bias'] >= 0).item())
+
+    d1_in = torch.tensor([float(xor1), float(bout0)])
+    d1_or = int((d1_in @ weights['d1_or.weight'].T + weights['d1_or.bias'] >= 0).item())
+    d1_nand = int((d1_in @ weights['d1_nand.weight'].T + weights['d1_nand.bias'] >= 0).item())
+    d1 = int((torch.tensor([float(d1_or), float(d1_nand)]) @ weights['d1.weight'].T + weights['d1.bias'] >= 0).item())
+
+    # bout1 = majority(NOT(a1), b1, bout0)
+    not_a1 = 1 - a1
+    bout1_in = torch.tensor([float(not_a1), float(b1), float(bout0)])
+    bout1 = int((bout1_in @ weights['bout1.weight'].T + weights['bout1.bias'] >= 0).item())
+
+    # Bit 2
+    xor2_or = int((inp @ weights['xor2_or.weight'].T + weights['xor2_or.bias'] >= 0).item())
+    xor2_nand = int((inp @ weights['xor2_nand.weight'].T + weights['xor2_nand.bias'] >= 0).item())
+    xor2 = int((torch.tensor([float(xor2_or), float(xor2_nand)]) @ weights['xor2.weight'].T + weights['xor2.bias'] >= 0).item())
+
+    d2_in = torch.tensor([float(xor2), float(bout1)])
+    d2_or = int((d2_in @ weights['d2_or.weight'].T + weights['d2_or.bias'] >= 0).item())
+    d2_nand = int((d2_in @ weights['d2_nand.weight'].T + weights['d2_nand.bias'] >= 0).item())
+    d2 = int((torch.tensor([float(d2_or), float(d2_nand)]) @ weights['d2.weight'].T + weights['d2.bias'] >= 0).item())
+
+    not_a2 = 1 - a2
+    bout2_in = torch.tensor([float(not_a2), float(b2), float(bout1)])
+    bout2 = int((bout2_in @ weights['bout2.weight'].T + weights['bout2.bias'] >= 0).item())
+
+    # Bit 3
+    xor3_or = int((inp @ weights['xor3_or.weight'].T + weights['xor3_or.bias'] >= 0).item())
+    xor3_nand = int((inp @ weights['xor3_nand.weight'].T + weights['xor3_nand.bias'] >= 0).item())
+    xor3 = int((torch.tensor([float(xor3_or), float(xor3_nand)]) @ weights['xor3.weight'].T + weights['xor3.bias'] >= 0).item())
+
+    d3_in = torch.tensor([float(xor3), float(bout2)])
+    d3_or = int((d3_in @ weights['d3_or.weight'].T + weights['d3_or.bias'] >= 0).item())
+    d3_nand = int((d3_in @ weights['d3_nand.weight'].T + weights['d3_nand.bias'] >= 0).item())
+    d3 = int((torch.tensor([float(d3_or), float(d3_nand)]) @ weights['d3.weight'].T + weights['d3.bias'] >= 0).item())
+
+    not_a3 = 1 - a3
+    bout3_in = torch.tensor([float(not_a3), float(b3), float(bout2)])
+    bout3 = int((bout3_in @ weights['bout3.weight'].T + weights['bout3.bias'] >= 0).item())
+
+    return [d3, d2, d1, d0, bout3]
+
+print("Verifying subtractor4bit...")
+errors = 0
+for a in range(16):
+    for b in range(16):
+        a3, a2, a1, a0 = (a >> 3) & 1, (a >> 2) & 1, (a >> 1) & 1, a & 1
+        b3, b2, b1, b0 = (b >> 3) & 1, (b >> 2) & 1, (b >> 1) & 1, b & 1
+        result = subtractor4(a3, a2, a1, a0, b3, b2, b1, b0)
+
+        expected_val = (a - b) % 16
+        expected_bout = 1 if a < b else 0
+        expected = [(expected_val >> 3) & 1, (expected_val >> 2) & 1,
+                    (expected_val >> 1) & 1, expected_val & 1, expected_bout]
+
+        if result != expected:
+            errors += 1
+            if errors <= 5:
+                print(f"ERROR: {a} - {b} = {result}, expected {expected}")
+
+if errors == 0:
+    print("All 256 test cases passed!")
+else:
+    print(f"FAILED: {errors} errors")
+
+mag = sum(t.abs().sum().item() for t in weights.values())
+print(f"Magnitude: {mag:.0f}")

model.py

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+import torch
+from safetensors.torch import load_file
+
+def load_model(path='model.safetensors'):
+    return load_file(path)
+
+def subtractor4(a3, a2, a1, a0, b3, b2, b1, b0, weights):
+    """4-bit subtractor: returns (A - B) mod 16 and borrow out"""
+    inp = torch.tensor([float(a3), float(a2), float(a1), float(a0),
+                        float(b3), float(b2), float(b1), float(b0)])
+
+    # Bit 0
+    d0_or = int((inp @ weights['d0_or.weight'].T + weights['d0_or.bias'] >= 0).item())
+    d0_nand = int((inp @ weights['d0_nand.weight'].T + weights['d0_nand.bias'] >= 0).item())
+    d0 = int((torch.tensor([float(d0_or), float(d0_nand)]) @ weights['d0.weight'].T + weights['d0.bias'] >= 0).item())
+    bout0 = int((inp @ weights['bout0.weight'].T + weights['bout0.bias'] >= 0).item())
+
+    # Bit 1
+    xor1_or = int((inp @ weights['xor1_or.weight'].T + weights['xor1_or.bias'] >= 0).item())
+    xor1_nand = int((inp @ weights['xor1_nand.weight'].T + weights['xor1_nand.bias'] >= 0).item())
+    xor1 = int((torch.tensor([float(xor1_or), float(xor1_nand)]) @ weights['xor1.weight'].T + weights['xor1.bias'] >= 0).item())
+    d1_in = torch.tensor([float(xor1), float(bout0)])
+    d1_or = int((d1_in @ weights['d1_or.weight'].T + weights['d1_or.bias'] >= 0).item())
+    d1_nand = int((d1_in @ weights['d1_nand.weight'].T + weights['d1_nand.bias'] >= 0).item())
+    d1 = int((torch.tensor([float(d1_or), float(d1_nand)]) @ weights['d1.weight'].T + weights['d1.bias'] >= 0).item())
+    not_a1 = 1 - a1
+    bout1 = int((torch.tensor([float(not_a1), float(b1), float(bout0)]) @ weights['bout1.weight'].T + weights['bout1.bias'] >= 0).item())
+
+    # Bit 2
+    xor2_or = int((inp @ weights['xor2_or.weight'].T + weights['xor2_or.bias'] >= 0).item())
+    xor2_nand = int((inp @ weights['xor2_nand.weight'].T + weights['xor2_nand.bias'] >= 0).item())
+    xor2 = int((torch.tensor([float(xor2_or), float(xor2_nand)]) @ weights['xor2.weight'].T + weights['xor2.bias'] >= 0).item())
+    d2_in = torch.tensor([float(xor2), float(bout1)])
+    d2_or = int((d2_in @ weights['d2_or.weight'].T + weights['d2_or.bias'] >= 0).item())
+    d2_nand = int((d2_in @ weights['d2_nand.weight'].T + weights['d2_nand.bias'] >= 0).item())
+    d2 = int((torch.tensor([float(d2_or), float(d2_nand)]) @ weights['d2.weight'].T + weights['d2.bias'] >= 0).item())
+    not_a2 = 1 - a2
+    bout2 = int((torch.tensor([float(not_a2), float(b2), float(bout1)]) @ weights['bout2.weight'].T + weights['bout2.bias'] >= 0).item())
+
+    # Bit 3
+    xor3_or = int((inp @ weights['xor3_or.weight'].T + weights['xor3_or.bias'] >= 0).item())
+    xor3_nand = int((inp @ weights['xor3_nand.weight'].T + weights['xor3_nand.bias'] >= 0).item())
+    xor3 = int((torch.tensor([float(xor3_or), float(xor3_nand)]) @ weights['xor3.weight'].T + weights['xor3.bias'] >= 0).item())
+    d3_in = torch.tensor([float(xor3), float(bout2)])
+    d3_or = int((d3_in @ weights['d3_or.weight'].T + weights['d3_or.bias'] >= 0).item())
+    d3_nand = int((d3_in @ weights['d3_nand.weight'].T + weights['d3_nand.bias'] >= 0).item())
+    d3 = int((torch.tensor([float(d3_or), float(d3_nand)]) @ weights['d3.weight'].T + weights['d3.bias'] >= 0).item())
+    not_a3 = 1 - a3
+    bout3 = int((torch.tensor([float(not_a3), float(b3), float(bout2)]) @ weights['bout3.weight'].T + weights['bout3.bias'] >= 0).item())
+
+    return [d3, d2, d1, d0, bout3]
+
+if __name__ == '__main__':
+    w = load_model()
+    print('Subtractor4bit examples:')
+    examples = [(7, 3), (5, 5), (3, 7), (15, 1), (0, 1)]
+    for a, b in examples:
+        a3, a2, a1, a0 = (a >> 3) & 1, (a >> 2) & 1, (a >> 1) & 1, a & 1
+        b3, b2, b1, b0 = (b >> 3) & 1, (b >> 2) & 1, (b >> 1) & 1, b & 1
+        result = subtractor4(a3, a2, a1, a0, b3, b2, b1, b0, w)
+        diff = result[0]*8 + result[1]*4 + result[2]*2 + result[3]
+        bout = result[4]
+        print(f'  {a:2d} - {b:2d} = {diff:2d} (bout={bout})')