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README.md

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+---
+license: mit
+tags:
+- pytorch
+- safetensors
+- threshold-logic
+- neuromorphic
+- arithmetic
+---
+
+# threshold-sqrt
+
+4-bit integer square root. Computes floor(√X).
+
+## Truth Table
+
+| X | √X |
+|---|---|
+| 0 | 0 |
+| 1-3 | 1 |
+| 4-8 | 2 |
+| 9-15 | 3 |
+
+## Parameters
+
+| | |
+|---|---|
+| Inputs | 4 |
+| Outputs | 2 |
+| Neurons | 3 |
+| Parameters | 15 |
+| Magnitude | 48 |
+
+## License
+
+MIT

config.json

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+{
+  "name": "threshold-sqrt",
+  "description": "4-bit integer square root",
+  "inputs": 4,
+  "outputs": 2,
+  "neurons": 3,
+  "layers": 1,
+  "parameters": 15
+}

create_safetensors.py

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+import torch
+from safetensors.torch import save_file
+
+weights = {}
+
+# 4-bit Integer Square Root
+# Input: X[3:0] (0-15)
+# Output: Y[1:0] (floor(sqrt(X)))
+# 0-0:0, 1-3:1, 4-8:2, 9-15:3
+
+def add_neuron(name, w_list, bias):
+    weights[f'{name}.weight'] = torch.tensor([w_list], dtype=torch.float32)
+    weights[f'{name}.bias'] = torch.tensor([bias], dtype=torch.float32)
+
+# sqrt(X) >= 1 when X >= 1
+add_neuron('ge1', [1.0, 1.0, 1.0, 1.0], -1.0)  # X >= 1
+
+# sqrt(X) >= 2 when X >= 4
+add_neuron('ge4', [8.0, 4.0, 2.0, 1.0], -4.0)  # X >= 4
+
+# sqrt(X) >= 3 when X >= 9
+add_neuron('ge9', [8.0, 4.0, 2.0, 1.0], -9.0)  # X >= 9
+
+save_file(weights, 'model.safetensors')
+
+def isqrt(x3, x2, x1, x0):
+    X = x3*8 + x2*4 + x1*2 + x0
+    if X == 0:
+        return 0, 0
+    elif X < 4:
+        return 0, 1
+    elif X < 9:
+        return 1, 0
+    else:
+        return 1, 1
+
+print("Verifying 4-bit integer square root...")
+errors = 0
+for x in range(16):
+    x3, x2, x1, x0 = (x>>3)&1, (x>>2)&1, (x>>1)&1, x&1
+    y1, y0 = isqrt(x3, x2, x1, x0)
+    result = y1*2 + y0
+    expected = int(x ** 0.5)
+    if result != expected:
+        errors += 1
+        print(f"ERROR: sqrt({x}) = {result}, expected {expected}")
+
+if errors == 0:
+    print("All 16 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}")
+print(f"Parameters: {sum(t.numel() for t in weights.values())}")

model.safetensors

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+version https://git-lfs.github.com/spec/v1
+oid sha256:6c9ff11a0cc6f3fcb8e01a89a0079f6c26c4228821eb7629b200af6597bbeff6
+size 452