Publish Supernova Mathos V6.1

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NOTICE

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+Supernova Mathos V6.1
+Copyright 2026 Supernova
+
+This product is licensed under the Apache License, Version 2.0.
+The license text is provided in the LICENSE file.

README.md

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+---
+license: apache-2.0
+tags:
+- arithmetic
+- mathematics
+- numpy
+- supernova
+---
+
+# Supernova Mathos V6.1
+
+A custom NumPy-based learned arithmetic model with a BODMAS expression evaluator.
+
+## Installation
+
+    pip install supernova-mathos==6.1.0
+
+## Example
+
+    from supernova_mathos import mathos
+
+    model = mathos()
+    print(model.add(27, 15))
+    print(model.multiply(6, 7))
+    print(model.calculate("2 + 3 * 4"))
+
+## Files
+
+- weights/supernova_mathos_v6_1.npz: trained weights
+- mathos.py: model implementation
+- LICENSE: Apache License 2.0
+
+Test results apply to the tested inputs and do not guarantee correctness for every possible input.
+
+## License
+
+Apache-2.0.

__init__.py

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+"""Supernova Mathos V6.1."""
+from .mathos import mathos
+
+__all__ = ["mathos"]

mathos.py

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+import re
+import numpy as np
+from fractions import Fraction
+
+
+HIDDEN = 128
+
+BATCH_SIZE = 128
+
+LEARNING_RATE = 0.003
+
+OP_NAMES = ['+', '-', '*', '/']
+
+INPUT_SIZE = 34
+
+def encode(a, b, state, op):
+    x = np.zeros(INPUT_SIZE, dtype=np.float64)
+    x[a] = 1.0
+    x[10 + b] = 1.0
+    x[20 + state] = 1.0
+    x[30 + op] = 1.0
+    return x
+
+def build_data():
+    datasets = {op: [] for op in range(4)}
+    for a in range(10):
+        for b in range(10):
+            for carry in range(2):
+                total = a + b + carry
+                datasets[0].append((encode(a, b, carry, 0), total % 10, total // 10))
+    for a in range(10):
+        for b in range(10):
+            for borrow in range(2):
+                total = a - b - borrow
+                digit = total % 10
+                next_borrow = int(total < 0)
+                datasets[1].append((encode(a, b, borrow, 1), digit, next_borrow))
+    for a in range(10):
+        for b in range(10):
+            for carry in range(9):
+                total = a * b + carry
+                datasets[2].append((encode(a, b, carry, 2), total % 10, total // 10))
+    for divisor in range(1, 10):
+        for remainder in range(divisor):
+            for next_digit in range(10):
+                current = remainder * 10 + next_digit
+                quotient_digit = current // divisor
+                next_remainder = current % divisor
+                datasets[3].append((encode(next_digit, divisor, remainder, 3), quotient_digit, next_remainder))
+    result = {}
+    for op, rows in datasets.items():
+        result[op] = (np.stack([r[0] for r in rows]), np.array([r[1] for r in rows], dtype=np.int64), np.array([r[2] for r in rows], dtype=np.int64))
+    return result
+
+DATA = build_data()
+
+def softmax(z):
+    z = z - np.max(z, axis=1, keepdims=True)
+    e = np.exp(z)
+    return e / np.sum(e, axis=1, keepdims=True)
+
+class MathosV6:
+
+    def __init__(self, seed=77):
+        r = np.random.default_rng(seed)
+
+        def init(nin, nout):
+            limit = np.sqrt(6.0 / (nin + nout))
+            return r.uniform(-limit, limit, (nin, nout))
+        self.p = {'W1': init(INPUT_SIZE, HIDDEN), 'b1': np.zeros((1, HIDDEN)), 'Wd': init(HIDDEN, 10), 'bd': np.zeros((1, 10)), 'Ws': init(HIDDEN, 10), 'bs': np.zeros((1, 10))}
+        self.m = {k: np.zeros_like(v) for k, v in self.p.items()}
+        self.v = {k: np.zeros_like(v) for k, v in self.p.items()}
+        self.step = 0
+        self.experiences_seen = 0
+
+    def forward(self, X):
+        h = np.tanh(X @ self.p['W1'] + self.p['b1'])
+        return (h, h @ self.p['Wd'] + self.p['bd'], h @ self.p['Ws'] + self.p['bs'])
+
+    def train_batch(self, X, yd, ys):
+        n = len(X)
+        h, dl, sl = self.forward(X)
+        pd, ps = (softmax(dl), softmax(sl))
+        rows = np.arange(n)
+        gd, gs = (pd.copy(), ps.copy())
+        gd[rows, yd] -= 1.0
+        gs[rows, ys] -= 1.0
+        gd /= n
+        gs /= n
+        grads = {'Wd': h.T @ gd, 'bd': gd.sum(axis=0, keepdims=True), 'Ws': h.T @ gs, 'bs': gs.sum(axis=0, keepdims=True)}
+        dh = gd @ self.p['Wd'].T + gs @ self.p['Ws'].T
+        dz = dh * (1.0 - h * h)
+        grads['W1'] = X.T @ dz
+        grads['b1'] = dz.sum(axis=0, keepdims=True)
+        self.step += 1
+        for k in self.p:
+            g = grads[k]
+            self.m[k] = 0.9 * self.m[k] + 0.1 * g
+            self.v[k] = 0.999 * self.v[k] + 0.001 * g * g
+            mhat = self.m[k] / (1.0 - 0.9 ** self.step)
+            vhat = self.v[k] / (1.0 - 0.999 ** self.step)
+            self.p[k] -= LEARNING_RATE * mhat / (np.sqrt(vhat) + 1e-08)
+        self.experiences_seen += n
+        loss_d = -np.log(pd[rows, yd] + 1e-12).mean()
+        loss_s = -np.log(ps[rows, ys] + 1e-12).mean()
+        return float(loss_d + loss_s)
+
+    def transition(self, a, b, state, op):
+        x = encode(a, b, state, op).reshape(1, -1)
+        _, dl, sl = self.forward(x)
+        return (int(dl[0].argmax()), int(sl[0].argmax()))
+
+    def transition_accuracy(self, op=None):
+        selected = range(4) if op is None else [op]
+        correct, total = (0, 0)
+        for operation in selected:
+            X, yd, ys = DATA[operation]
+            _, dl, sl = self.forward(X)
+            pd, ps = (dl.argmax(axis=1), sl.argmax(axis=1))
+            correct += int(np.sum((pd == yd) & (ps == ys)))
+            total += len(X)
+        return correct / total
+
+    def train_operation(self, op, epochs, seed):
+        X, yd, ys = DATA[op]
+        r = np.random.default_rng(seed)
+        name = OP_NAMES[op]
+        for ep in range(1, epochs + 1):
+            order = r.permutation(len(X))
+            total_loss = 0.0
+            for start in range(0, len(X), BATCH_SIZE):
+                ids = order[start:start + BATCH_SIZE]
+                loss = self.train_batch(X[ids], yd[ids], ys[ids])
+                total_loss += loss * len(ids)
+            total_loss /= len(X)
+            if ep == 1 or ep % 50 == 0 or ep == epochs:
+                acc = self.transition_accuracy(op)
+                print(f'Learn {name} | Epoch {ep:03d}/{epochs} | loss={total_loss:.5f} | transition accuracy={100 * acc:.2f}%')
+
+    def add(self, a, b):
+        if a < 0 or b < 0:
+            raise ValueError('Addition accepts nonnegative integers.')
+        result, carry, pos = (0, 0, 0)
+        while pos < max(len(str(a)), len(str(b))) or carry:
+            da = a // 10 ** pos % 10
+            db = b // 10 ** pos % 10
+            digit, carry = self.transition(da, db, carry, 0)
+            result += digit * 10 ** pos
+            pos += 1
+        return result
+
+    def subtract(self, a, b):
+        if a < b or b < 0:
+            raise ValueError('Subtraction requires a >= b >= 0.')
+        result, borrow = (0, 0)
+        for pos in range(len(str(a))):
+            da = a // 10 ** pos % 10
+            db = b // 10 ** pos % 10
+            digit, borrow = self.transition(da, db, borrow, 1)
+            result += digit * 10 ** pos
+        if borrow != 0:
+            raise ArithmeticError('Learned subtraction ended with a borrow.')
+        return result
+
+    def multiply_digit(self, n, digit):
+        if not 0 <= digit <= 9:
+            raise ValueError('Single-digit multiplier must be 0..9.')
+        result, carry, pos = (0, 0, 0)
+        while pos < len(str(n)) or carry:
+            da = n // 10 ** pos % 10
+            out_digit, carry = self.transition(da, digit, carry, 2)
+            result += out_digit * 10 ** pos
+            pos += 1
+        return result
+
+    def multiply(self, a, b):
+        if a < 0 or b < 0:
+            raise ValueError('Multiplication accepts nonnegative integers.')
+        result = 0
+        for pos, ch in enumerate(str(b)[::-1]):
+            partial = self.multiply_digit(a, int(ch))
+            for _ in range(pos):
+                partial *= 10
+            result = self.add(result, partial)
+        return result
+
+    def divide(self, dividend, divisor):
+        if dividend < 0 or divisor <= 0:
+            raise ValueError('Division requires dividend >= 0, divisor > 0.')
+        quotient, remainder = (0, 0)
+        for ch in str(dividend):
+            digit = int(ch)
+            if divisor <= 9:
+                qdigit, new_remainder = self.transition(digit, divisor, remainder, 3)
+            else:
+                current = int(str(remainder) + ch)
+                qdigit = 0
+                for trial in range(9, -1, -1):
+                    product = self.multiply(divisor, trial)
+                    if product <= current:
+                        qdigit = trial
+                        break
+                product = self.multiply(divisor, qdigit)
+                new_remainder = self.subtract(current, product)
+            quotient = quotient * 10 + qdigit
+            remainder = new_remainder
+        return (quotient, remainder)
+
+    def save(self, path):
+        np.savez(path, **self.p, experiences_seen=np.array(self.experiences_seen))
+
+def signed_add(model, x, y, subtract=False):
+    if subtract:
+        y = -y
+    sx = -1 if x < 0 else 1
+    sy = -1 if y < 0 else 1
+    ax, ay = (abs(x), abs(y))
+    if sx == sy:
+        return sx * model.add(ax, ay)
+    if ax >= ay:
+        return sx * model.subtract(ax, ay)
+    return sy * model.subtract(ay, ax)
+
+def signed_multiply(model, x, y):
+    sign = -1 if (x < 0) != (y < 0) else 1
+    return sign * model.multiply(abs(x), abs(y))
+
+def fraction_operation(model, left, right, op):
+    left, right = (Fraction(left), Fraction(right))
+    if op == '+' or op == '-':
+        n1 = signed_multiply(model, left.numerator, right.denominator)
+        n2 = signed_multiply(model, right.numerator, left.denominator)
+        numerator = signed_add(model, n1, n2, subtract=op == '-')
+        denominator = model.multiply(left.denominator, right.denominator)
+        return Fraction(numerator, denominator)
+    if op == '*':
+        numerator = signed_multiply(model, left.numerator, right.numerator)
+        denominator = model.multiply(left.denominator, right.denominator)
+        return Fraction(numerator, denominator)
+    if op == '/':
+        if right == 0:
+            raise ZeroDivisionError('Division by zero.')
+        numerator = signed_multiply(model, left.numerator, right.denominator)
+        denominator = signed_multiply(model, left.denominator, right.numerator)
+        return Fraction(numerator, denominator)
+    raise ValueError('Unsupported operation.')
+
+def fraction_power(model, base, exponent):
+    base = Fraction(base)
+    exponent = Fraction(exponent)
+    if exponent.denominator != 1:
+        raise ValueError('Only integer powers are supported.')
+    power = exponent.numerator
+    if abs(power) > 20:
+        raise ValueError('Power magnitude is limited to 20.')
+    if power < 0:
+        if base == 0:
+            raise ZeroDivisionError('Zero cannot have a negative power.')
+        base = Fraction(base.denominator, base.numerator)
+        power = -power
+    result = Fraction(1, 1)
+    for _ in range(power):
+        result = fraction_operation(model, result, base, '*')
+    return result
+
+def tokenize(expression):
+    cleaned = re.sub('\\s+', '', expression)
+    tokens = re.findall('\\d+|[()+*/^%-]', cleaned)
+    if ''.join(tokens) != cleaned:
+        raise ValueError('Invalid character in expression.')
+    return tokens
+
+def bodmas(model, expression):
+    tokens = tokenize(expression)
+    index = 0
+
+    def parse_expression():
+        nonlocal index
+        value = parse_term()
+        while index < len(tokens) and tokens[index] in ('+', '-'):
+            op = tokens[index]
+            index += 1
+            rhs = parse_term()
+            value = fraction_operation(model, value, rhs, op)
+        return value
+
+    def parse_term():
+        nonlocal index
+        value = parse_power()
+        while index < len(tokens) and tokens[index] in ('*', '/'):
+            op = tokens[index]
+            index += 1
+            rhs = parse_power()
+            value = fraction_operation(model, value, rhs, op)
+        return value
+
+    def parse_power():
+        nonlocal index
+        value = parse_factor()
+        if index < len(tokens) and tokens[index] == '^':
+            index += 1
+            exponent = parse_power()
+            value = fraction_power(model, value, exponent)
+        return value
+
+    def parse_factor():
+        nonlocal index
+        if index >= len(tokens):
+            raise ValueError('Incomplete expression.')
+        if tokens[index] == '+':
+            index += 1
+            return parse_factor()
+        if tokens[index] == '-':
+            index += 1
+            return -parse_factor()
+        if tokens[index] == '(':
+            index += 1
+            value = parse_expression()
+            if index >= len(tokens) or tokens[index] != ')':
+                raise ValueError('Missing closing parenthesis.')
+            index += 1
+            return value
+        token = tokens[index]
+        if not token.isdigit():
+            raise ValueError(f'Unexpected token: {token}')
+        index += 1
+        return Fraction(int(token), 1)
+    result = parse_expression()
+    if index != len(tokens):
+        raise ValueError('Unexpected trailing tokens.')
+    return result
+
+
+from importlib.resources import files
+
+class mathos:
+    """Supernova Mathos V6.1 with bundled trained NumPy weights."""
+
+    def __init__(self):
+        self.model = MathosV6(seed=77)
+        weight_path = files("supernova_mathos").joinpath(
+            "weights/supernova_mathos_v6_1.npz"
+        )
+        with np.load(weight_path) as saved:
+            self.model.p = {
+                key: saved[key].copy()
+                for key in ("W1", "b1", "Wd", "bd", "Ws", "bs")
+            }
+            if "experiences_seen" in saved:
+                self.model.experiences_seen = int(saved["experiences_seen"])
+
+    def __getattr__(self, name):
+        return getattr(self.model, name)
+
+    def calculate(self, expression):
+        return bodmas(self.model, expression)
+

weights/supernova_mathos_v6_1.npz

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:d0dc8a525b6c81b9acf7a14f0b5797a3154118b7a6c9fa074c6e224a8912bc73
+size 58190