API REFERENCE/omnibias-core

omnibias.core.verified.tm_neuron

0.5.0rc1Release candidatePython >=3.10Apache-2.0

Coefficient recurrences, activation contracts, jet algebra, and verified arithmetic shared by the numerical backends.

import omnibias.core.verified.tm_neuron

Module contract & mathematical conventions

Taylor-model neuron (theory 09-05).

A unit whose output is a TaylorModel, not a float. Affine image plus sigma via the closed-form tower (founding bias collapse delta -> 0) and a Lagrange remainder. Temperature collapse (beta -> inf, feasibility) does not appear. Do not conflate the two.

Sound enclosure of a shallow monotone cell over the supplied input domain. theorem_prover_verified is not asserted.

Shared formulas do not imply universal floating-point identity. Verify dtype, shape, derivative-order support, and the stated numerical assumptions for the path you use.

Module source ↗Source revision 9a2d73df0573Running reference examples →

CONSTANT

DEFAULT_SPEC

omnibias.core.verified.tm_neuron.DEFAULT_SPECSource ↗

DEFAULT_SPEC = TMNeuronSpec()

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Read the implementation

DEFAULT_SPEC = TMNeuronSpec()

Related APIsomnibias.core.verified.tm_neuron.TMNeuronSpec↗

CONSTANT

DISCLAIMER

omnibias.core.verified.tm_neuron.DISCLAIMERSource ↗

DISCLAIMER = 'TM hidden state; sound remainder, not a deep-net certificate, not ImageNet'

This exported constant is defined by the expression above. Its exact value and annotation come from the pinned source; use it with the module contract.

Regression example · honesty

This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_honesty() -> None:
    payload = honesty_payload()
    assert payload["imagenet_claim"] is False
    assert payload["stretch_claim"] is False
    assert payload["theorem_prover_verified"] is False
    assert "not a deep-net" in DISCLAIMER

python -m pytest packages/omnibias-core/tests/verified/test_tm_neuron.py -k test_honesty -q

Read the implementation

DISCLAIMER = (
    "TM hidden state; sound remainder, not a deep-net certificate, not ImageNet"
)

CLASS

TMNeuronSpec

omnibias.core.verified.tm_neuron.TMNeuronSpecSource ↗

class TMNeuronSpec

Dataclass constructor fields; inherited fields, if any, are declared by the base class. A field(...) expression describes a default factory or field options, not a literal argument default.

The module contract describes the context for this operation. Its signature, explicit validation, return expressions, and implementation are recorded below.

Parameters

Name	Type & default	Contract
orderdataclass field	intDefault: 1	See the operation contract and implementation below.
activationdataclass field	strDefault: 'sigmoid'	See the operation contract and implementation below.

Regression example · g1 soundness grid and sample

This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g1_soundness_grid_and_sample() -> None:
    spec = TMNeuronSpec(order=1, activation="sigmoid")
    tm = tm_dense(input_tm(0.0, 0.2, spec.order), 1.0, 0.0, spec)
    assert contains_grid_and_sample(tm, "sigmoid", 0.0, 0.2)

python -m pytest packages/omnibias-core/tests/verified/test_tm_neuron.py -k test_g1_soundness_grid_and_sample -q

Fields & methods

orderfield

order: int = 1

Declared int field on TMNeuronSpec. Default expression: 1.

Regression example · g1 soundness grid and sample

This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g1_soundness_grid_and_sample() -> None:
    spec = TMNeuronSpec(order=1, activation="sigmoid")
    tm = tm_dense(input_tm(0.0, 0.2, spec.order), 1.0, 0.0, spec)
    assert contains_grid_and_sample(tm, "sigmoid", 0.0, 0.2)

python -m pytest packages/omnibias-core/tests/verified/test_tm_neuron.py -k test_g1_soundness_grid_and_sample -q

View source ↗

activationfield

activation: str = 'sigmoid'

Declared str field on TMNeuronSpec. Default expression: 'sigmoid'.

View source ↗

Read the implementation

class TMNeuronSpec:
    order: int = 1
    activation: str = "sigmoid"

FUNCTION

compose_sigma_tm

omnibias.core.verified.tm_neuron.compose_sigma_tmSource ↗

compose_sigma_tm(tm: TaylorModel, name: str, order: int) -> TaylorModel

sigma of a 1-D TM: polynomial tower plus Lagrange remainder.

Parameters

Name	Type & default	Contract
tmpositional-or-keyword	TaylorModelRequired	See the operation contract and implementation below.
namepositional-or-keyword	strRequired	See the operation contract and implementation below.
orderpositional-or-keyword	intRequired	See the operation contract and implementation below.

ReturnsTaylorModel

Explicit validation & failure cases

• When order < 1, raises ValueError('TM-sigma needs order >= 1').

These are explicit source guards. Backend operations may also raise for invalid shapes, dtypes, or unsupported devices.

Executed regression · g2 non vacuous

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g2_non_vacuous() -> None:
    ex = worked_example()
    assert float(ex["remainder_width"]) < 0.1
    assert ex["vacuous"] is False
    assert float(ex["width"]) < 0.1

python -m pytest "packages/omnibias-core/tests/verified/test_tm_neuron.py::test_g2_non_vacuous" -q

Read the implementation

def compose_sigma_tm(tm: TaylorModel, name: str, order: int) -> TaylorModel:
    """``sigma`` of a 1-D TM: polynomial tower plus Lagrange remainder."""
    if order < 1:
        raise ValueError("TM-sigma needs order >= 1")
    mid = tm.coeffs[0].mid
    tower = sigma_tower_interval(name, Interval.point(mid), order)
    shifted = tm - mid
    poly = TaylorModel.constant(tower[0], tm.center, tm.radius, tm.order)
    power = TaylorModel.constant(1.0, tm.center, tm.radius, tm.order)
    fact = 1
    for k in range(1, order + 1):
        fact *= k
        power = power * shifted
        poly = poly + power * (tower[k] * Interval.from_rational(Fraction(1, fact)))
    rng = hull([tm.bound(), Interval.point(mid)])
    tail = sigma_tower_interval(name, rng, order + 1)[order + 1]
    h_range = tm.bound() - Interval.point(mid)
    lagrange = tail * Interval.from_rational(Fraction(1, math.factorial(order + 1))) * _even_pow(
        h_range, order + 1
    )
    result = TaylorModel(tm.center, tm.radius, poly.coeffs, poly.remainder + lagrange)
    direct = sigma_value_interval(name, tm.bound())
    poly_bound = result._poly_bound()
    cap = direct - poly_bound
    new_lo = max(result.remainder.lo, cap.lo)
    new_hi = min(result.remainder.hi, cap.hi)
    if new_lo <= new_hi:
        return TaylorModel(tm.center, tm.radius, result.coeffs, Interval(new_lo, new_hi))
    return result

Related APIsomnibias.core.verified.Interval↗omnibias.core.verified.hull↗omnibias.core.verified.sigma_tower_interval↗omnibias.core.verified.sigma_value_interval↗omnibias.core.verified.TaylorModel↗

FUNCTION

contains_grid_and_sample

omnibias.core.verified.tm_neuron.contains_grid_and_sampleSource ↗

contains_grid_and_sample(tm: TaylorModel, fn: str, lo: float, hi: float, *, n_grid: int=65, n_sample: int=32, seed: int=20260821) -> bool

Core verified contract: enclosure holds a grid and a random sample.

Parameters

Name	Type & default	Contract
tmpositional-or-keyword	TaylorModelRequired	See the operation contract and implementation below.
fnpositional-or-keyword	strRequired	See the operation contract and implementation below.
lopositional-or-keyword	floatRequired	See the operation contract and implementation below.
hipositional-or-keyword	floatRequired	See the operation contract and implementation below.
n_gridkeyword-only	intDefault: 65	See the operation contract and implementation below.
n_samplekeyword-only	intDefault: 32	See the operation contract and implementation below.
seedkeyword-only	intDefault: 20260821	See the operation contract and implementation below.

Returnsbool

Executed regression · g1 soundness grid and sample

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g1_soundness_grid_and_sample() -> None:
    spec = TMNeuronSpec(order=1, activation="sigmoid")
    tm = tm_dense(input_tm(0.0, 0.2, spec.order), 1.0, 0.0, spec)
    assert contains_grid_and_sample(tm, "sigmoid", 0.0, 0.2)

python -m pytest "packages/omnibias-core/tests/verified/test_tm_neuron.py::test_g1_soundness_grid_and_sample" -q

Read the implementation

def contains_grid_and_sample(
    tm: TaylorModel,
    fn: str,
    lo: float,
    hi: float,
    *,
    n_grid: int = 65,
    n_sample: int = 32,
    seed: int = 20260821,
) -> bool:
    """Core verified contract: enclosure holds a grid and a random sample."""
    box = tm.bound()
    xs = [lo + (hi - lo) * i / (n_grid - 1) for i in range(n_grid)]
    rng = random.Random(seed)
    xs.extend(rng.uniform(lo, hi) for _ in range(n_sample))
    for x in xs:
        if fn == "sigmoid":
            ez = math.exp(-x) if x >= 0.0 else math.exp(x)
            true = 1.0 / (1.0 + ez) if x >= 0.0 else ez / (1.0 + ez)
        elif fn == "tanh":
            true = math.tanh(x)
        else:
            raise ValueError(f"unsupported sample activation {fn!r}")
        if not box.contains(true):
            return False
    return True

FUNCTION

depth_honesty

omnibias.core.verified.tm_neuron.depth_honestySource ↗

depth_honesty(*, layers: int=6) -> dict[str, float | bool | int]

G3: a 6-layer random-sign nest. Explosion is allowed and recorded.

Parameters

Name	Type & default	Contract
layerskeyword-only	intDefault: 6	See the operation contract and implementation below.

Returnsdict[str, float | bool | int]

Executed regression · g3 depth honesty records explosion

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g3_depth_honesty_records_explosion() -> None:
    report = depth_honesty()
    assert "enclosure_exploded" in report
    if float(report["remainder_width"]) > 1e3:
        assert report["enclosure_exploded"] is True

python -m pytest "packages/omnibias-core/tests/verified/test_tm_neuron.py::test_g3_depth_honesty_records_explosion" -q

Read the implementation

def depth_honesty(*, layers: int = 6) -> dict[str, float | bool | int]:
    """G3: a 6-layer random-sign nest. Explosion is allowed and recorded."""
    rng = random.Random(20260821)
    weights = [rng.uniform(-3.0, 3.0) for _ in range(layers)]
    biases = [rng.uniform(-0.5, 0.5) for _ in range(layers)]
    tm = nest_layers(weights, biases)
    width = tm.remainder.width
    exploded = width > 1e3
    return {
        "layers": layers,
        "remainder_width": width,
        "bound_width": tm.bound().width,
        "enclosure_exploded": exploded,
    }

Related APIsomnibias.core.verified.tm_neuron.nest_layers↗

FUNCTION

honesty_payload

omnibias.core.verified.tm_neuron.honesty_payloadSource ↗

honesty_payload() -> dict[str, bool]

The module contract describes the context for this operation. Its signature, explicit validation, return expressions, and implementation are recorded below.

Returnsdict[str, bool]

Executed regression · honesty

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_honesty() -> None:
    payload = honesty_payload()
    assert payload["imagenet_claim"] is False
    assert payload["stretch_claim"] is False
    assert payload["theorem_prover_verified"] is False
    assert "not a deep-net" in DISCLAIMER

python -m pytest "packages/omnibias-core/tests/verified/test_tm_neuron.py::test_honesty" -q

Read the implementation

def honesty_payload() -> dict[str, bool]:
    return {
        "imagenet_claim": False,
        "stretch_claim": False,
        "deep_net_certificate": False,
        "ns_regularity": False,
        "theorem_prover_verified": False,
    }

FUNCTION

input_tm

omnibias.core.verified.tm_neuron.input_tmSource ↗

input_tm(lo: float, hi: float, order: int) -> TaylorModel

Identity Taylor model on [lo, hi].

Parameters

Name	Type & default	Contract
lopositional-or-keyword	floatRequired	See the operation contract and implementation below.
hipositional-or-keyword	floatRequired	See the operation contract and implementation below.
orderpositional-or-keyword	intRequired	See the operation contract and implementation below.

ReturnsTaylorModel

Explicit validation & failure cases

• When hi < lo, raises ValueError(f'empty box: [{lo}, {hi}]').

These are explicit source guards. Backend operations may also raise for invalid shapes, dtypes, or unsupported devices.

Executed regression · g2 non vacuous

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g2_non_vacuous() -> None:
    ex = worked_example()
    assert float(ex["remainder_width"]) < 0.1
    assert ex["vacuous"] is False
    assert float(ex["width"]) < 0.1

python -m pytest "packages/omnibias-core/tests/verified/test_tm_neuron.py::test_g2_non_vacuous" -q

Regression example · g1 soundness grid and sample

This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g1_soundness_grid_and_sample() -> None:
    spec = TMNeuronSpec(order=1, activation="sigmoid")
    tm = tm_dense(input_tm(0.0, 0.2, spec.order), 1.0, 0.0, spec)
    assert contains_grid_and_sample(tm, "sigmoid", 0.0, 0.2)

python -m pytest packages/omnibias-core/tests/verified/test_tm_neuron.py -k test_g1_soundness_grid_and_sample -q

Read the implementation

def input_tm(lo: float, hi: float, order: int) -> TaylorModel:
    """Identity Taylor model on ``[lo, hi]``."""
    if hi < lo:
        raise ValueError(f"empty box: [{lo}, {hi}]")
    center = 0.5 * (lo + hi)
    radius = 0.5 * (hi - lo)
    return TaylorModel.identity(center, radius, order)

FUNCTION

nest_layers

omnibias.core.verified.tm_neuron.nest_layersSource ↗

nest_layers(weights: Sequence[float], biases: Sequence[float], *, lo: float=0.0, hi: float=0.2, spec: TMNeuronSpec | None=None) -> TaylorModel

The module contract describes the context for this operation. Its signature, explicit validation, return expressions, and implementation are recorded below.

Parameters

Name	Type & default	Contract
weightspositional-or-keyword	Sequence[float]Required	See the operation contract and implementation below.
biasespositional-or-keyword	Sequence[float]Required	See the operation contract and implementation below.
lokeyword-only	floatDefault: 0.0	See the operation contract and implementation below.
hikeyword-only	floatDefault: 0.2	See the operation contract and implementation below.
speckeyword-only	TMNeuronSpec | NoneDefault: None	See the operation contract and implementation below.

ReturnsTaylorModel

Executed regression · g3 depth honesty records explosion

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g3_depth_honesty_records_explosion() -> None:
    report = depth_honesty()
    assert "enclosure_exploded" in report
    if float(report["remainder_width"]) > 1e3:
        assert report["enclosure_exploded"] is True

python -m pytest "packages/omnibias-core/tests/verified/test_tm_neuron.py::test_g3_depth_honesty_records_explosion" -q

Read the implementation

def nest_layers(
    weights: Sequence[float],
    biases: Sequence[float],
    *,
    lo: float = 0.0,
    hi: float = 0.2,
    spec: TMNeuronSpec | None = None,
) -> TaylorModel:
    cfg = DEFAULT_SPEC if spec is None else spec
    tm = input_tm(lo, hi, cfg.order)
    for weight, bias in zip(weights, biases, strict=True):
        tm = tm_dense(tm, weight, bias, cfg)
    return tm

Related APIsomnibias.core.verified.tm_neuron.input_tm↗omnibias.core.verified.tm_neuron.tm_dense↗

FUNCTION

source_imports_no_backend

omnibias.core.verified.tm_neuron.source_imports_no_backendSource ↗

source_imports_no_backend(path: Path | None=None) -> bool

G4: the authored module must not import torch / jax / tensorflow / keras.

Parameters

Name	Type & default	Contract
pathpositional-or-keyword	Path | NoneDefault: None	See the operation contract and implementation below.

Returnsbool

Executed regression · g4 no backend leak

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g4_no_backend_leak() -> None:
    assert source_imports_no_backend()

python -m pytest "packages/omnibias-core/tests/verified/test_tm_neuron.py::test_g4_no_backend_leak" -q

Read the implementation

def source_imports_no_backend(path: Path | None = None) -> bool:
    """G4: the authored module must not import torch / jax / tensorflow / keras."""
    src = Path(path) if path is not None else Path(__file__)
    tree = ast.parse(src.read_text(encoding="utf-8"))
    blocked = {"torch", "jax", "tensorflow", "keras"}
    for node in ast.walk(tree):
        if isinstance(node, ast.Import):
            for alias in node.names:
                if alias.name.split(".", 1)[0] in blocked:
                    return False
        elif isinstance(node, ast.ImportFrom) and node.module:
            if node.module.split(".", 1)[0] in blocked:
                return False
    return True

FUNCTION

tm_dense

omnibias.core.verified.tm_neuron.tm_denseSource ↗

tm_dense(tm_in: TaylorModel, weight: float, bias: float, spec: TMNeuronSpec | None=None) -> TaylorModel

Affine w * x + b then TM-sigma. Pure Python; no torch / jax.

Parameters

Name	Type & default	Contract
tm_inpositional-or-keyword	TaylorModelRequired	See the operation contract and implementation below.
weightpositional-or-keyword	floatRequired	See the operation contract and implementation below.
biaspositional-or-keyword	floatRequired	See the operation contract and implementation below.
specpositional-or-keyword	TMNeuronSpec | NoneDefault: None	See the operation contract and implementation below.

ReturnsTaylorModel

Executed regression · g2 non vacuous

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g2_non_vacuous() -> None:
    ex = worked_example()
    assert float(ex["remainder_width"]) < 0.1
    assert ex["vacuous"] is False
    assert float(ex["width"]) < 0.1

python -m pytest "packages/omnibias-core/tests/verified/test_tm_neuron.py::test_g2_non_vacuous" -q

Regression example · g1 soundness grid and sample

This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g1_soundness_grid_and_sample() -> None:
    spec = TMNeuronSpec(order=1, activation="sigmoid")
    tm = tm_dense(input_tm(0.0, 0.2, spec.order), 1.0, 0.0, spec)
    assert contains_grid_and_sample(tm, "sigmoid", 0.0, 0.2)

python -m pytest packages/omnibias-core/tests/verified/test_tm_neuron.py -k test_g1_soundness_grid_and_sample -q

Read the implementation

def tm_dense(
    tm_in: TaylorModel,
    weight: float,
    bias: float,
    spec: TMNeuronSpec | None = None,
) -> TaylorModel:
    """Affine ``w * x + b`` then TM-sigma. Pure Python; no torch / jax."""
    cfg = DEFAULT_SPEC if spec is None else spec
    pre = tm_in * Interval.point(weight) + Interval.point(bias)
    return compose_sigma_tm(pre, cfg.activation, cfg.order)

Related APIsomnibias.core.verified.tm_neuron.compose_sigma_tm↗

FUNCTION

worked_example

omnibias.core.verified.tm_neuron.worked_exampleSource ↗

worked_example() -> dict[str, float | bool]

Order-1 sigmoid TM on [0, 0.2] about 0.1.

Returnsdict[str, float | bool]

Executed regression · g2 non vacuous

Recorded coverage confirms this test executed the API body. This example belongs to the pinned upstream test suite. It may use fixtures and imports from its full file. Run it from that checkout with its test dependencies installed.

Full file, imports & fixtures ↗

def test_g2_non_vacuous() -> None:
    ex = worked_example()
    assert float(ex["remainder_width"]) < 0.1
    assert ex["vacuous"] is False
    assert float(ex["width"]) < 0.1

python -m pytest "packages/omnibias-core/tests/verified/test_tm_neuron.py::test_g2_non_vacuous" -q

Read the implementation

def worked_example() -> dict[str, float | bool]:
    """Order-1 sigmoid TM on ``[0, 0.2]`` about ``0.1``."""
    spec = TMNeuronSpec(order=1, activation="sigmoid")
    tm = tm_dense(input_tm(0.0, 0.2, spec.order), 1.0, 0.0, spec)
    box = tm.bound()
    return {
        "lo": box.lo,
        "hi": box.hi,
        "width": box.width,
        "remainder_width": tm.remainder.width,
        "vacuous": box.width >= 1e6,
    }

Related APIsomnibias.core.verified.tm_neuron.TMNeuronSpec↗omnibias.core.verified.tm_neuron.input_tm↗omnibias.core.verified.tm_neuron.tm_dense↗

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