LogLogLikelihood — transformers/LogisticLogLikelihood.py

Logistic log-likelihood transformer. Computes the per-record log-likelihood contribution of a logistic regression model using a polynomial approximation of the softplus function, compatible with EZKL's fixed-point arithmetic.

eta = (mask * x) @ beta ll_i = y * eta - softplus(eta) SLT_i = Concat(ll_i, TS_i)

When summed (via Adder), the SMT root gives the total log-likelihood of the dataset under the model — used for both the full and reduced models in the LRT.

Constructor

python LogLogLikelihood(size=0, length_transform_salt=0, beta=None, mask=None)

Parameter	Type	Default	Description
size	int	0	Expected output shape.
length_transform_salt	int	0	Dimensionality of TS_i.
beta	torch.Tensor	None	Coefficient vector, shape (n_coefs, 1).
mask	torch.Tensor	None	Binary feature-selection mask applied to x before the dot product. Enables the reduced model to use a subset of features.

softplus_piecewise(eta)

A degree-6 polynomial approximation of log(1 + exp(eta)) (softplus), valid on [-K, K] where K=10. Outside this range:

• eta <= -K → returns 0 (left tail).
• eta >= K → returns eta (right tail, i.e., the linear asymptote).

Parameter	Type	Description
eta	torch.Tensor	Linear predictor value.

Returns torch.Tensor — piecewise approximation of softplus(eta).

Note

The polynomial approximation is necessary because torch.log and torch.exp in their standard forms produce arithmetic circuits that are too large for practical EZKL proof generation. The piecewise polynomial keeps circuit size tractable.

logistic_ll_piecewise(eta, y)

Computes the log-likelihood contribution for a single record.

ll = y * eta - softplus(eta)

Parameter	Type	Description
eta	torch.Tensor	Linear predictor (mask * x) @ beta.
y	torch.Tensor	Binary label {0, 1}.

Returns torch.Tensor — per-record log-likelihood scalar.

forward(a, salt, beta, mask)

Parameter	Type	Description
a	torch.Tensor	Salted raw value. First x_dim columns are features; column x_dim is label y.
salt	torch.Tensor	Transform salt TS_i.
beta	torch.Tensor	Coefficient vector.
mask	torch.Tensor	Feature-selection mask. For the full model all entries are 1; for the reduced model only the intercept column is 1.

Returns torch.Tensor — Concat(ll_i, salt). Default (all-zero) records return 0 contribution.

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See index.md for the shared interface inherited by all transformers.