Examples

Task, latent, and enumeration examples

Compact modeling patterns for task learning, structured latent models, automatic fitting, enumeration, companion packages, and notebook material.

Task learning

LLM teachers and local models.

An LLM can be used as a teacher for labeling, extraction, or routing. mixle trains a local model and uses calibration/cascades to decide when to answer locally. The local URL in the snippets is just an OpenAI-compatible endpoint.

LLM active labeling

from mixle.task import *

# pool = ["free prize today", ...]
# calibration = ["cheap loan offer", ...]
# requests = ["winner click now", ...]
teacher = llm_labeler(
    OpenAICompatLLM(
        "http://localhost:11434/v1",
        "llama3.1",
    ),
    ["spam", "ham"],
)

cascade = Cascade(
    CalibratedTaskModel(
        active_distill(
            teacher,
            pool,
            budget=60,
        ).model,
    ).calibrate(calibration, teacher(calibration)),
    teacher,
    cost=CostModel(c_frontier=0.01),
)
cascade.serve(requests)
cascade.report()

LLM field extraction

from mixle.task import *

# train_lines = [
#     "INV-1001 Acme charged $42.10 on 2026-07-01",
#     "Payment to Globex $18.50 on 2026-07-02",
#     ...
# ]
# test_lines has the same shape.
fields = ["id", "amount", "date", "vendor"]
teacher = llm_extractor(
    OpenAICompatLLM(
        "http://localhost:11434/v1",
        "llama3.1",
    ),
    fields,
)

extraction_f1(
    distill_extractor(teacher, train_lines, fields),
    teacher(test_lines),
    test_lines,
)

Probability models

Structured estimators and enumeration.

Heterogeneous latent model

from mixle.inference import *
from mixle.stats import *

# data is a list of numeric sequences:
# data[:2] == [
#     [-1.2, -0.9, -1.0, 0.8, 1.1],
#     [1.0, 1.3, 0.9, -0.8, -1.1],
# ]

fit = optimize(data, HiddenMarkovEstimator([
    GaussianEstimator(),
    GaussianEstimator(),
]))

fit.log_density(data[0])

Automatic estimator inference

from numpy.random import *
from mixle.inference import *
from mixle.utils.automatic import *

# data is a list of mixed records:
# data[:2] == [
#     (1, None, "a", [("a", 1), ("b", 2)]),
#     (3, 2, "b", [("a", 1), ("b", 2), ("c", 3)]),
# ]

est = get_estimator(data, pseudo_count=1e-4)
model = estimate(
    data,
    est,
    prev_estimate=initialize(data, est, RandomState(1)),
)
model.log_density(data[0])

Ecosystem

Companion packages.

The core package stays focused on modeling. Physics-constrained inverse problems, serving infrastructure, and notebook collections live in adjacent packages.

mixle-pde PDE and ODE-constrained Bayesian inverse problems for mixle, including differentiable solvers and state-space models. mixle-pde source Solver catalog, inverse-problem examples, geophysics, electrostatics, propagation, and tests. mixle-mlops OpenAI-compatible gateway for mixle models and open LLMs, with accounts, RAG, MCP, and deployment tooling. mixle-mlops source Gateway, frontend, registry, cloud deployment assets, and model-evolution worker. mixle-notebooks Worked examples, courses, benchmarks, and notebook material for core and physics workflows. Artifact tutorial Core tutorial for saving, restoring, evaluating, and handing off fitted model artifacts.

Scripts

Repository examples.

The longer examples live as source files so they can be run, edited, and tested directly.

LLM active labeling Use an LLM teacher for a small label budget, then serve locally. LLM field extraction Distill JSON field extraction into a local sequence tagger. Task cascade Distill a teacher into a calibrated local cascade. Automatic fitting Infer a first estimator from raw data and inspect the route. Structured leaves Compose record, sequence, and latent structure in one model. Enumeration Rank, seek, and stream high-probability structured outcomes. Production lifecycle Save, restore, evaluate, and serve durable model artifacts. Full gallery Browse the complete examples directory.