notebooks/success_conditioning_tutorial.py

import marimo

__generated_with = "0.23.15"
app = marimo.App(width="medium")


@app.cell
def _():
    import marimo as mo

    return (mo,)


@app.cell
def _(mo):
    mo.md(r"""
    # Success conditioning, from identity to failure mode

    ![Four verified contracts](https://huggingface.co/spaces/DineshAI/FEmXFeqYNZ/resolve/main/images/reproduction_summary.svg)

    This tutorial opens with the published evidence; no expensive experiment
    is required. The formal reproduction uses exact dynamic programming,
    24 independent constrained solves, a symbolic monotonicity certificate,
    and 63,360 analytic threshold cells.
    """)
    return


@app.cell
def _(mo):
    q_good = mo.ui.slider(0.50, 0.99, value=0.70, step=0.01, label="Good-action success")
    q_bad = mo.ui.slider(0.01, 0.49, value=0.30, step=0.01, label="Bad-action success")
    mo.hstack([q_bad, q_good], justify="space-around")
    return q_bad, q_good


@app.cell
def _(mo, q_bad, q_good):
    behavior = 0.5
    value = behavior * q_bad.value + behavior * q_good.value
    conditioned_good = behavior * q_good.value / value
    new_value = (1 - conditioned_good) * q_bad.value + conditioned_good * q_good.value
    influence = (
        behavior * (q_bad.value - value) ** 2
        + behavior * (q_good.value - value) ** 2
    ) / value**2
    relative_improvement = (new_value - value) / value
    mo.md(
        f"""
        ## A two-action success-conditioned update

        Behavior success is **{value:.4f}**. Conditioning raises the good-action
        probability from `0.5` to **{conditioned_good:.4f}** and success to
        **{new_value:.4f}**.

        The statewise identity is visible numerically:

        | quantity | value |
        |---|---:|
        | relative improvement | `{relative_improvement:.8f}` |
        | action-influence | `{influence:.8f}` |

        Their difference is `{abs(relative_improvement - influence):.2e}`.
        """
    )
    return


@app.cell
def _(mo):
    mo.md(r"""
    ## Why thresholding can break alignment

    Faithful randomized labels preserve expected reward. A threshold label
    instead asks which action most often exceeds `θ`. Near `θ=1`, volatile
    low-mean actions can win that tail-probability contest through luck. The
    published paper-setting sweep finds:

    | statistic | observed |
    |---|---:|
    | faithful conditioned return | `0.507143` |
    | best proxy gain beyond faithful | `0.004927–0.005400` |
    | first harmful threshold | `0.968–0.970` |
    | return at threshold `0.999` | `0.500024–0.500030` |

    [Read the complete illustrated report](https://github.com/MachineLearning-Nerd/icml26-repro-FEmXFeqYNZ-success-conditioning/blob/main/reports/success-conditioning/report.md)
    or inspect the [canonical raw-evidence page](https://huggingface.co/spaces/DineshAI/FEmXFeqYNZ).
    """)
    return


if __name__ == "__main__":
    app.run()