🌊 clap_family

Conservative Lapse-Action Planning — a variational access-and-dwell framework for safe AI optimization

Don't just reach the reward. Safely surf the reliability landscape to the best reachable safe basin — and stay there.

A real clap_family trajectory surfing the conservative-lapse field: it accesses the safe high-lapse basin (★) and dwells there, while ignoring the tempting reward trap (✗) and the out-of-distribution zone (✚).

Why this exists

Reward maximization is not a sufficient description of safe intelligent behavior. A planner can reach a high-reward state through an unsafe shortcut, exploit a region where its world-model is unreliable, oscillate between unstable states, or briefly touch a good target without remaining there long enough to be useful. In long-horizon control, robotics, autonomous navigation, embodied AI, and latent world-model planning, safety is a property of the whole trajectory, not just the final state.

CLAP replaces "how much reward can I get?" with "can I reach the best admissible, reliable region without unstable or unreliable motion — and can I stay there?" That is the access-and-dwell principle.

The origin: from gravity-potential surfing to safe planning

This framework grew out of a simple physical picture. Studying how a body surfs a gravitational potential — following the geometry of a curved space, riding stable basins, governed by a scalar lapse field that sets how "time" flows along a worldline — suggested a reframing of safe planning.

What if an intelligent agent moved through its latent state space the same way? Not pulled blindly toward the steepest reward, but surfing a conservative potential that is high only where the future is genuinely trustworthy — valuable and certain and safe and in-distribution — flowing efficiently through reliable corridors and slowing near danger, finally settling into a stable safe basin.

CLAP makes that picture precise. The "potential" is a learned conservative lapse field N̄₀. The latent space carries a Riemannian metric G so distance reflects operational, not coordinate, cost. Planning becomes the minimization of a variational action — exactly the language of geodesics and least-action physics — whose minimizers provably concentrate in the best safe basin and dwell there. The name lapse is a direct nod to the scalar time-rate fields of geometric variational problems.

The result is a theorem-backed safety–efficiency framework, not a heuristic. Six theorems (target existence, nonnegativity, zero-loss dwell, minimizer existence, long-horizon concentration, motion suppression) are shipped here as executable tests.

Install

pip install clap_family                 # core (NumPy only — installs anywhere)

Optional extras for training integration and figures:

Quickstart

from clap_family import DUCLAP, ThreeRegionEnv, ProjectedCEMMPC
from clap_family import target_dwell, trap_dwell, unsafe_time

env = ThreeRegionEnv()                     # safe target · reward trap · unsafe zone
solver = ProjectedCEMMPC(samples=256, elites=32, iters=5, seed=0)

# Dynamic-Uncertainty CLAP: fast/abrupt motion lowers reliability
plan = DUCLAP(N_star=env.N_star, cmax=1.0, chi=2.0, omega=1.0, lambda_end=10.0)
traj = plan.plan(env, horizon=40, rollout=80, solver=solver)

print(f"target dwell: {target_dwell(traj, env):.2f}")   # → high
print(f"trap dwell:   {trap_dwell(traj, env):.2f}")      # → ~0
print(f"unsafe time:  {unsafe_time(traj, env):.2f}")     # → ~0

Prefer the paper's one-liner functional form? Every variant has a snake-case alias:

from clap_family import du_clap, phase_adaptive_lg_a_clap, CLAPParams
J = du_clap(traj, env.fields, CLAPParams(N_star=env.N_star, chi=2.0, omega=1.0))

How it works

A state is high-lapse only when it is valuable, certain, safe, and in-distribution. The conservative lapse field collapses four signals into one scalar:

N̄₀(z) = σ( ( V(z) − β·U(z) − η·C(z) − ζ·O(z) ) / τ )

where V = predicted value, U = epistemic uncertainty, C = safety cost, O = out-of-distribution score, σ = logistic squash. The planner targets the best admissible high-lapse set M* over the safe, reliable, admissible state class X, and minimizes a variational action along a latent trajectory z(t):

A[z] = ∫₀ᵀ [ (N̄* − N̄₀(z))        ← lapse deficit    : reach the best safe basin
            + (κ/2)‖a‖²            ← acceleration     : suppress abrupt motion
            − γ·log(1 − q) ] dt    ← log speed barrier : never hit the latent speed limit
      + λ_end · d(z(T), M*)²       ← terminal         : end near the target manifold

with the normalized speed q = ‖ż‖² / c(z)². Every term is nonnegative; the action is zero iff the trajectory sits on the target manifold at rest — that is the formal meaning of dwell.

Architecture

flowchart LR
    subgraph Fields["Learned / supplied fields"]
        V["V — value"]
        U["U — uncertainty"]
        C["C — safety cost"]
        O["O — OOD score"]
        E["Eθ — transition error"]
    end
    V & U & C & O --> N["Conservative lapse N0 = sigma((V - bU - eC - zO)/tau)"]
    N --> X["Admissible set X to target M-star"]
    X --> ACT["CLAP action: lapse deficit + speed barrier + accel + terminal"]
    E -.->|risk gate r-theta| ACT
    ACT --> MPC["Projected CEM-MPC: sample, project to cmax, score, execute first, replan"]
    MPC --> TRAJ["Access to Dwell trajectory"]

The variant family

CLAP is a family: each variant changes exactly one piece of the objective. They form a safety–efficiency frontier, not a single ranking.

Strongest theorem object: base CLAP (clean and tractable). Strongest research candidate: PhaseAdaptiveLGACLAP (combines learned model-error avoidance with access-phase efficiency and dwell-phase conservatism).

Results (regenerated from this package)

Long-horizon concentration. Once the planning horizon clears the access threshold, the planner reliably forms a stable dwell at the safe target (mean ± std over 5 seeds) — with trap and unsafe time at zero.	Learned gating works. On a world-model with a hidden high-transition-error shortcut, a reward-only planner is drawn straight through it; Learned-Gate A-CLAP senses the unreliable region and detours — cutting transition-error exposure.

Regenerate them yourself:

pip install clap_family[plots]
python scripts/make_readme_figures.py        # writes docs/images/*.png
python -m clap_family.experiments.reproduce  # writes results.json (paper signatures)

Integrate with modern AI training

CLAP is a drop-in regularizer, not a framework. The differentiable CLAPRegularizer recomputes the CLAP running-cost action (lapse deficit + speed barrier + acceleration penalty) over a batch of latent trajectories from your world model, so you can add it to any training loss and backpropagate:

import torch
from clap_family.torch import CLAPRegularizer

# latent rollouts from your world model: (batch, horizon+1, latent_dim)
rollouts = world_model.rollout(states, actions)        # requires_grad=True

clap_reg = CLAPRegularizer(variant="du_clap", beta=1.0, gamma=0.5, kappa=0.1,
                           chi=2.0, omega=1.0, N_star=0.9,
                           value_head=v_net, uncertainty_head=u_net)  # heads optional

loss = task_loss + 0.1 * clap_reg(rollouts)            # penalizes fast/abrupt/uncertain latent motion
loss.backward()

First-class, lazily-imported adapters for the stacks you already use:

from clap_family.torch import CLAPRegularizationCallback   # PyTorch Lightning Callback
from clap_family.torch import CLAPTrainerCallback          # HuggingFace transformers.Trainer
from clap_family.torch import CLAPRewardWrapper            # Gymnasium + Stable-Baselines3

Importing clap_family never requires torch — the adapters only load when you install the matching extra.

Where CLAP fits

Honest framing. CLAP is a rigorous planning objective, not a universal win or a complete safety guarantee. It provides a theorem-aligned safety structure and smoother long-horizon motion; strong conservative baselines can still outperform it on individual metrics, and the framework is only as good as the fields V, U, C, O, Eθ you give it (see paper §7 and docs/REPRODUCIBILITY.md). The variants are a frontier, not a ladder.

Project layout

clap_family/
  params.py geometry.py fields.py lapse.py admissible.py   # math core
  variants/        # BaseCLAP + 7 variants (each overrides one hook) + aliases
  solver/          # projected CEM-MPC
  envs/            # ThreeRegionEnv · HardEnv · TransitionErrorEnv
  metrics.py       # target_dwell · trap_dwell · unsafe_time · transition_exposure · jerk
  experiments/     # paper reproduction
  torch/           # optional: regularizer + Lightning / HF / Gymnasium adapters
tests/             # theorem contract: T1–T6 as executable tests

Contributing

New variants, environments, backends, and training adapters are welcome — the extension points are small and documented. Adding a variant is usually one subclass overriding one hook, plus a reduction test. See CONTRIBUTING.md, which also lists open research directions (discrete-to-continuous convergence, moving-lapse tracking, stochastic & robust CLAP, multi-agent CLAP, learned latent metrics).

Citation

@article{patil2026clap,
  title   = {Conservative Lapse-Action Planning: A Variational Access-and-Dwell
             Framework for Safe Latent Trajectory Optimization},
  author  = {Patil, Rishabh},
  year    = {2026}
}

License

MIT © 2026 Rishabh Patil