---
tags:
- lan
- ssm
- hssm
- angle
- collapsing-bound
library_name: onnx
license: bsd-2-clause
---

# angle_extended (LAN)

Likelihood approximation network for the angle_extended sequential sampling model: the standard angle model -- constant drift v with a linearly collapsing decision bound whose collapse angle is theta -- with the drift bounds widened from (-3, 3) to (-6, 6) for designs that produce strong evidence. Parameters are v, a, z, t, theta, in that order, and the network was trained on the full ssm-simulators bounds for the model.
Recovery verdict: PASS. Judged alone on a 240-fit sweep (12 design cells x 20 paired datasets, 81 family-corrected tests) this network records zero coverage failures, zero bias failures, and zero cells the design could not identify, with 84% of parameter records converged (r-hat <= 1.01, bulk ESS >= 400). The extended drift range is exercised, not merely declared: density checks and recovery truths reach |v| near 4.5 and beyond. The sweep contains no analytical or blackbox reference arm -- none exists for a collapsing- bound model -- so, as with every LAN in this family, coverage is judged against nominal rather than against an exact-likelihood ceiling.
Density: the worst Hellinger distance to a 20k-trial simulation is 0.054, which is BELOW the Monte Carlo sampling floor at that sample size (ratio 0.92 against a gate bar of 3.0) -- the network is closer to the simulator than the simulator is to itself at 20k trials. Total probability mass stays within 0.4% of 1.0 on every draw.
A minority of truth draws produce genuinely hard posteriors -- long sampler trajectories, occasional non-convergence; wall time and convergence correlate at -0.50 across the sweep. This is posterior geometry at specific truths, not a defect localised to the network, and no design cell fell below the judgement threshold because of it.

## Architecture

- **Network Type:** lan
- **Layer Sizes:** [128, 128, 128, 128, 1]
- **Activations:** ['tanh', 'tanh', 'tanh', 'tanh', 'linear']

## Training

- **Epochs:** 20
- **Optimizer:** adam
- **Learning Rate:** 0.001
- **Loss:** huber

## Usage with HSSM

```python
import hssm

# p_outlier=0.0 is deliberate. HSSM attaches a 5% lapse by default, but the
# training data contains no lapses, so the default misspecifies every fit --
# the bias stays fixed while the posterior sd shrinks as 1/sqrt(n), so
# coverage gets WORSE as the dataset grows. Set a lapse only if your data
# actually has one.
model = hssm.HSSM(data=data, model="angle_extended", p_outlier=0.0)

# On an HSSM release that predates the built-in config, pass the network
# and the box explicitly. Keep the parameter order exactly as written: it
# is the ONNX input column order, and a wrong order does not raise -- it
# silently evaluates the wrong likelihood.
model = hssm.HSSM(
    data=data,
    model="angle_extended",
    loglik="angle_extended.onnx",
    loglik_kind="approx_differentiable",
    p_outlier=0.0,
    model_config={
        "list_params": ["v", "a", "z", "t", "theta"],
        "backend": "jax",
        "bounds": {
            "v": (-6.0, 6.0), "a": (0.3, 3.0), "z": (0.1, 0.9),
            "t": (0.001, 2.0), "theta": (-0.1, 1.3),
        },
    },
)
```

## Citation

If you use this model, please cite:

- [LANfactory](https://github.com/lnccbrown/LANfactory)
- [HSSM](https://github.com/lnccbrown/HSSM)