axisnorm, axisexp, axisbernstein poi models

[pmlugato]

Summary

Adds three new param model classes (AxisNormModel, AxisExpModel,
AxisBernsteinModel) for per-cell signal normalization and exponential or
first-order Bernstein polynomial background parameterization. All three classes
live in rabbit/param_models/param_model.py and are registered in
rabbit/param_models/helpers.py. Multiple models can be composed on a single
fit via repeated --paramModel flags, handled automatically by
CompositeParamModel. Also fixes load_models to derive the composite's
allowNegativeParam from its sub-models rather than from the CLI flag, so axis
models that manage their own reparameterization internally are not incorrectly
squared by the fitter when composited.

Changes

param_model.py

AxisNormModel: new class. Assigns one independent normalization parameter
per (process, cell) where cells are defined by caller-specified axes looked
up from indata.channel_info. allowNegativeParam=True; non-negativity is
enforced by applying tf.square inside compute() (a softplus alternative is
commented out — avoids the zero-gradient saddle at raw=0 but both produce
equivalent results at the minimum). Default raw = sqrt(1) = 1 so norm=1
at initialization. All other channels and processes are left at 1.0.

AxisExpModel: new class. Assigns per-cell lnAmpl and per-group slope
parameters producing rnorm = exp(lnAmpl + slope·x) across the shape axis.
Both parameters are unconstrained reals (allowNegativeParam=True); slope=0
(flat background) is an interior point so the Hessian is non-degenerate there.
Slope can optionally be shared across a coarser axis grouping via an optional
5th CLI argument slope_axes, reducing parameters and stabilizing the Hessian
when per-cell slopes are under-constrained.

AxisBernsteinModel: new class. Assigns two non-negative parameters
(c₀, c₁) per (process, cell) and produces
rnorm(x_m) = c₀·(1−x_m) + c₁·x_m (first-order Bernstein polynomial) where
x_m ∈ [0,1] is the normalized mass bin center. Non-negativity is enforced
via softplus applied inside compute() (allowNegativeParam=True; raw
optimizer parameters are unconstrained reals). Default raw parameter is
softplus⁻¹(1) ≈ 0.5413, so c₀=c₁=1 at initialization (flat unit
background). An alternative (lnAmpl, frac) parameterization is available as
commented-out code: rnorm = 2·exp(lnAmpl)·[sigmoid(frac)·(1−x) + sigmoid(−frac)·x].
This decouples overall amplitude from shape, reducing the near-null-space
dimensionality per near-empty cell from 2D to 1D (same structure as
AxisExpModel), at the cost of less directly interpretable parameters.

param_models/helpers.py

Registers AxisNormModel, AxisExpModel, and AxisBernsteinModel in the
built-in model loader so they resolve without a full dotted module path.
load_models derives the composite's allowNegativeParam as
any(m.allowNegativeParam for m in models) so that axis models with
allowNegativeParam=True are not incorrectly squared by the fitter when used
inside a CompositeParamModel.

Usage examples

# Exponential background with slope shared per eta bin
rabbit_fit.py tensor.hdf5 -o results/ \
  --paramModel AxisNormModel <channel> signal   pt,eta,charge \
  --paramModel AxisExpModel  <channel> bkgExp   mass pt,eta,charge eta

# First-order Bernstein background, one (c₀,c₁) per cell
rabbit_fit.py tensor.hdf5 -o results/ \
  --paramModel AxisNormModel      <channel> signal     pt,eta,charge \
  --paramModel AxisBernsteinModel <channel> background mass pt,eta,charge