507 add new node implementing jaakkola jordans lower bound on sigmoid log sigmoid in bishop prml

[mhidalgoaraya]

Add Jaakkola-Jordan Lower Bound Implementation for Sigmoid Node

This PR implements the Jaakkola-Jordan lower bound approximation for the sigmoid function as described in Bishop's "Pattern Recognition and Machine Learning" (PRML).

New Sigmoid Node Implementation:

• Added a new Sigmoid node with three interfaces: out, in, and ζ (zeta)
• Implemented the Jaakkola-Jordan lower bound using a variational parameter ζ
• Added corresponding average energy computation for the sigmoid node

Updated Message Passing Rules:

• ζ (zeta) rule: Computes the optimal variational parameter as ζ = √(μ² + σ²) where μ and σ are the mean and standard deviation of the input
• in rule: Updated to handle both Categorical and PointMass output distributions, computing weighted mean and precision using the Jaakkola-Jordan approximation
• out rule: Computes the output categorical distribution using the logistic function with the variational parameter

Mathematical Foundation:

• The lower bound uses: σ(x) ≥ σ(ζ) * exp((x-ζ)/2 - λ(ζ)(x²-ζ²))
• Where λ(ζ) = (σ(ζ) - 0.5)/(2ζ) and σ(ζ) is the logistic function
• The optimal ζ is computed as ζ = √(μ² + σ²) for maximum bound tightness

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 76.22%. Comparing base (be9acdc) to head (39d3242).
⚠️ Report is 58 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #529      +/-   ##
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+ Coverage   75.99%   76.22%   +0.23%     
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  Files         205      210       +5     
  Lines        6077     6163      +86     
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+ Hits         4618     4698      +80     
- Misses       1459     1465       +6     

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[bvdmitri]

I like the addition! @ismailsenoz could you also look at it?