# Self-Evidencing Through Hierarchical Gradient Decomposition: A Dissipative System That Maintains Non-Equilibrium Steady-State by Minimizing Variational Free Energy

arXiv: https://arxiv.org/abs/2510.17916 · HTML: https://mlsanity.com/paper/2510.17916/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 76 references that are in the map.
- First posted on arXiv 20 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science](https://mlsanity.com/paper/1707.04780/) (2017)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Dense Associative Memory for Pattern Recognition](https://mlsanity.com/paper/1606.01164/) (2016)
- [Large Associative Memory Problem in Neurobiology and Machine Learning](https://mlsanity.com/paper/2008.06996/) (2020)
- [Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of neoHebbian Three-Factor Learning Rules](https://mlsanity.com/paper/1801.05219/) (2018)
- [The free energy principle for action and perception: A mathematical review](https://mlsanity.com/paper/1705.09156/) (2017)
- [A free energy principle for a particular physics](https://mlsanity.com/paper/1906.10184/) (2019)
- [Feedback alignment in deep convolutional networks](https://mlsanity.com/paper/1812.06488/) (2018)
- [The free energy principle made simpler but not too simple](https://mlsanity.com/paper/2201.06387/) (2022)
- [From Past to Future: Rethinking Eligibility Traces](https://mlsanity.com/paper/2312.12972/) (2023)

## Built on by (most cited first, 1 of 1)

- [Gradient-Free Warm-Start Library Recovery: an Amortized-Regret Separation](https://mlsanity.com/paper/2606.21253/) (2026)

## Abstract (arXiv)

The Free Energy Principle (FEP) states that self-organizing systems must minimize variational free energy to persist, but the path from principle to implementable algorithm has remained unclear. We present a constructive proof that the FEP can be realized through exact local credit assignment. The system decomposes gradient computation hierarchically: spatial credit via feedback alignment, temporal credit via eligibility traces, and structural credit via a Trophic Field Map (TFM) that estimates expected gradient magnitude for each connection block. We prove these mechanisms are exact at their respective levels and validate the central claim empirically: the TFM achieves 0.9693 Pearson correlation with oracle gradients. This exactness produces emergent capabilities including 98.6% retention after task interference, autonomous recovery from 75% structural damage, self-organized criticality (spectral radius p ~= 1.0), and sample-efficient reinforcement learning on continuous control tasks without replay buffers. The architecture unifies Prigogine's dissipative structures, Friston's free energy minimization, and Hopfield's attractor dynamics, demonstrating that exact hierarchical inference over network topology can be implemented with local, biologically plausible rules.