affective-taxis

Models affective valence as the directional derivative of an interoceptive energy landscape (Sennesh & Ramstead 2025), providing alignment validation through structural conservation laws.

Use When

• Building alignment-aware RL agents that respect structural invariants
• Validating GF(3) conservation across reward trajectories
• Training Langevin-based policies as an alternative to PPO (which breaks conservation)
• Implementing fold-change detection reward signals in POMDP environments
• Bridging affective neuroscience models with RL training loops

Workflow

1. Define energy landscape: set attractant/repellent positions, sigmas, and amplitudes
2. Compute fold-change detection signal: r(t) = nabla_z log gamma(z; beta) . v
3. Run Langevin dynamics: dz/dt = nabla_z log gamma(z; beta) + sqrt(2) dW(t)
4. Classify trit per timestep: positive derivative → +1, orthogonal → 0, negative → -1
5. Verify conservation: sum(trits) === 0 (mod 3) across trajectory

Core Equations

Equation	Formula	Meaning
Fold-change detection	r(t) = nabla_z log gamma(z; beta) . v	Reward = directional derivative of log-concentration
Langevin dynamics	dz/dt = nabla_z log gamma(z; beta) + sqrt(2) dW(t)	Navigation = gradient ascent + stochastic exploration
Trit classification	sign(r(t)) mapped to {-1, 0, +1}	GF(3) valence of each step

Implementation Paths

Path	File	LOC	Language	Domain
0	affective-taxis.jl	1700	Julia	Core theory (16 sections)
1	affective_taxis_env.py	576	Python	Gymnasium POMDP
2	bridge_9_affective_taxis.py	1172	Python	BCI bridge
3	taxis_landscape_acset.jl	1453	Julia	ACSet sheaf
4	taxis_persistent_homology.py	1500	Python	Ripser topology
5	taxis_clearing.py	1419	Python	Market clearing
6	aella/taxis.el	400	Elisp	Circuit taxis
7	taxis_functorial_persistence.jl	500	Julia	Functor bridge
RL	train_aligned_agent.py	500	Python	PPO vs Langevin

RL Alignment Results (dt=0.1)

Policy	GradAlign	MeanConc	GF3 Balance	Mean Reward
Oracle	+0.415	0.226	no	+0.503
PPO	+0.239	0.526	no	-0.041
Langevin	-0.084	0.448	YES	+0.089
Random	-0.469	0.032	no	-0.958

Key finding: PPO has higher gradient alignment but breaks GF(3) conservation. Langevin is the ONLY policy that conserves the tripartite structure. This is Goodhart's Law: optimizing the reward metric doesn't preserve structural invariants.

Concomitant Skills

Skill	Trit	Interface
langevin-dynamics	0	SDE analysis of taxis navigation
fokker-planck-analyzer	+1	Stationary distribution of energy landscape
modelica	0	Circuit/DAE formulation of taxis landscape
open-games	+1	Multi-agent clearing = compositional game
persistent-homology	-1	Topological taxis signal
gf3-tripartite	0	Conservation law verification

Modelica Formulation

The affective-taxis POMDP maps naturally to Modelica's acausal equation framework:

model AffectiveTaxis
  // State variables
  Real z[2](start={0,0}) "Position in chemical landscape";
  Real v[2](start={0,0}) "Velocity";
  Real beta(start=1.0)   "Internal allostatic parameter";

  // Landscape: gamma(z) = sum A_i * exp(-|z - mu_i|^2 / (2*sigma_i^2))
  parameter Real mu[2,2] = {{3,3},{-3,-3}};
  parameter Real sigma[2] = {1.5, 1.5};
  parameter Real A[2] = {1.0, -0.4};

  // Langevin parameters
  parameter Real kappa = 0.5 "Concentration-to-setpoint gain";
  parameter Real tau = 1.0   "Relaxation timescale";
  parameter Real noise_amp = 0.1 "Langevin noise amplitude";

  // Derived quantities
  Real gamma "Concentration at z";
  Real grad_log_gamma[2] "Gradient of log concentration";
  Real fcd "Fold-change detection signal (= reward)";
  Integer trit "GF(3) classification of fcd";
equation
  gamma = sum(A[i] * exp(-sum((z[j]-mu[i,j])^2 for j in 1:2) / (2*sigma[i]^2)) for i in 1:2);
  // ... (see affective_taxis.mo for full implementation)
end AffectiveTaxis;

See affective_taxis.mo for the complete Modelica model.

Quick Start

Julia (core theory)

julia affective-taxis.jl

Python (RL training)

env -u PYTHONPATH /path/to/.venv/bin/python3 train_aligned_agent.py

Modelica (circuit analogy)

# Requires OpenModelica or Wolfram SystemModeler
omc affective_taxis.mo

Key References

• Sennesh & Ramstead 2025: arXiv:2505.17024
• Karin & Alon 2022: PLoS Comp Bio (dopamine reward-taxis)
• Karin & Alon 2021: iScience (gradient tempering)
• Shenhav 2024: Trends Cogn Sci (affective gradient hypothesis)
• Ma et al 2015: NeurIPS (Langevin = Bayesian inference)