Dynamic Curvature Adaptation

This repository contains the official simulation suite for the Curvature Adaptation Hypothesis (CAH), a unified theory of cortical state that bridges cellular-level dendritic gating with functional geometric routing.

The Dynamic Curvature Adaptation manuscript is available here: https://doi.org/10.5281/zenodo.18615180

Figure 5: Thermodynamic Return on Curvature-Sensitive Control. Simulation of total metabolic cost (C_Total) as a function of SST gating intensity (γ). Red Line: Healthy hierarchical networks exhibit a transition near γ ≈ 0.8, beyond which local control expenditure is offset by a marked reduction in distributed signaling burden. This indicates that the architecture can convert gating cost into a real energetic return by gaining access to a more transport-efficient routing regime. Grey Line: Pathological networks with 30% synaptic pruning fail to realize the same return. Although maintenance cost is still incurred, pruning raises resistance to the transition and prevents the architecture from securing a comparable reduction in signaling cost, leaving the system trapped in a more metabolically expensive regime. Green Region: The macroscopic thermodynamic discount—the energetic advantage obtained when local control successfully purchases more efficient large-scale routing. In later refinements of CAH, this advantage is interpreted less as a simple reward for maximal global hyperbolicity and more as evidence that selective curvature-sensitive routing can produce a genuine return on investment under the right structural conditions."

Overview

The Curvature Adaptation Hypothesis (CAH) proposes that the brain does not operate within a single fixed geometric manifold. Instead, it may dynamically regulate its effective information geometry in response to hierarchical demand. In its foundational form, CAH identifies a plausible biophysical actuator—the Martinotti-cell subtype of Somatostatin (SST) interneurons—which regulates the apical-somatic conductance ratio (γ) and thereby modulates access to distinct routing regimes.

Within this framework, SST-mediated gating can shift cortical dynamics from a relatively flat baseline (κ≈0) toward more transport-efficient negative-curvature routing conditions (κ<0). The key claim is not simply that “more hyperbolic is better,” but that curvature-sensitive routing can reduce the effective relay burden of hierarchical inference, allowing the cortex to secure a real thermodynamic advantage under the right structural conditions.

Figure 2: Spiking Neural Network Validation. A PyNEST simulation of 280 integrate-and-fire neurons illustrating a plausible microcircuit mechanism for curvature-sensitive routing control. Left (0-500ms): Strong SST interneuron gating (red) suppresses pyramidal cell activity (blue), maintaining the network in a relatively conservative baseline regime. Right (500-1000ms): A step current activates VIP interneurons (green), which suppress the SST gates. This disinhibition allows the pyramidal population to spontaneously reorganize into highly synchronized 40Hz gamma-band pillars, providing a biologically plausible temporal signature of the local control dynamics that could open access to a more strongly integrated large-scale routing regime.

Key Theoretical Findings

Topological Robustness: Access to the negative-curvature routing transition is supported not only by precise global architecture, but also by preserved local degree structure and synaptic availability. The transition survives degree-preserving scrambling, but becomes substantially harder to access under synaptic loss.

Pathological Failures of Geometric Regulation: We model cognitive health and disease as distinct routing conditions rather than as simple fixed manifold states:

• Healthy: Flexible, regulated access to more transport-efficient routing regimes under hierarchical demand.

• Manic: Reduced selectivity of geometric regulation, where VIP-like hub integration biases the system toward less regulated, shortcut-dominated routing.

• Neurodegenerative: Restricted geometric access, where stochastic pruning raises resistance to efficient hierarchical routing and degrades large-scale integrative capacity.

Installation

The script energy_ROI_tracker.py depends on the physics engine in run_CAH_scaling_analysis.py. Please ensure both files are downloaded to the same directory before running.

Note: The PyNEST simulation requires NEST to be installed.

git clone https://github.com/MPender08/dendritic-curvature-adaptation.git
cd dendritic-curvature-adaptation

This project requires Python 3.8+ and the following scientific libraries:

pip install networkx numpy matplotlib pot tqdm joblib scipy

Simulation Suite

1. Finite-Size Scaling and Robustness (run_CAH_scaling_analysis.py)

python run_CAH_scaling_analysis.py

Reproduces Figure 1 from the manuscript. Tests whether the routing transition remains accessible across depths (N=3,5,7) and under degree-preserving topological scrambling. Optimization: Utilizes a Sparse Neighborhood Transport algorithm to reduce computational complexity for large graphs (N=7, ~8500 nodes), ignoring zero-mass entries in the distance matrix to accelerate the OT solver.

2. Pathological Hubs (Manic State) (run_CAH_with_Hubs.py)

python run_CAH_with_Hubs.py

Reproduces Figure 2. Introduces high-centrality “VIP-like” hub nodes to show how hyper-connectivity biases the system away from its conservative baseline and toward less regulated, shortcut-dominated routing.

3. Synaptic Pruning (Geometric Collapse) (run_CAH_Pruning.py)

python run_CAH_Pruning.py

Reproduces Figure 3. Simulates 30% stochastic spine loss to show how neurodegenerative pruning restricts geometric access and degrades hierarchical integration.

4. Metabolic ROI Tracker (energy_ROI_tracker.py)

python energy_ROI_tracker.py

Reproduces Figure 4. Quantifies the metabolic ROI of SST-mediated gating by comparing local control cost against reduced distributed signaling burden in healthy versus pruned networks.

Acknowledgments

Gemini AI was utilized as an interactive technical sounding board to rapidly prototype structural arguments and optimize PyTorch/NEST simulations. The author takes full and exclusive responsibility for the originality, validity, and final synthesis of the theoretical framework presented herein.