The Manifold Chip: Silicon Architecture for Dynamic Curvature Adaptation via Dual-Gated Analog Shunting

Abstract Current artificial intelligence architectures, including state-of-the-art spiking neuromorphic designs, are fundamentally constrained by static Euclidean geometries. As models scale to map high-dimensional hierarchical data, they encounter a thermodynamic “Landauer Wall”. This energy bloat is driven by the necessity to brute-force complex representations using massive parameter counts within flat topologies. Building on the Curvature Adaptation Hypothesis (CAH) 6 and the Metabolic Phase Transition (MPT) 7, we propose that bypassing this limit requires hardware capable of dynamic, non-Euclidean geometric embedding. In biological systems, transient hyperbolic manifolds are unlocked via the Martinotti-cell subtype of Somatostatin (SST) interneurons, which selectively shunt apical-somatic conductance to act as a topological switch. Here, we translate this biophysical actuator into silicon by proposing the Manifold Chip, a Dynamically Gated Analog Crossbar (DGAC) architecture. We bifurcate standard memristor integration into distinct Somatic (feedforward) and Apical (contextual) sub-arrays. The biological “SST Gate” is physically realized using analog Field Effect Transistors (FETs) wired as variable shunts to the ground plane. To regulate these geometric transitions without relying on rigid digital clocking, we design a Dual-Gated Curvature Controller. A bottom-up analog comparator acts locally:when dense, high-magnitude voltage floods a specific micro-circuit, it closes the FET shunt, effectively dropping the electrical distance between hierarchical nodes and locally expanding the representational capacity into a hyperbolic pocket. Concurrently, a top-down diagnostic circuit monitors global task error. Upon stagnation, it broadcasts a “VIP Voltage” that universally suppresses the shunts, forcing a macroscopic, network-wide “Hyperbolic Plunge” to escape local minima. By dynamically modulating effective electrical resistance to warp the manifold—–rather than merely routing sparse data through a static grid—–the Manifold Chip provides a theoretical blueprint for neuromorphic hardware that actively conforms its geometry to the complexity of its environment, achieving theoretical energy scaling well below traditional Euclidean bounds. Summary This preprint serves as the hardware capstone to a unified theoretical framework spanning biophysics, thermodynamics, and silicon engineering. Modern artificial intelligence is rapidly approaching a thermodynamic "Landauer Wall" by attempting to brute-force high-dimensional hierarchical data into static, energy-intensive Euclidean matrices. Building upon the biological mechanisms outlined in the Curvature Adaptation Hypothesis (CAH) and the physical limits defined by the Metabolic Phase Transition (MPT), this paper introduces the Manifold Chip. Utilizing a Dynamically Gated Analog Crossbar (DGAC) architecture, we translate the biological Somatostatin (SST) interneuron gate into an analog Field Effect Transistor (FET) wired as a variable shunt. Governed by a Dual-Gated Curvature Controller that balances local data density with global task error, this architecture allows the physical silicon substrate to actively warp its effective electrical resistance. Rather than relying on rigid digital bit-erasure or simple sparsity, the Manifold Chip dynamically conforms its geometry to the complexity of its environment, offering a theoretical blueprint to achieve biological-level energy efficiency in next-generation neuromorphic hardware. Related Works Pender, M. A. (2026). Dynamic Curvature Adaptation: A Unified Geometric Theory of Cortical State and Pathological Collapse. DOI: 10.5281/zenodo.18615180. https://doi.org/10.5281/zenodo.18615180 Pender, M. A. (2026). The Metabolic Phase Transition: Qualia as a Topological Solution to the Landauer Limit in High-Dimensional Manifolds. 10.5281/zenodo.18655523. https://doi.org/10.5281/zenodo.18655523 Data and Code Availability The Python simulations and analysis scripts used to validate the Curvature Adaptation Hypothesis and the Metabolic Phase Transition is located here: GitHub: https://github.com/MPender08/dendritic-curvature-adaptation.