Solving complex problems transparently
Research
Mechanica Labs studies the internal computations of neural networks using algebraic structure, geometry, and rigorous mechanism-level analysis. Our goal is to identify the principles that govern how models represent and compute, and to develop a mathematical framework that generalizes across architectures and tasks.
Mechanistic Interpretability
We investigate how neural networks implement specific computations by analyzing their internal circuits, subspaces, and representations. Our work focuses on identifying algorithmic mechanisms that emerge during training—particularly in settings where the target function has clear algebraic or combinatorial structure, such as modular arithmetic or group operations. By isolating these mechanisms and characterizing their invariances, symmetries, and decomposition properties, we aim to establish general templates for how neural networks encode discrete computations.
Algebraic and Geometric Structures
We apply tools from algebraic geometry, topology, and representation theory to describe the structure and organization of learned features. This includes modeling representations using geometric and topological invariants, analyzing how group actions and symmetries are reflected in learned embeddings, and identifying fiber, orbit, and quotient structures that mirror the underlying algebra of the task. This perspective provides a rigorous way to characterize the internal state space of a network and to understand why certain representations are stable, efficient, or universal across architectures.
Crystallography and Mining Applications
We extend symmetry- and geometry-aware explainable machine learning methods to problems in crystallography and mineral exploration. Current work involves lattice and space-group prediction, symmetry-consistent representation learning, and mineralogical and geological inference. These applications serve as a bridge between abstract representation theory and physical systems where symmetry, periodicity, and geometric constraints play a central role.