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Quantum Gravity and Cognition
The talk demonstrates how to model ARC‑style grid reasoning as trajectories on a latent manifold using curvature and parallel‑transport concepts.
What if solving a reasoning task could feel like traversing curved space? In this talk, we explore a novel approach to cognition that treats symbolic thought as a geometric process. Inspired by quantum gravity, we model transformations in ARC-style grid tasks as paths over an emergent latent manifold — where meaning arises from entropy, transitions resemble spacetime curvature, and reasoning becomes a form of parallel transport.
I have code that shows how to encode discrete instructions into a continuous manifold…which opens up a lot of cool use cases for things in physics, AI, chemistry, materials, etc.
I’ll just be going threw a a code notebook that shows off the math and parallels to other advanced pure math topics & theoretical physics…but its all testable which is cool.
- PyTorchPyTorch is the open-source machine learning framework: it provides a Python-first tensor library with strong GPU acceleration and a dynamic computation graph for building deep neural networks.PyTorch, developed by Meta AI, is a premier open-source deep learning framework favored in both research and production environments. Its core is a powerful tensor library (like NumPy) optimized for GPU acceleration, delivering 50x or greater speedups for complex computations. The key differentiator is its 'Pythonic' design and dynamic computation graph (eager execution), which allows for rapid prototyping and simplified debugging compared to static-graph frameworks. Leveraging its Autograd system for automatic differentiation, practitioners build and train models for computer vision and NLP; major companies like Tesla (Autopilot) and Microsoft utilize PyTorch for critical AI applications.
- PyTorch GeometricPyTorch Geometric (PyG) is the specialized library for building and training Graph Neural Networks (GNNs) on structured data like graphs, point clouds, and manifolds, all within the PyTorch framework.PyTorch Geometric (PyG) is a powerful, modular extension for deep learning on irregular data structures (graphs, meshes, point clouds). It provides a comprehensive suite of state-of-the-art Graph Neural Network (GNN) models and a simplified API for rapid development. Key features include the `torch_geometric.data.Data` object for efficient graph representation, a specialized `DataLoader` for mini-batching large and small graphs, and optimized CPU/CUDA kernels for performance. PyG accelerates geometric deep learning: users can implement a GNN model in 10-20 lines of code and leverage multi-GPU support for scalable training on common benchmark datasets (e.g., Cora, QM9).
- ARC grid tasksThe Abstraction and Reasoning Corpus (ARC) is a psychometric benchmark: 1000 unique grid-based tasks evaluating an AI's general fluid intelligence via few-shot abstract reasoning.ARC grid tasks, formally the Abstraction and Reasoning Corpus, serve as a critical benchmark for Artificial General Intelligence (AGI). Introduced by François Chollet in 2019, the corpus comprises 1000 unique tasks: 400 for training and 400 for evaluation. Each task presents a small set (typically three) of input-output pairs, which are 2D colored grids (10 possible colors). The core challenge is to deduce the implicit transformation rule from these few examples (few-shot learning) and apply it to an unseen test grid, generating the correct output grid. This methodology specifically targets an agent’s capacity for abstract reasoning and generalization, prioritizing skill-acquisition efficiency over brute-force pattern recognition.
- spectral tripleA spectral triple $\left(A, H, D\right)$ is the core analytic structure in Noncommutative Geometry, generalizing Riemannian spin manifolds by encoding geometric and metric data via an algebra, a Hilbert space, and a Dirac-type operator.Spectral triples, $\left(A, H, D\right)$, are the foundational analytic structure in Noncommutative Geometry (NCG), a concept pioneered by Alain Connes. The triple comprises a $\ast$-algebra $A$, a separable Hilbert space $H$, and an unbounded self-adjoint Dirac-type operator $D$. This framework replaces a classical Riemannian spin manifold's smooth functions and Dirac operator with operator-algebraic data. The key constraint is the bounded commutator condition, $\left[a, D\right] < \infty$ for all $a \in A$. This analytic data is sufficient to recover the manifold's metric structure and allows for the generalization of the Atiyah-Singer index theorem. A critical application is the almost-commutative model, which successfully incorporates the Standard Model of particle physics within this geometric framework.