The Terrain of LearningGeometry of Reasoning and Dynamics of Intelligence

From space to terrain, from terrain to motion, from motion to convergence, from convergence to reasoning

Start Reading

Vol.I: The Terrain of Learning

Vol.II: Walking and Belief

Vol.III: The Geometry of Reasoning

Vol.IV: Algorithmic Landscapes

Vol.I: The Terrain of Learning (3 chapters)

Building geometric intuition. Parameter space, representation space, loss terrain, gradient fields, Euler steps — where the model's body lives, how its vision forms, how the terrain guides motion.

Vol.II: Walking and Belief (3 chapters)

Optimizers as ways of walking, non-Euclidean distance, dynamical systems and fixed points. ResNet = explicit Euler, GPT autoregression = Euler in hidden state space, DEQ = fixed point iteration.

Vol.III: The Geometry of Reasoning (3 chapters)

Chain of thought is not reasoning itself, but the visible projection of the reasoning trajectory. Attractors, verifiers, RLHF — how the reasoning field is reshaped by training.

Vol.IV: Algorithmic Landscapes (3 chapters)

Classical algorithms geometrized. Linear regression, PCA, SVM, Attention, LoRA, Diffusion — one figure, one formula, one experiment per chapter.

Author

Li Zixi (Mr. Pallas's Cat)

Author