Blog

Layerwise geometry of factual resistance in Qwen2.5-3B-Instruct: a shared false-belief representation emerges before becoming causally aligned with factual resistance.

Tracking RoPE's implicit positional manifold through the residual stream of Qwen2.5-3B: it stays Fourier/RoPE-like along displacement, and is approximately linearly transported (rotated, stretched, occasionally reorganized) along depth.

Comparing how different models carve up space on shared labeled grids: scan-line profiles, an exact axis-alignment tax, and a general run-based lower bound on tree complexity.

Motor cortex population activity from a macaque maze-reaching task: PCA latent trajectories, early vs. late session geometry via participation ratio, Procrustes distance, and RSA.

A command-line tool that profiles tensor artifacts (.npy, .npz) for sparsity, entropy, and spectral structure, then routes each to the best compression strategy: quantization, sparse COO storage, or truncated SVD.

How discrete tick size and integer inventory reshape a continuous market-making model on prediction markets like Kalshi, and the dimensionless ratio that decides when the exchange grid actually matters.

A recursive, self-similar approach to the infinite binary tree puzzle, reduced to a pair of fixed-point equations and solved by binary search.

Our first time taking a swing away from the books: a round-by-round write-up of Pandera's run to 23rd worldwide.

The March 2025 puzzle.

The February 2025 puzzle.

A games-night wordplay that decodes to a familiar phrase.

A single reference built from my notes learning C++ and CUDA, from language basics and OOP through kernels, unified memory, streams, and an n-body simulator.

A Philosophy of Study. Mathematics as the language of generative structure, and why emergence itself is worth studying.