What I cannot create, I do not understand. — Richard Feynman, American theoretical physicist

Most of what I know about my own research, I did not learn from reading the paper. I learned it from watching the algorithm do something I did not expect, and then working backwards to figure out why. Indeed, a figure in a paper is a single frozen moment of a process, and it is in interacting with that process (changing an input, stepping through a decision, breaking an assumption on purpose) that a reader builds the intuition the paper was trying to transfer in the first place. This page collects interactive explainers for the concepts behind my research, each one a small simulation that lets you poke at an idea until it stops being abstract. Fundamentally, I believe that good visualization is a form of argument, and that the best way to understand a theory of learning is to watch it learn.

Each card opens its own simulation, written in the register of the papers it draws from and linked to the original work - please reach out if something is unclear or if you would like to see a concept covered!

~/education/cobweb 1/3
cognitive science CogSci 2026 ACS 2025 ACL Findings 2026

Cobweb: Concept Formation as Information Gain

An interactive walkthrough of Fisher’s (1987) Cobweb as recent work implements it: an incremental learner that sorts each experience into a taxonomy of probabilistic concepts, choosing among four restructuring operators to maximize the information its concepts carry about their members. The simulation steps through each operator, traces a prediction through the hierarchy, revisits three classic categorization experiments, and closes on the applications of Cobweb to semantic retrieval and lifelong topic modeling.
concepts/
  • instances, concepts, and the taxonomy that links them
  • the four operators: insert, create, merge, and split
  • prediction by best-first search over pointwise mutual information
  • central tendency and frequency (Hayes-Roth & Hayes-Roth, 1977)
  • exemplar similarity over prototype distance (Medin & Schaffer, 1978)
  • the prototype-to-exemplar transition (Smith & Minda, 1998)
  • applications to retrieval and topic modeling

open the simulationpapercobwebcobweb-psych

~/education/trellis 2/3
cognitive architecture ACS 2026

TRELLIS: A Unified Account of Concepts and Chunks

An interactive walkthrough of TRELLIS, which extends Cobweb from concepts that generalize to chunks that compose. Every element of an experience is described twice, by its content and by its context, and stored in two linked Cobweb taxonomies; parsing and generation then reduce to sorting, and learning needs no mechanism beyond Cobweb’s own. The simulation inspects both descriptions, steps a greedy parser through its recognition gate, varies the recall threshold that governs generation, and closes on learning curves for three synthetic grammars.
concepts/
  • concepts versus chunks: generalization and composition
  • content and context instances for every element
  • two intertwined taxonomies in place of a grammar
  • greedy parsing with a recognition gate
  • generation, recall thresholds, and errors of commission
  • errors of omission and commission as evaluation

open the simulationpaper

~/education/diffusion 3/3
generative models ACS 2026

Diffusion Models and Concept Formation

An interactive walkthrough of the argument that diffusion models, built for image synthesis, implicitly form a concept hierarchy like Cobweb’s. The noisy marginals of a diffusion model are Gaussian smoothings of the data whose modes merge into a taxonomy of prototypes as noise grows, and a basic level of greatest distinctiveness emerges at an intermediate noise level. The simulation computes these quantities exactly on toy data and closes on the paper’s comparison with Cobweb on MNIST and Fashion-MNIST.
concepts/
  • noisy marginals as kernel densities, and noise level as depth
  • modes, score ascent, and Tweedie prototypes
  • parent pooling and the law of total variance
  • recovering a mode-path taxonomy bottom-up
  • distinctiveness and the basic level
  • matching diffusion modes to Cobweb concepts

open the simulationpaper