Research

Mental Representations

Meaning isn't stored in a single place. It's distributed.

There is no single neuron or brain region that "holds" the word dog. Meaning emerges from patterns of activation distributed across millions of interconnected neurons, shaped by every context in which that word has appeared. Click words from the two groups below. Notice that words within the same category activate overlapping but distinct patterns, while words from different categories share only a small core of neurons encoding general biological knowledge.

// research Distributed representations are central to my view of linguistic knowledge: not a rule system applied to input, but a high-dimensional space of patterns learned from exposure. This framing motivates my interest in storage: a holistically stored phrase is one whose representational geometry has been shaped by its full usage history, not merely assembled from its parts.

Learning

Prediction error drives shifts in representations.

A core claim of usage-based linguistics is that linguistic knowledge is learned, not innate, and that the mechanism is error-driven: representations are updated proportionally to how wrong a prediction was. The Rescorla-Wagner model formalizes this: ΔV = αβ(λ − ΣV), where α is cue salience, β is learning rate, λ is the expected outcome value (the associative strength the cue would carry once fully conditioned, analogous to a training label), and ΣV is the total current prediction across all active cues. The term (λ − ΣV) is the prediction error: how far the system's current prediction falls from the expected outcome. The notation V for associative strength follows the original Rescorla-Wagner convention. This rule captures several counterintuitive effects (blocking, extinction, overexpectation) purely from the logic of prediction error minimization.

// research Error-driven learning is the primary mechanism in my models of how linguistic representations change with exposure, including how binomial order preferences become entrenched. The key prediction: as a phrase becomes more predictable, prediction error decreases, and the representation shifts from computed to stored.

Computational Modeling

How much of language is memorized, and how much is assembled?

One test case for the storage-computation tradeoff is binomial expressions: phrases like bread and butter or black and white, where word order is conventionalized. A purely compositional system derives a phrase's meaning by combining its parts, treating both orderings as equivalent (since the operation is symmetric). A holistic system stores the canonical form as its own unit, with a representation shaped by its specific usage history. Under holistic storage, the two orderings are no longer equivalent; they occupy distinct positions in representational space.

Frequency is what predicts where a binomial falls on this continuum: high-frequency binomials are more likely to have developed holistic representations; low-frequency ones remain compositional. The visualization below uses GloVe word embeddings (reduced to 2D) to illustrate this. At Compositional, both orderings of a phrase map to the same point (their meaning is just the average of the two words, regardless of order). Drag toward Holistic: the two orderings separate, with high-frequency binomials (larger, brighter) diverge more than low-frequency ones (smaller, dimmer).

Noisy-Channel Comprehension & Frequency-Dependent Preference Extremity

Language is transmitted through a noisy channel. Words get swallowed in a crowd, misheard over a bad connection, or garbled by a fast speaker. A rational listener doesn't simply record what they heard — they infer what the speaker most likely intended, given both the signal that arrived and prior knowledge about what speakers tend to say. This is the core insight behind noisy-channel models of comprehension (Gibson et al., 2013): perception is not passive recording but active probabilistic inference.

For binomials, the relevant "noise" is word-order error: the possibility that a speaker intended one ordering but produced the other. A listener who hears butter and bread doesn't necessarily update toward believing that order is acceptable — they may instead infer that the speaker meant bread and butter and made a slip. The noisy-channel model formalizes this: P(Sᵢ | Sₚ) ∝ P(Sᵢ) · P(Sᵢ→Sₚ), where Sᵢ is the inferred intended ordering, Sₚ is what was perceived, P(Sᵢ) encodes abstract ordering preferences (shorter before longer, animate before inanimate, and so on), and P(Sᵢ→Sₚ) is the probability that the intended form was distorted into the perceived form. Frequency does not strengthen the prior — it determines N: how many times a learner encounters the expression.

This framework can be used to model how ordering preferences evolve across generations of learners. In an iterated learning paradigm, each generation hears N tokens, updates beliefs via noisy-channel inference, and passes the language on. When listeners infer slightly more noise than speakers actually produce, a small bias compounds across generations: the preferred ordering becomes increasingly dominant, but only for high-N expressions. Low-frequency binomials lack the exposure for the compounding to take hold, so their preferences stay weak and variable. Toggle noise below to see: without noise, all N-curves collapse to the diagonal and frequency has no effect.

// research This model (Houghton & Morgan, 2024) demonstrates that frequency-dependent preference extremity can arise purely from noisy-channel processing, and that it requires listeners to infer more noise than speakers actually produce. The model accounts for the corpus-wide distribution of binomial ordering preferences across 594 binomials from Morgan & Levy (2015). It also offers a natural explanation for why the most frozen, non-reversible binomials — bread and butter, black and white, rise and fall — tend to be the most frequent: high frequency means more exposures, more inferential compounding, and stronger polarization away from the dispreferred order. Freezing is not an accident of convention; it is a predictable consequence of being heard often.

Statistics

Quantifying uncertainty, updating beliefs from data.

Most of my work combines Bayesian modeling and mixed-effects regression, chosen because they make assumptions explicit and quantify uncertainty rather than collapsing it into a p-value. This section walks through the intuition behind each.

For Bayesian modeling, I walk through an extended example from the social deduction game Werewolf, a game I genuinely enjoy and one that maps almost perfectly onto the structure of Bayesian inference. No statistics background required.

The Setup

You're playing Werewolf: 5 players, 1 is secretly the werewolf. You don't know who. During the game you observe someone acting suspiciously. Should that update your belief that they're the werewolf? It depends entirely on their baseline rate of acting suspicious, and critically on whether that rate differs between their werewolf and innocent roles. Compare two players from past games:

Behavioral History

Before the current round starts, you've been keeping mental tally marks across all previous rounds. For each player you track two columns: how often they acted suspiciously when they were the werewolf, and how often they acted suspiciously when they were innocent. We encode these counts as Beta distributions:

These distributions are fixed for the duration of the current round — you're using what you learned before to make inferences now.

Updating P(W)

A new round begins. P(W) = 1/5 — one werewolf among five players. Each observation updates it via Bayes' rule, and the result becomes the new P(W) going into the next observation. The likelihoods come directly from the behavioral history:

How much P(W) moves is controlled by the likelihood ratio P(S|W) / P(S|I). For Charles, 0.80 / 0.80 = 1: S is equally likely under either role, so it leaves P(W) unchanged. For Spencer, 0.80 / 0.20 = 4: each S quadruples the odds he's the werewolf. Same observation, same rule — different behavioral history, different inference.

The key takeaway: what you know about a player from past rounds directly shapes what you can infer from their behavior now. The priors θ_w and θ_i aren't just background noise. They encode the entire history of how each player has acted across roles. A player who was always suspicious as the werewolf and always suspicious as an innocent gives you nothing to work with. A player whose suspicious behavior reliably tracks their role is the one whose actions actually move the needle.

// research The Bayesian framework is more than a statistical convenience. Comprehenders appear to function as probabilistic inference engines, combining prior knowledge with incoming evidence. My experimental work tries to measure both quantities directly, and the connection to neural network behavior (Kapatsinski, 2026) suggests these may not be two separate stories.

Mixed-effects regression is the everyday workhorse of experimental linguistics. It models how one variable predicts another while accounting for structure in the data: multiple observations from the same participant, the same words appearing across participants. Treating those groups as independent inflates confidence; mixed effects pool information across groups in a principled way, a process called partial pooling.

The Question

Does word frequency predict reaction time in a lexical decision task? High-frequency words should be recognized faster. But the size of that effect probably varies across participants: some readers are more sensitive to frequency than others. A mixed-effects model estimates both the population-level trend and participant-specific deviations from it simultaneously.

The Model

The random effects [b₀ᵢ, b₁ᵢ] are assumed jointly normal, centered at zero:

Why Not Just Fit Each Participant Separately?

Each participant contributes only a limited number of observations, so per-participant ordinary least squares estimates are noisy. The mixed model exploits the fact that participants are drawn from the same population: extreme estimates get pulled toward the group mean in proportion to how uncertain they are. This shrinkage improves estimation without assuming everyone is identical. The dashed white line in the demo below is the fixed effect; the colored lines show each participant's model-estimated slope, already partially pooled toward the population.

// research Mixed-effects models are foundational to my experimental work. When measuring reading times, ordering preferences, or recognition responses, the model must account for the fact that items and participants each introduce their own variance. The random effects structure reflects the actual data-generating process and determines which conclusions the data can support.