Joshua Nunley

Joshua Nunley

Laws and institutions shape individual outcomes through complex interactions with citizens' diverse circumstances, yet how different voting methods navigate this coupled landscape remains poorly understood. We model collective governance as optimization on NK fitness landscapes, where shared bits (laws) are updated by voting while individual bits (personal traits) remain fixed. A cross-dependency parameter $α$ controls how legislation's effects depend on individual circumstances. We compare eight standard voting methods and a generalized scoring family across landscape ruggedness $K \in \{1,\ldots,20\}$ and $α\in [0,1]$ with 1000 runs per configuration. Under direct democracy, the optimal voting method undergoes sharp phase transitions as a function of landscape complexity: cardinal score voting dominates on smooth landscapes, ordinal scoring with $p=0.35$ at low-to-moderate ruggedness, Borda count across a wide middle range, and STAR voting at the highest complexity. A two-parameter empirical formula reduces the $(K, α)$ plane to a single complexity axis for visualization. Borda count achieves the highest mean fitness and lowest variance across most of the parameter space. We further introduce a representative democracy model parameterized by identity weight $β$ and candidate self-interest $p_{\mathrm{self}}$. Representation reshapes the complexity-dependent structure even under favorable conditions: cardinal score voting dominates across most regimes, with plurality emerging as the top method at high $β$ and low-to-moderate $p_{\mathrm{self}}$.

Joshua Nunley

Communication is typically understood as indication: signals that transfer information from sender to receiver. We present a minimal predator avoidance task in which pairs of evolved CTRNN agents use communication for robust survival, and in which agents hear their own vocalizations, as in natural systems. Across 112 perfect-fitness agents from over 2,000 evolutionary runs, three dominant strategies emerge (accounting for 81% of agents): safety calling (39%), where agents signal from safe cover; alarm indication (22%), where agents vocalize when a threat is present without relying on self-hearing; and self-regulatory calling (20%), where agents depend on hearing their own call to sustain escape behavior. Self-hearing dependency is common among agents that call during an active threat (47%), but rare among agents that call only after reaching safe cover (10%; p < 10^-4). This pattern is consistent with a difference in causal order: safety callers act then communicate, while self-regulatory callers communicate in order to act. Removing self-hearing selectively impairs self-regulatory callers (fitness 0.40) while safety callers remain functional (0.90; p < 10^-9). These results show that communication can evolve to serve the caller's own behavioral regulation, not just information transfer to others.

Joshua Nunley

How does the brain predict physical outcomes while acting in the world? Machine learning world models compress visual input into latent spaces, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world models: architectures preserving sensory topology so that physics prediction becomes geometric propagation rather than abstract state transition. We implement this using neural fields with motor-gated channels, where activity evolves through local lateral connectivity and motor commands multiplicatively modulate specific populations. Three experiments support this approach: (1) local connectivity is sufficient to learn ballistic physics, with predictions traversing intermediate locations rather than "teleporting"; (2) policies trained entirely in imagination transfer to real physics at nearly twice the rate of latent-space alternatives; and (3) motor-gated channels spontaneously develop body-selective encoding through visuomotor prediction alone. These findings suggest intuitive physics and body schema may share a common origin in spatially structured neural dynamics.

Joshua Nunley

This paper presents a direct framework for sequence models with hidden states on closed subgroups of U(d). We use a minimal axiomatic setup and derive recurrent and transformer templates from a shared skeleton in which subgroup choice acts as a drop-in replacement for state space, tangent projection, and update map. We then specialize to O(d) and evaluate orthogonal-state RNN and transformer models on Tiny Shakespeare and Penn Treebank under parameter-matched settings. We also report a general linear-mixing extension in tangent space, which applies across subgroup choices and improves finite-budget performance in the current O(d) experiments.