GlossoGen: Emergent Language in Complex Multi-Agent LLM Interactions

The growing rate at which LLM agents interact with one another raises key questions about language evolution in multi-LLM-agent settings, with implications for safety and monitorability as well as for linguistic accounts of LLMs. To address these questions, we introduce GlossoGen, a novel platform for studying multi-agent language evolution in complex scenarios. Within GlossoGen, we build the SaveVeyru scenario, which requires agents with partial information to communicate under pressure. We find that language evolution does occur between LLM agents, that the resulting languages are compositional and morphologically productive, and that they deviate from the LLMs' English prior in ways that render them incomprehensible to humans. Moreover, we identify several qualities essential to this evolution: pressure towards efficiency; the strength of the models backing the agents; and access to a "postmortem" stage in which agents can agree on linguistic conventions. Importantly, we observe that different conditions govern the transmission of language to new agents. Specifically, we find that agents learn new languages from usage alone, take an active role in this learning, and that while stronger models are required for novel language emergence, weaker models can learn an existing language once it has emerged. Taken together, our results indicate that current LLMs have the potential for cumulative cultural evolution -- previously attested only in humans -- with mixed populations of agents developing capacities that go beyond their lowest common denominator.

Emergence Invariance: From Symbolized Thought to Interface Refinement

Language can be viewed as a formalized subset of thought: a consequence-governed symbolic structure projected from wider situated cognition. Large language models trained at scale exhibit compensatory emergence: sparse architectural primitives support in-context learning, multi-step reasoning, tool use, and chain of thought. Yet a language-first probabilistic architecture inherits substantive, substrate, and high-level incompletenesses relative to human cognition. Their coexistence makes an LLM a human-like thought-form generator that reconstructs increasingly human-like reasoning forms from an incomplete substrate. We ask whether emergence can compensate for every missing distinction. We formalize the philosophical premise as the Symbolization--Substructure Thesis and introduce emergence invariance. For a scale-indexed family acting through a shared task interface $φ$, $\mathcal{R}_s^*=\mathcal{R}_φ^*+C_s$: scale can reduce the compensation gap $C_s$, while a positive interface floor $\mathcal{R}_φ^*$ persists. We prove that, under a fixed input law, one interface is universally no less informative exactly when its completed information $σ$-field refines the other, and that total compensation occurs exactly when both the interface floor and asymptotic compensation gap vanish. The framework unifies existing results on grounding, memory, position, attention, Bayesian inheritance, scientific abduction, and reasoning control. In a matched DeepSeek V4-Flash API study, thinking improves pointer chasing from $0/16$ to $14/16$ when relevant distinctions are available; exact observational twins remain at their $50\%$ construction floor; and restoring decisive memory moves matched performance from $50\%$ to $100\%$. These results provide initial evidence for the predicted separation between scaling within an interface and refining the interface itself.

The Kinetics of Training: A Driven-Nucleation Rate Law for Emergence, Plasticity Loss, and Circuit Control in Language Models

A capability appears in a language model when the last parts of its circuit align in one stochastic attempt, and getting all but one right is worth nothing. We show this no-partial-credit joint alignment is the rate-limiting step of capability formation. Two fingerprints: in a shortcut-free apparatus a five-part circuit missing three waits as long as a three-part circuit missing three (1.19-1.37), so the wait counts missing parts, not size; and on Pythia across seven capabilities and three scales, ablating one part leaves a median 17% of the capability in 32 of 32 discriminating cells, where partial credit predicts 50-83% (p = 2e-10), while a random non-part head leaves 100%. One rare event whose barrier grows with missing parts yields a rate equation -- sites x attempts x drive x exp(-beta*K), minus destruction -- read three ways, each preregistered with frozen constants. Forward: a capability flat at baseline ignites at a step of our choosing once the mix passes a concentration floor (10/10 above, 0/12 below), and while still flat its arrival is datable from its precursor to 5% median error on six held-out models. Backward: the delay to learn a withheld capability grows with waiting until, past a critical step, it never ignites -- yet validation loss falls smoothly throughout, so standard monitors are blind to it. We locate the damage (heads commit to the base data) and isolate the cure: re-initializing only the query-key slices restores learnability (6/6) while the value slices do nothing (0/6). We prove the mechanism in a controlled gated-attention model: occupation forces a deadline whose consequences need no mixing assumption. Completed: SGD's noise fails the fluctuation-dissipation test, so we install one and anneal, melt and pin circuits on schedule. Scope: conjunction circuits in transformers to 1.4B.

The Orthogonalized Read Is a Removable Training Scaffold for Recurrent Memory

A recent report finds that orthogonalizing the mLSTM memory matrix at read time (five Newton-Schulz iterations, trained through) substantially improves noisy associative recall. The effect replicates, but it is not a memory improvement. Training on this task is a long chance plateau followed by a sharp escape, and the orthogonalized read acts by re-conditioning the learning problem during the plateau. Three properties establish this. It must be self-consistent: an exact recursive least-squares read (the Mesa layer) reproduces it, while straight-through halves, delta-rule writes, frozen random keys, and plain normalization all fail. It is uniform: across a learning-rate x hardness grid it multiplies the escape hazard roughly six-fold with no detectable hardness dependence, widening the workable learning-rate corridor that narrows for the baseline. And it is removable: applied to failed models at inference it rescues none, and annealed away on an escape-triggered schedule it leaves numerically stock mLSTMs at full accuracy. Much of the published gain needs no architecture at all: solved-rate at a fixed budget measures escape hazard, which follows a heat/noise law (learning-rate elasticity +3.0, gradient-noise elasticity -1.65) under which the original vocab-96 result is a large-batch noise condition rather than a capacity one. Decoding the memory state directly shows failed models carry roughly half their associations in linearly recoverable form: the plateau is a readout failure over half-written storage. Two conclusions travel beyond the intervention: recall benchmarks used for architecture selection partly measure trainability, and the system is a fully instrumented model organism of "emergence," in which a sharp behavioral threshold demonstrably arises from a censored metric over gradually accumulating structure.

From Approximation to Emergence: A Theory of Deep Learning

Deep learning has outgrown any single mathematical explanation. From Approximation to Emergence develops a unified, proof-oriented account of modern deep learning theory, tracing a path from the classical foundations of approximation, optimization, and generalization to the contemporary mechanisms of overparameterization, robustness, generative modeling, transformers, in-context learning, scaling laws, interpretability, alignment, and emergence. Rather than presenting isolated results, the book organizes a broad literature into a coherent research narrative: each theory is examined through the object it controls, the assumptions that make it valid, and the phenomena it leaves unexplained. Written for researchers, graduate students, and mathematically trained practitioners, this monograph offers a rigorous map of deep learning theory as it stands today: powerful, incomplete, and increasingly centered on the question of how learned mechanisms arise from scale, data, architecture, and training.