Write-Protected Discrete Bottlenecks for Language-Grounded World Models: A Structural Limitation and Sufficient Fix

Large language models (LLMs) exhibit strong general-purpose reasoning capabilities, yet they frequently hallucinate when used as world models (WMs), where strict compliance with deterministic transition rules--particularly in corner cases--is essential. In contrast, Symbolic WMs provide logical consistency but lack semantic expressivity. To bridge this gap, we propose Neuro-Symbolic Synergy (NeSyS), a framework that integrates the probabilistic semantic priors of LLMs with executable symbolic rules to achieve both expressivity and robustness. NeSyS alternates training between the two models using trajectories inadequately explained by the other. Unlike rule-based prompting, the symbolic WM contributes candidate-level scores through log-linear reranking, without requiring the LLM to interpret rule text. Rule-guided sampling prioritizes transitions that are weakly covered by symbolic rules, using 35--60% of the training pairs while outperforming full-data supervised fine-tuning in five of six settings. Experiments on ScienceWorld, WebShop, and PlanCraft demonstrate consistent gains in WM prediction accuracy and data efficiency; one-step lookahead on open-ended WebShop also improves agent reward. Our models, rules, and code are available at https://github.com/tianyi-lab/NeSyS.

Neural Collapse predicts that balanced one-hot classification pushes model representations to be equally far from each other; a symmetric configuration that depends only on the output label and ignores any semantic similarity in the inputs. This creates a puzzle: next-token prediction language models are trained predominantly (as context length increases) with one-hot labels: the same context is very unlikely to appear twice in training with different labels. However, they clearly learn latent structural features. That is, despite the one-hot training regime, a language model's contextual embeddings represent the fact that the next word in ''Mary broke the ___'' is likely to be filled by tokens in the latent classes of a) medium-sized, b) rigid, c) inanimate nouns. How does gradient descent find such categorical semantic structure when co-occurrence statistics collapse to one-hot sparsity, eliminating any shared next-tokens among different contexts? To investigate this tension we identify three synthetic controlled settings where inputs have latent semantic factors but are mapped to distinct one-hot labels. We find that semantic geometry emerges early in training, and that representations cluster by shared attributes despite receiving no explicit supervision to do so. This structure is transient: with sufficient capacity and time, the model eventually reaches the predicted symmetric state where all representations are equally separated. We study this phase transition through Gram matrix analysis and propose a preliminary modification to the commonly used unconstrained features model to capture the emergent semantic geometry.

Fine-tuning a language model on contexts whose correct completion has a near-synonym competitor often fails silently. The cross-entropy loss decreases monotonically while the correct token never overtakes the competitor in rank. We study this regime across five transformer architectures spanning two families and a fivefold parameter range, on ten hand-selected near-synonym contexts. We instrument these failures with an order parameter combining the predicted distribution and pairwise embedding overlaps. It decomposes additively into a signal, tracking the model's commitment to the correct token over its nearest competitor, and a background drag, set by how the embedding bulk leaks probability into the score. This isolates two failure modes. In kinematic failure the signal stays small. In structural failure the drag actively worsens as fine-tuning proceeds. We observe sharp catapult-like jumps in the order parameter that resemble a phase transition. A central negative result organises the paper. The transitions are phantoms. The spontaneous-symmetry-breaking interpretation is ruled out by direct measurement. Catapult-like jumps still appear under LoRA fine-tuning with the token embedding matrix exactly unchanged during training, where no geometric phase transition is possible. The discontinuity lives entirely in the softmax readout. A small number of dimensionless quantities organise the trajectory across architectures. One is consistent across all five under full fine-tuning. A second sorts architectures into two classes by bulk embedding distribution and predicts LoRA sufficiency. As a blind test, the framework predicts the critical learning rate of a held-out architecture, not used to fit any parameter, to within 2.1% of a subsequent learning-rate sweep. Findings concern the near-synonym mechanism only and should not be extrapolated without recalibration.