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This paper investigates the phenomenon of continuous mixture collapse in language models (LLMs), revealing that pretrained models struggle to maintain weighted mixtures of token embeddings due to inherent distortions in transformer architectures and training dynamics. Through theoretical analysis and empirical validation, the authors identify three distinct sources of failure: geometric distortion, amplification of dominant components, and contraction of mixtures into indistinguishable states. The findings highlight that preserving these mixtures necessitates context-dependent corrections, which can become increasingly complex as the number of components grows.
Continuous mixture collapse in LLMs reveals that even minor distortions can lead to significant reasoning failures, challenging the reliability of latent-state methods.
LLMs latent-state reasoning methods replace discrete intermediate tokens with continuous states, such as weighted mixtures of token embeddings, to retain multiple possible reasoning directions rather than committing to one. Yet pretrained language models often fail to preserve these mixtures. We study why through a combination of theoretical analysis and controlled empirical investigations on a variety of models. We identify three independent, distinct sources of failure. First, transformer architectures already distort mixture geometry, and training substantially amplifies this effect. Moreover, the failure can occur even if the model transports mixtures perfectly linearly: the softmax readout and autoregressive feedback form a dynamical system that either amplifies small differences until one component of the mixture dominates or contracts different mixtures until they become indistinguishable. We verify this theoretical prediction empirically: the observed transition between contraction and amplification occurs near the theoretical threshold derived by our analysis, and pretrained-model rollouts lie predominantly on the amplifying side. Finally, we generalize to mixtures of many components and show that exact preservation generally requires context-dependent correction, whose required dimensionality can grow with the number of components.