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This research demystifies the emergence of semantic structure in language models by formalizing a "Context Staircase" where embeddings progressively align with increasingly complex contextual distributions during training. By deriving evolution equations for gradient flow under small initialization, the study reveals an implicit bias where models first capture simple, context-free label relations before integrating higher-order context dependencies. These findings offer critical theoretical insight into how data statistics and architecture jointly shape the representational space of modern AI systems.
Context Staircase: Signature-Aligned Dynamics of Token Embeddings under Small Initialization
arXiv:2608.30315v1 Announce Type: cross Abstract: Token embeddings are the basic representational units that connect discrete tokens with continuous computation in language models. Although modern language models learn embeddings from random initialization through gradient-based training, the dynamical mechanism by which meaningful embedding structures emerge remains unclear. In this work, we identify that the evolving embedding structures are closely related to token-conditioned label and contextual distributions, which we formalize as probability signatures. We observe a progressive learning process, which we term Context Staircase: embeddings learn the low-order statistic signatures of the data before the high-order ones. More specifically, we observe that early in training they align with the simplest, context-free signature linking a token to its label, and as training proceeds, they progressively reflect signatures involving more and more context tokens. We then analyze the gradient flow of embeddings under small initialization to explain this phenomenon, deriving embedding evolution equations for feed-forward and self-attention architectures. We further extend these observations to real language-model training. Finally, we show that these embedding structures play an important role in both task learning and the incorporation of semantic structure into the embedding space. Overall, our results provide a dynamic explanation of how data statistics and architecture jointly shape token embeddings in language models, and reveal an implicit bias in the space of data statistics: training proceeds from simpler, low-order statistical relations toward increasingly complex, context-dependent ones.
Abstract:Token embeddings are the basic representational units that connect discrete tokens with continuous computation in language models. Although modern language models learn embeddings from random initialization through gradient-based training, the dynamical mechanism by which meaningful embedding structures emerge remains unclear. In this work, we identify that the evolving embedding structures are closely related to token-conditioned label and contextual distributions, which we formalize as probability signatures. We observe a progressive learning process, which we term Context Staircase: embeddings learn the low-order statistic signatures of the data before the high-order ones. More specifically, we observe that early in training they align with the simplest, context-free signature linking a token to its label, and as training proceeds, they progressively reflect signatures involving more and more context tokens. We then analyze the gradient flow of embeddings under small initialization to explain this phenomenon, deriving embedding evolution equations for feed-forward and self-attention architectures. We further extend these observations to real language-model training. Finally, we show that these embedding structures play an important role in both task learning and the incorporation of semantic structure into the embedding space. Overall, our results provide a dynamic explanation of how data statistics and architecture jointly shape token embeddings in language models, and reveal an implicit bias in the space of data statistics: training proceeds from simpler, low-order statistical relations toward increasingly complex, context-dependent ones.
Machine Learning (cs.LG); Computation and Language (cs.CL)
arXiv:2608.30315 [cs.LG]
(or arXiv:2608.30315v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2608.30315 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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