This work investigates the layer-wise evolution of ID, and shows that closed-class items expand earlier and collapse sooner than open-class ones, and recovers a token's grammatical role, and uses them to interpret how the semantic content of each PoS evolves across layers in a downstream classification task.
Abstract
Transformer representations describe trajectories through high-dimensional vector spaces, which are shaped dynamically as tokens incorporate relational context across layers. Such data tend to concentrate on lower-dimensional sub-manifolds, a form of compression quantified by the Intrinsic Dimensionality (ID), the minimum number of independent variables needed to represent them without significant information loss. In this work, we ask whether the grammatical role of tokens, as marked by their part-of-speech (PoS) tag, shapes the local geometry of this manifold. To this end: (1) We investigate the layer-wise evolution of ID, finding that closed-class items expand earlier and collapse sooner than open-class ones; (2) We show its expansion and contraction to be explained by changes in the neighborhood structure, and hence in the relations between words within a sentence; (3) We compare encoders (ModernBERT, bigbird-roberta-large) and decoders (gemma-2-2B, Llama-3.2-3B), finding that the two families evolve differently across layers, consistently with how each integrates context;(4) We show that geometric features alone recover a token's grammatical role, and use them to interpret how the semantic content of each PoS evolves across layers in a downstream classification task.
A scale-dependent transition between two ID regimes is found: at low lexical diversity, conditions with fewer unique final words produce higher ID, while at high lexical diversity, this ordering reverses, and conditions with more unique words produce higher ID.
Arwa Osman, Marco Baroni, Iuri Macocco· 0 citations
Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety. We ask whether sentence-level classification signal lives in the Riemannian geometry of contextual token embeddings, and probe it by extracting per-token pullback metrics from a learned encoder's analytical Jacobian and aggregating them with the Fr\'echet mean on the symmetric positive definite (SPD) manifold; we call this procedure Riemannian Mean Pooling (RMP). Across three datasets with non-trivial linguistic structure (CoLA, CREAK, RTE), RMP outperforms Euclidean mean pooling, while on FEVER-Symmetric, a benchmark constructed to remove annotation-driven lexical artifacts, the method correctly stays at chance. Ablations show that a randomly initialised encoder combined with Fr\'echet aggregation already beats Euclidean pooling on two of the three signal-bearing datasets, localising the source of the gain to the geometric aggregation rather than to learned manifold structure; the trained encoder contributes additional signal specifically on CREAK, the most knowledge-heavy of the three signal-bearing datasets.
S. Konior, Alexandre Quemy, Przemyslaw Klocek et al.· 0 citations
ESM3 is a multimodal protein language model that ingests a protein through several channels at once, including amino-acid sequence, three-dimensional structure, secondary structure (SS8), solvent accessibility (SASA), and discrete functional annotations, summing their embeddings into a single residual stream.
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.
Junjie Yao, Liangkai Hang, Zhi-Qin John Xu· 0 citations
We represent lexical tokens as unitary matrices and encode each sentence as their ordered product. The noncommutativity of matrix product captures word order without positional encodings (PEs). The same algebra yields several capabilities, including antisymmetric self-attention with no query, key, or value projections, and parallel composition of variable-length text chunks at a reduced attention cost. Furthermore, it provides a canonical-coset readout layer that encodes all true unitary degrees of freedom compactly, while supporting continual learning through nested group extensions that enlarge the operator space with each new task preserving prior representations exactly. Across standard text-classification benchmarks, the method matches or exceeds bag-of-words baselines. Achieving higher accuracy on IMDB and comparable performance on AG News. Notably, this is accomplished by replacing the conventional $\sim$30,000-dimensional vocabulary space with a dense, 64-parameter real-valued encoding, highlighting the expressive efficiency of our parameterization.
Carla Quispe Flores, Stanley Salvatierra, Renan Cabrera· 0 citations
B\"urger et al.\ (2024) demonstrated that truth representations in large language models are universal across statement polarity but reside within a multidimensional subspace. The truth value of a statement is linearly readable from a residual stream of language model, but it is not clear how much of that representation fits on a single direction, which component builds it, or what it is made of. We conducted a study based on these questions, with one instrument: a training-free axis, the dominant direction of the singular value decomposition (SVD) of hidden-state differences over true/false minimal pairs, identified without labels up to one global sign. Extensive evaluation across 14 models from 6 diverse architectural families (including MoE), read and extract at cost $O(d)$ per token. We close with a pre-registered prediction on whether the arrangement extends to categories whose truth is computed rather than retrieved.
Francesco Vicidomini· 0 citations
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