Do Transformer representations progressively structure across depth and time? Results from 8 open models

A new preprint analyzing 8 open Transformer models finds that internal representations show statistically significant structured progression across depth (p = 0.00019996, 8/8 leave-one-model-out checks) and a coherent cross-model depth profile (mean r = 0.789), but no universal temporal trajectory, as a common temporal pattern failed to replicate (0/8 checks). The study, 'Progressive Representational Structuring in Small Language Models: Functionally Labelled Trajectories Across Depth and Time' (DOI: 10.5281/zenodo.22116637), also found no significant structural similarity among models with similar functional outcomes (p = 0.408) or same architecture family (p = 0.771).

Hi everyone, I’ve just published a new preprint that brings together several months of experiments on hidden-state dynamics in small open Transformer models. The question is fairly simple: During inference, do internal representations simply change from layer to layer, or is there evidence of a more structured progression across depth and generation time? I tried to study this without assuming that hidden-state dynamics are equivalent to “reasoning”. The working framework is: tokens → embeddings → contextualisation → relational structuring → functional structuring → decision formation → projection This is a descriptive hypothesis about representation dynamics, not a claim that these stages correspond to a universal reasoning mechanism. The expanded study uses 8 locally instrumented open models, with synchronized hidden-state and output observations and explicit separation between: depth — what changes as information passes through Transformer layers time — what changes as autoregressive generation progresses A few results were particularly interesting. First, local ordering across model depth survived expansion. The observed ordering was significantly more structured than random layer permutations p = 0.00019996 and remained supported when each model was removed from the panel one at a time 8/8 leave-one-model-out checks . Second, cross-model depth profiles remained surprisingly coherent. The mean correlation across normalized depth profiles was approximately r = 0.789. This does not mean that all models follow the same trajectory. Rather, it suggests that some aspects of where changes occur along depth may be more shared than I initially expected. Third, functionally labelled events were not uniformly distributed across depth. Event type showed a statistically supported association with normalized layer depth p = 0.0024 . I’m deliberately calling this an association, not evidence of a causal mechanism. But one of the most useful results was actually a failure to replicate. In an earlier smaller panel, a common temporal pattern in local trajectory instability looked promising. After expanding the panel, that common temporal mode disappeared — it survived 0/8 leave-one-model-out checks. Two other intuitive hypotheses also failed: models with similar observed functional outcomes were not significantly more structurally similar p = 0.408 , and models from the same architecture family were not significantly more similar either p = 0.771 . To me, this is probably the most important part of the result. The data do not support a simple story where architecture determines one characteristic trajectory or where one universal temporal dynamic explains inference. What remains is a narrower hypothesis: Transformer inference may contain reproducible structure along depth while remaining highly conditional in time and behavior. I refer to this as Progressive Representational Structuring. The framework is summarized by: Representation ≠ Function ≠ Behavior A representation can contain information without that information yet serving the same function, and a functional transition does not guarantee a particular final behavior. I would be especially interested in feedback from people working on: mechanistic interpretability, activation patching, probing, hidden-state geometry, steering, representation engineering, or larger open models. In particular, I’m curious whether others observe similar ordered depth structure without a universal temporal trajectory. Preprint: Progressive Representational Structuring in Small Language Models: Functionally Labelled Trajectories Across Depth and Time DOI: 10.5281/zenodo.22116637 This is still descriptive work. Causal intervention and structural-transfer experiments are separate next steps rather than claims of this paper. Progressive Representational Structuring in Small Language Models: Functionally Labelled Trajectories Across Depth and Time | Zenodo https://doi.org/10.5281/zenodo.22116637