Transformers converge to invariant algorithmic cores
arXiv:2602. 22600v2 Announce Type: replace-cross Abstract: Training selects for behavior, not circuitry: many weight configurations can implement the same function.
arXiv:2605. 27259v2 Announce Type: replace Abstract: We propose Kan Extension Transformers (KETs) as a categorical design language for a diverse group of Transformer implementations.
arXiv:2602. 22600v2 Announce Type: replace-cross Abstract: Training selects for behavior, not circuitry: many weight configurations can implement the same function.
The paper introduces TANGO, a Token‑Aggregated Nonlinear Gating Operator that blends cross‑token mixing and token‑wise transformation in transformer architectures. By computing a nonlinear gate per source token and averaging these gates for each destination, TANGO forms a source‑conditioned linear operator that improves predictive performance. Experiments on web text, formal mathematics, and code show that full‑prefix TANGO achieves the lowest test negative log‑likelihood across 16 settings, while a narrower variant offers substantial throughput gains with only a modest increase in loss.
arXiv:2601. 11618v2 Announce Type: replace-cross Abstract: Geometric Attention (GA) specifies an attention layer by four independent inputs: a finite carrier (what indices are addressable), an evidence-kernel rule (how masked proto-scores and a link induce nonnegative weights), a probe family (which observables are treated as admissible), and an anchor/update rule (which representative kernel is selected and how it is applied).
arXiv:2607. 04319v1 Announce Type: cross Abstract: A companion paper showed that a transformer's feed-forward layer can be rebuilt from explicit fuzzy set operations - intersection, set-difference, and a self-forgetting sequence quantifier - so its hidden units read as named logical operators at no cost to language-model quality.
arXiv:2606. 00091v1 Announce Type: cross Abstract: Joint Embedding Predictive Architectures (JEPAs) have reshaped self-supervised representation learning in vision.
The projection of queries and keys are central to the attention mechanism in Transformer architectures. While they are mathematically symmetric, they play different roles in attention mechanisms.
arXiv:2608. 02050v1 Announce Type: cross Abstract: Can a strictly local, iterated, weight-shared computation primitive support language modelling, and which of those three properties actually drives the model's behaviour?
A companion paper showed that a transformer's feed-forward layer can be rebuilt from explicit fuzzy set operations - intersection, set-difference, and a self-forgetting sequence quantifier - so its hidden units read as named logical operators at no cost to language-model quality. That left the other half of the transformer opaque.
arXiv:2606. 06712v1 Announce Type: cross Abstract: We study the transformation of autoregressive models (ARLMs) into diffusion language models (DLMs).
arXiv:2609.15975v1 Announce Type: cross Abstract: Transformer representations evolve through learned additive transformations that either preserve their current direction or redirect it. We study thi...
The paper introduces the Communication Map, a method that charts every potential communication channel in a transformer model using only its weights. It generalizes previous coupling metrics into a single coefficient covering all 18 connection classes, revealing that 70‑89% of head pairs are non‑randomly oriented and identifying strong or avoiding couplings. The authors demonstrate the map’s utility by recovering known induction circuits and uncovering a two‑dimensional stream subspace whose removal eliminates induction capabilities across several models.
The paper proposes that two architectural assumptions—(1) attention and MLPs share a key‑value form <phi(S)>U, and (2) components read from an additive residual stream—are sufficient to answer three interpretability questions: component interaction, information routing, and token attribution. By treating these selections as a computational graph, the authors develop Unpack, a backward attribution method that validates interaction scores, recovered routes, and token attribution against established tests across models ranging from 160M to 6.9B parameters. The study also shows that contribution and causal effect can differ, with a recognizable signature in how components change when a task is removed.