arXiv:2606. 15036v1 Announce Type: new Abstract: We train a two-layer transformer encoder to classify rational elliptic curves $E/\mathbb{Q}$ of conductor $\leq 10000$ as either rank 0 or rank 1 from the first 128 normalized Frobenius traces.
arXiv:2607. 18759v1 Announce Type: new Abstract: Transformers with relative positional encodings often extrapolate to sequences longer than those seen during training, whereas transformers with learned absolute encodings typically do not.
arXiv:2608. 04213v1 Announce Type: new Abstract: Existing studies on self-supervised learning for white-box networks typically decouple the derivation of white-box networks via optimization algorithms from self-supervised learning paradigms.
arXiv:2607. 18363v1 Announce Type: cross Abstract: Feed-forward networks hold two thirds of a transformer's non-embedding parameters, yet the architecture has not received a necessity test that controls parameters, compute, and depth at once.
arXiv:2607. 08946v1 Announce Type: new Abstract: A transformer can be built from operators that are legible by construction -- bounded, named units that read as fuzzy set operations rather than dense activations -- but legibility must be pressed for during training, and the pressure has a failure mode.
arXiv:2607. 23050v1 Announce Type: new Abstract: Neural scaling laws describe how loss decreases as models, data, and compute grow, but they do not answer a prior question: for a fixed task, what is the minimum model capacity required to solve it?
arXiv:2602. 18849v2 Announce Type: replace-cross Abstract: We develop a sensitivity analysis for transformer attention in a geometry aligned with tokenwise computation.
arXiv:2608. 03620v1 Announce Type: cross Abstract: Activation patching and weight-space ablation both claim a component is causally responsible for a behavior, yet they act on different objects: one forward pass versus the parameters behind every forward pass.
arXiv:2607. 11990v1 Announce Type: cross Abstract: Feedforward network (FFN) blocks account for a large fraction of the parameters and computation in Transformer architectures, yet their internal structure remains difficult to interpret due to the additive superposition induced by the residual stream.
arXiv:2606. 19491v1 Announce Type: new Abstract: Pretrained transformers sit near singular minima of the loss, where the Fisher information metric degenerates along dead directions: directions in parameter space along which the directional Fisher vanishes.
arXiv:2608. 09558v1 Announce Type: new Abstract: How expressive is prompting a transformer?
arXiv:2607. 20594v1 Announce Type: cross Abstract: When does a weight-tied looped transformer -- one block applied T times -- implement an actual algorithm?
arXiv:2607. 09842v1 Announce Type: new Abstract: We investigate whether identity-specifying system prompts produce statistically distinguishable geometric fingerprints in the hidden-state trajectories of four open-weight transformer language models spanning four post-training regimes: no training (Gemma-4-E4B base), multimodal RLHF (Gemma-4-E4B-it), RL distillation (DeepSeek-R1-Distill-Qwen-7B), and SFT (Qwen2.