arXiv:2610. 41218v1 Announce Type: new Abstract: Why does length generalization (LG) depend so sharply on the positional encoding (PE)?
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.
The paper investigates how treating each entity in a graph or language model as having its own coordinate frame—viewed as a symmetry—constrains the form of attention mechanisms. It shows that with orthogonal transports, invariant attention scores depend only on norms and transported inner products, while equivariant messages lie in the span of the entity vectors and their transported counterparts. The authors demonstrate that standard attention corresponds to a flat shared frame, and that incorporating per‑entity frames allows relations to be represented as operators that compose via parallel transport, yielding empirical gains on synthetic relational tasks and natural language benchmarks.
arXiv:2608.20647v1 Announce Type: new Abstract: Splitting a bidirectional LSTM's contextual representation into a forward-only $F_i$ (strictly a function of tokens $1..i$) and a backward-only $B_i$ (...
arXiv:2609.01129v1 Announce Type: new Abstract: We identify a recurrent algebraic regularity in Transformer attention: a sparse subset of effective OV operators $T=OV^\top$ nearly closes under compos...
arXiv:2605. 25889v4 Announce Type: replace-cross Abstract: Vision-Language-Action (VLA) models reach high success rates on clean inputs but collapse under small adversarial perturbations: a $16/255$ PGD attack drops OpenVLA-7B's LIBERO success from $95\%$ to under $5\%$.
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.
The information bottleneck (IB) trades compression of an input $X$ against prediction of a target $Y$ through a multiplier $β=1/λ$, yet each operating point is usually served by training, or fully con...
arXiv:2609.24209v1 Announce Type: new Abstract: The Platonic Representation Hypothesis (PRH) claims that independently trained models converge on a shared statistical model of reality, yet recent wor...
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:2607. 14144v2 Announce Type: replace Abstract: The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality.
arXiv:2602. 18849v2 Announce Type: replace-cross Abstract: We develop a sensitivity analysis for transformer attention in a geometry aligned with tokenwise computation.
The paper introduces the Lattice Representation Hypothesis (LRH) to explain why different alignment criteria—such as neighbor overlap, spanning trees, and distances—yield varying views on model representation convergence. It shows that the Platonic Representation Hypothesis (PRH) reflects agreement at the top of a lattice, while evidence comes from criteria near the bottom, and that the Aristotelian Representation Hypothesis (ARH) limits convergence to local neighborhoods due to calibration effects. Experiments on numerous pretrained vision and language models, along with theoretical analyses of linear autoencoders and contrastive Gibbs models, support the LRH’s claim that training procedures and objectives determine which criteria are reliably met across runs.