arXiv:2602. 07834v2 Announce Type: replace Abstract: The pointwise determinant ratio \[ R_\psi(z)\equiv \log\!
arXiv:2409. 15600v3 Announce Type: replace Abstract: A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general.
arXiv:2607. 04306v1 Announce Type: new Abstract: Distilling a fine-tuned teacher into a LoRA-adapted student is a standard recipe for parameter-efficient compression, but output-level KD does not explicitly control which rank-$r$ weight subspace the adapter occupies.
arXiv:2606. 01443v1 Announce Type: cross Abstract: A central difficulty in training Joint-Embedding Predictive Architectures (JEPAs) is preventing representation collapse.
arXiv:2606. 13823v1 Announce Type: new Abstract: We study training-free fixed-length descriptors for multivariate time series and ask not merely whether such a descriptor performs well, but when it can be expected to work at all.
arXiv:2606. 05957v1 Announce Type: new Abstract: Singular learning theory and information geometry have studied the same parameter spaces in mostly separate vocabularies: the former computes Bayesian invariants in resolved coordinates, the latter works in original coordinates under a non-degeneracy assumption that overparameterised models routinely violate.
arXiv:2606. 03003v1 Announce Type: cross Abstract: A latent world model built from an equivariant encoder $E$ and an equivariant predictor $f$ inherits a provable symmetry of its training loss: when the world's dynamics genuinely carries a group $G$ acting on latents by an orthogonal representation $\rho(g)$, the one-step prediction relMSE is exactly invariant across the whole group, so fitting the dynamics on a restricted slice of orientations mathematically determines it on the entire orbit (j\v{u} y\=i f\v{a}n s\=an).
arXiv:2605. 29151v2 Announce Type: replace-cross Abstract: We prove real-rootedness for the Poincar\'e polynomial \[ P_n(t)=\sum_{i=0}^{n-3} \dim H^{2i}(\overline{\mathcal M}_{0,n};\mathbb{Q})t^i \] of the Deligne--Mumford moduli space $\overline{\mathcal M}_{0,n}$ of stable $n$-pointed rational curves, proving a conjecture of Aluffi--Chen--Marcolli.
arXiv:2607. 11956v1 Announce Type: cross Abstract: Data Shapley is the standard principled answer to which training points are worth what, and its k-nearest-neighbor (KNN) specialization is the version deployed in practice: the exact estimator shipped by toolkits such as pyDVL and OpenDataVal.
arXiv:2608. 01268v1 Announce Type: cross Abstract: Detecting that a stream of high-dimensional embeddings has changed is usually framed as a choice of statistic.
arXiv:2608. 15351v1 Announce Type: new Abstract: Nominal LoRA rank is a design parameter; calibrated spectral evidence is a separate inferential quantity.
arXiv:2608. 15466v1 Announce Type: new Abstract: Distributional changes can be invisible to means and covariances yet appear in skewness, asymmetric interactions, or other third-order structure.
arXiv:2606. 20547v1 Announce Type: new Abstract: We place the attention token on the group: a token is an element $g_i$ of a matrix Lie group $G$ -- a bare transformation, with no feature payload and no external action $\rho(g)$ carrying it.