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).
By Hongbo Wang (Stony Brook University)
arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.
By Raziyeh Takbiri
arXiv:2606. 05169v1 Announce Type: new Abstract: We give a stereological theory of LLM benchmark coverage.
By Jason Z Wang
arXiv:2606. 02608v1 Announce Type: new Abstract: We study a Marchenko--Pastur (MP) random-matrix approach to pruning deep neural networks with very small post-pruning fine-tuning budgets.
By Leonid Berlyand, Theo Bourdais, Houman Owhad, Yitzchak Shmalo
arXiv:2608. 13201v1 Announce Type: cross Abstract: We develop the statistical and algorithmic theory of inverse optimal transport (IOT) under the feature-parameterized cost C_theta(i,j) = -theta^T phi(i,j).
By Han Dong, Jiaming Li, Yongqiang Gong, Ruixi Li, Yin Liu
arXiv:2607. 13612v1 Announce Type: cross Abstract: Joint-Embedding Predictive Architectures (JEPAs) are the dominant design for latent world models, yet they are usually justified by empirical performance rather than a normative principle.
By Fabio Arnez, Alexandra Gomez-Villa
arXiv:2608. 15351v1 Announce Type: new Abstract: Nominal LoRA rank is a design parameter; calibrated spectral evidence is a separate inferential quantity.
By Mohammed Ahnouch, Lotfi Elaachak
arXiv:2608. 16925v1 Announce Type: new Abstract: We build an instrument that reads, from a single fit and with no oracle, whether the operator a hybrid PDE-parameter estimator postulates is wrong-and separates that from a merely unidentifiable parameter.
By Eric Fock
arXiv:2607. 13380v1 Announce Type: new Abstract: Predictive Coding (PC) offers a biologically motivated alternative to backpropagation via local weight updates, yet routing error between layers still relies on an autograd Jacobian-transpose ($J^\top$) product - the last non-local operation in PC.
By Junlong Shen, Xingyu Li
arXiv:2607. 11920v1 Announce Type: cross Abstract: Evaluating decisions made under uncertainty is hard when labeled outcomes are scarce, costly, or confounded with luck.
By Jeff Helzner
A deep network's loss is invariant to continuous symmetries of its parameters: the logit shift, the ReLU rescaling, the LayerNorm scale, the per-head attention rotation. Adam's per-coordinate preconditioner drifts along each symmetry orbit, which pulls the trajectory off the symmetry quotient where the optimization lives and blurs the singular-learning rate the quotient makes readable.
arXiv:2607. 05872v1 Announce Type: new Abstract: Memory-efficient optimizers such as GaLore train large language models by projecting gradients onto a rank-r subspace recomputed every T steps, assuming this subspace is a slowly drifting object that can be tracked.
By Noel Thomas