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:2608. 05136v1 Announce Type: new Abstract: Gradient descent on a factored model $W = UV^\top$ is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not.
By Devender Singh
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:2605. 18106v3 Announce Type: replace-cross Abstract: A striking geometric disparity has long persisted in the practice of deep learning.
By Tim Tsz-Kit Lau, Weijie Su
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.
By Tejas Pradeep Shirodkar, P. J. Narayanan
arXiv:2607. 00603v1 Announce Type: new Abstract: We give a descent-free, alignment-free measurement of singular structure on trained networks.
By Tejas Pradeep Shirodkar
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.
By Tejas Pradeep Shirodkar
arXiv:2607. 12501v3 Announce Type: replace Abstract: The Forward-Forward algorithm trains each layer locally, so that a scalar goodness - the sum of squared activations - is high on real inputs and low on contrastive ones.
By Paolo Giannitrapani
arXiv:2606. 31963v1 Announce Type: new Abstract: Modern LLM workflows move coordinate-indexed objects across checkpoints: steering vectors, sparse autoencoders, top-$k$ neuron sets, attribution lists, and merge alignments.
By John Sweeney
arXiv:2606. 25971v1 Announce Type: new Abstract: Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object.
By Alexander H\"agele, Alejandro Hern\'andez-Cano, Atli Kosson, Martin Jaggi
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:2411. 16073v4 Announce Type: replace-cross Abstract: Inspired by the Well-initialized Lottery Ticket Hypothesis (WLTH), we introduce Soft-TransFormers (Soft-TF), a continual learning framework that adapts a frozen pre-trained Transformer through task-specific soft subnetworks: real-valued multiplicative masks over the query, key, value, and output projections of selected self-attention layers.
By Haeyong Kang, Chang D. Yoo