#01Nov 8, 2026
stat.ML
Identifiable alignment of unpaired representations
Stas Syrota, Albert Lopez I Serrano, Johanne Franck and 1 more
Aligning two models without paired data requires a distance that both share, yet existing methods use Euclidean or spherical geometry. This is either an arbitrary choice or imposed by their loss function. We show that, under a precise form of the manifold hypothesis, the pullback of the data metric gives such a distance for any two models of one data-generating process. This holds whether the models are encoders, decoders or both, and whatever their architecture, loss, prior or training data. The alignment map preserves this distance and the distribution of representations, and is identifiable if and only if the data distribution breaks every symmetry of the data manifold. We show that this symmetry breaking holds generically. Identifiability makes the alignment coupling the unique optimum of Gromov--Wasserstein and of its weighted combinations with a linear program. The linear program alone has the same optimum if almost every data point has a distinct distribution of distances. The coupling, and with it the alignment map, is recovered exactly from permuted samples, even without identifiability, and consistently from independent ones. Our method, Neural Gromov--Monge Alignment (NGMA), uses no pairs or labels and outperforms every unpaired and label-informed baseline. It relies on pullback distances to align image models with different priors and single-cell models trained on disjoint cells, where Euclidean distances fail.
#02Nov 8, 2026
cs.LG
Decomposing Earth Embeddings with Sparse Autoencoders
Vitus Benson, Fanny Yang, Markus Reichstein
Earth observation foundation models produce global metre-resolution embeddings that underpin work across agriculture, ecology, hydrology, and beyond. Yet these embeddings are opaque: each dimension entangles unrelated physical concepts, which makes them difficult to interpret and their robustness hard to assess. Here, we propose sparse autoencoders (SAEs) as a principled way to decompose Earth embeddings into sparse, approximately monosemantic features over an overcomplete dictionary. Because LLM judges of interpretations do not transfer to satellite pixels, and spatial autocorrelation matters, we introduce a tailored evaluation protocol. It scores any SAE on reconstruction at matched sparsity, alignment with reference concepts, and spatial scale, each against baselines that include an SAE whose decoder is a frozen random dictionary. On this protocol, SAEs reconstruct AlphaEarth and Tessera embeddings better than every baseline at matched sparsity. Their features align with far fewer reference concepts than raw embedding dimensions (on AlphaEarth, 88% align with at most one of 20 concept groups, most with none, against a median of 12 per raw dimension). They also carry more of their variance at fine spatial scales (23 to 32% within a 640 m patch for BatchTopK and Matryoshka, against 9%). An SAE with a frozen random decoder shares both properties, which therefore follow from sparsity, whereas only a learned dictionary reconstructs the embedding accurately: on AlphaEarth, trained SAEs leave eight times less variance unexplained. We test the sparse code on two applications, discovering land-cover sub-concepts and detecting out-of-distribution pixels by area-of-applicability estimation. Both indicate how sparse features could be used, but neither is yet reliable enough for practical use. Together, these results are a step toward Earth observation models whose features can be inspected.
#03Nov 8, 2026
cs.LG
Self-Supervised Collapse Prevention with Score-Based Entropy Maximization
Adarsh Kappiyath, Silpa Vadakkeeveetil Sreelatha, Xiatian Zhu and 3 more
Diffusion models have demonstrated the effectiveness of score-based objectives for generative modeling, yet their potential for self-supervised representation learning remains underexplored. We introduce Entropy-Based Regularization (EBReg), a framework that uses latent score estimation to regularize the latent distribution during self-supervised training. EBReg jointly learns an encoder and a latent score model, and utilizes the learned score to provide a diversity-preserving signal that prevents representational collapse. Motivated by a mutual-information lower bound, we formulate the objective as view alignment with smoothed marginal entropy maximization and optimize the marginal entropy without explicit density evaluation. The same score model can additionally be used at test time to refine corrupted representations toward the training latent distribution. Empirically, EBReg learns competitive representations on ImageNet-1K, achieving 75.57% linear-probe accuracy with ViT-L. Across diverse architectures, score-guided test-time adaptation further improves robustness on ImageNet-C, yielding an average relative accuracy gain of approximately 5%.
#04Nov 8, 2026
cs.LG
The comparison of density estimation for transfer learning in Banach, Hilbert, Euclidean spaces
Maryam Alsadat Kazemian, Azam Bastanfard
Domain adaptation or DA methods are indispensable when target labels or computational resources are scarce, yet the domain kernel density and subspace alignment approaches completely assume a Hilbertian geometry. They measure distributional discrepancy with symmetric L2 divergences over Euclidean feature spaces or reproducing kernel Hilbert spaces (RKHS). This preprint summarizes the manuscript Non-Hilbertian Domain Adaptation. Total Variation Alignment via L1 Density Regularization on Feature Manifolds, which proposes Banach Manifold Transfer Learning or BMTL. BMTL makes two coupled design decisions. The first one is that features are embedded on a geodesic manifold rather than treated as points of a flat Euclidean space, and the second one is that the density matching regularizer is formulated in an L1 Banach norm, whose minimization is equivalent, by Scheffe's theorem, to contracting the Total Variation or TV distance between domain densities, a bounded metric that weights all regions of the sample space uniformly. The L2 formulation, by contrast, squares deviations and therefore amplifies errors in the tails, over emphasizing density outliers that do not reflect meaningful distributional shift. Experiments on MNIST-USPS, COIL20, and Office+Caltech10 show consistent gains; the L1 variant beats an otherwise identical L2 ablation on every task, for example 92.44% vs. 89.80% on USPS->MNIST and surpasses the strongest baseline DMDA by +3.68% on average over twelve Office+Caltech transfers. This document situates the contribution with an explicit comparison of Euclidean, Hilbert, and Banach geometries.
#05Nov 8, 2026
cs.LG
Computationally Efficient Offline Policy Optimization with All-Policy Linear Realizability
Zhijie Zheng
We study offline policy optimization in finite-horizon Markov decision processes where every deterministic Markov policy has an action-value function linear in known features, with coefficient norm at most $B$. From independent complete trajectories of one unknown Markov behavior policy, and under all-policy occupancy coverage, we give an algorithm with $\widetilde O(\varepsilon^{-2})$ sample dependence and computational complexity polynomial in $\log(2+B)$. The algorithm performs exactly one convex regression per layer. Its stopped-return targets are the values of a single consistent Markov witness policy. A shared reference design and bounded prediction constraints convert fast clipped-regression error into pointwise confidence for the raw linear predictions. Truncated leverage controls the performance loss without requiring empirical covariance approximation at scale $B^{-2}$. Rounding confidence radii upward preserves the exact witness and yields a polynomial-time bit implementation for rational numerical inputs. The guarantees allow any fixed initial-state distribution; realizability and coverage need only be checked for deterministic policies. We also establish a covariance-coverage variant with uniform approximate realizability and polynomial dependence on $B$. A two-action lower bound shows that the accuracy exponent $2$ is necessary.