Location encoders turn coordinates into high-dimensional descriptors by contrastively aligning them with paired Earth observation imagery, and the construction has a structural ceiling. LoCA proves that any Lipschitz location encoder produces an output of intrinsic dimension at most two, no matter the architecture or bandwidth, which forces the contrastive loss to stay strictly above its asymptotic optimum. Joint training also collapses the encoder's embedding covariance to low rank. Existing encoders escape this only by training against a frozen image encoder, which the authors reinterpret as a covariance regulariser handing the location encoder a high-rank target to fold onto.
Extending that to multimodal inputs needs two things the authors name: co-alignment across modalities, since adapters alone cannot align independently pretrained encoders, and high effective rank, since the location encoder inherits its target's spectrum. LoCA is a two-stage pipeline that supplies both. Stage one jointly trains Sentinel-1 and Sentinel-2 encoders contrastively to produce a co-aligned, high-rank multimodal target; stage two freezes them and trains location and tabular metadata encoders as projection adapters with multi-view contrastive learning. Against five state-of-the-art encoders on 17 tasks spanning land cover, wildfire forecasting, geophysical, socio-economic, biodiversity and climate work, LoCA takes the most task wins, is the only model to beat every other on a majority of tasks, and wins 68.8 percent of per-task comparisons.
The limitation is that the dimension bound is proved for the Lipschitz contrastive construction this family uses, not for every possible location encoder.
https://arxiv.org/abs/2610.32894
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.