Air Quality Downscaling with Station-Guided Pseudo-Supervision

Super-resolving coarse atmospheric fields to local PM$_{2.5}$ variations is uniquely challenged by a mismatch in spatial support: while pixels represent regional averages, ground-truth observations are discrete, unaligned samples of a continuous spatial signal. To bridge this gap, we present a station-guided framework for high-resolution PM$_{2.5}$ downscaling over Europe. Taking coarse CAMS atmospheric composition fields alongside heterogeneous side information (i.e., human activity, land cover, elevation, satellite aerosol observations, and wind fields) our framework jointly super-resolves ($\times 40$, $\approx$ 1 km) and bias-corrects CAMS rasters, without relying on temporal sequence modelling. To address the challenge of densely supervising our multi-scale transformer network with sparse in-situ data, we introduce a time-agnostic propagation strategy that utilises spatial Gaussian blending of interpolated OpenAQ observations. Extensive qualitative and station-level evaluations across Europe demonstrate that our model recovers fine-grained spatial structures and effectively mitigates localised CAMS biases.

fmxcoders: Factorized Masked Crosscoders for Cross-Layer Feature Discovery

Many features in pretrained Transformers span multiple layers: they emerge through stages of inference, persist in the residual stream, or are built jointly by parallel MLPs. Crosscoders (namely, sparse dictionaries trained jointly across layers) aim to recover these cross-layer features in a single shared latent space. We show that standard crosscoders largely fail at this purpose. Although their decoder weight norms spread evenly across layers, a functional coherence metric we introduce reveals that each latent's activation is effectively driven by only one or two layers on average. While functionally coherent latents act as human-interpretable concept detectors (e.g., US states and cities), the layer-localized latents that crosscoders predominantly learn collapse onto surface-level patterns such as digit detectors. We trace this failure to two structural limitations: unconstrained cross-layer parameterization and unregularized cross-layer dependence. We address both by introducing fmxcoders, which (i) replace the encoder and decoder with low-rank tensor factorizations that draw every latent's per-layer weights from a shared cross-layer basis, and (ii) apply stochastic layer masking, a denoising regularizer along the layer axis that penalizes latents whose contribution collapses when a single layer is masked. Across GPT2-Small, Pythia-410M, Pythia-1.4B, and Gemma2-2B, fmxcoders lift mean probing F1 by 10-30 points, surpassing per-layer SAE baselines that standard crosscoders fail to reach, reduce reconstruction MSE by 25-50%, and roughly double mean functional coherence. An LLM-as-a-judge evaluation further shows that fmxcoders recover 3-13$\times$ more semantically coherent latents than standard crosscoders across all four base LLMs.

PolySAE: Modeling Feature Interactions in Sparse Autoencoders via Polynomial Decoding

Sparse autoencoders (SAEs) have emerged as a promising method for interpreting neural network representations by decomposing activations into sparse combinations of dictionary atoms. However, SAEs assume that features combine additively through linear reconstruction, an assumption that cannot capture compositional structure: linear models cannot distinguish whether "Starbucks" arises from the composition of "star" and "coffee" features or merely their co-occurrence. This forces SAEs to allocate monolithic features for compound concepts rather than decomposing them into interpretable constituents. We introduce PolySAE, which extends the SAE decoder with higher-order terms to model feature interactions while preserving the linear encoder essential for interpretability. Through low-rank tensor factorization on a shared projection subspace, PolySAE captures pairwise and triple feature interactions with small parameter overhead (3% on GPT2). Across four language models and three SAE variants, PolySAE achieves an average improvement of approximately 8% in probing F1 while maintaining comparable reconstruction error, and produces 2-10$\times$ larger Wasserstein distances between class-conditional feature distributions. Critically, learned interaction weights exhibit negligible correlation with co-occurrence frequency ($r = 0.06$ vs. $r = 0.82$ for SAE feature covariance), suggesting that polynomial terms capture compositional structure, such as morphological binding and phrasal composition, largely independent of surface statistics.