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Oct 27

OTProf: estimating high-resolution profiles of optical turbulence ($C_n^2$) from reanalysis using deep learning

Accurate, high-resolution vertical profiles of optical turbulence (C_n^2), which reflect local meteorology and topography, are crucial for ground-based optical astronomy and free-space optical communication. However, measuring these profiles or generating them with numerical weather models requires substantial operational or computational effort. In this work, we present OTProf, a deep-learning method that estimates high-resolution C_n^2 profiles from widely available coarse-resolution ERA5 reanalysis data. OTProf is based on the Squeezeformer architecture, modified for super-resolution by introducing grid-agnostic interpolation in the latent space. We train and evaluate OTProf in the Netherlands using high-resolution C_n^2 data obtained from the Weather Research and Forecasting (WRF) model. The commonly used Hufnagel-Valley model serves as the baseline. Overall, OTProf reproduces the vertical structure of WRF-based C_n^2 more accurately than Hufnagel-Valley and yields more accurate estimates of the Fried parameter r_0 and the scintillation index σ_I^2. Out-of-domain performance is assessed using a smaller WRF-based C_n^2 dataset covering the Canary Islands. Initial results indicate a performance drop because the orography differs markedly from the training domain. We show that output bias correction based on a few local simulations can help OTProf to adapt, but more work for domain adaptation is needed. OTProf is therefore primarily recommended for in-domain applications, e.g., generating C_n^2 climatologies from long ERA5 records.

  • 3 authors
·
Oct 21

A Controlled Study of Attention-Only Transformers

Feed-forward networks hold two thirds of a transformer's non-embedding parameters, yet the architecture has not received a necessity test that controls parameters, compute, and depth at once. We pretrain attention-only decoder transformers (Simple Attention Networks, SANs) against standard transformers matched separately for parameter count, training FLOPs, and depth (2 to 48 layers), for up to 105B tokens at 6M to 87M parameters. Deleting feed-forward layers in place is costly: the standard transformer leads by 0.47 nats at matched depth and 0.26 nats at matched FLOPs. Reallocating the freed budget into attention depth closes the gap: at matched parameters the difference is 0.006 nats (0.27 percent of loss), reproducible to one part in ten thousand across seed pairs, shrinking across 5B, 30B, and 105B budgets, and holding near 0.02 nats across a 29x size range. Three measurements localize the remaining gap to parametric recall: attention-only models are better on context-grounded answers and worse where knowledge must come from weights. Weight spectra show why: routing matrices (Q/K) crystallize early, content matrices accumulate rank slowly, and removing feed-forward layers relocates this accumulation to the attention output projection. QK-normalization, not feed-forward layers or residual gating, keeps 48-layer attention-only stacks trainable. The deficit concentrates on low-context query prediction and localizes there entirely by the largest budget. A pre-registered test confirms the account: it predicts a 0.02 to 0.05 nat gap on knowledge-dense web text; a matched pair trained on fineweb-edu measures 0.040. Within the tested regime, attention does the rest.

  • 8 authors
·
Jul 19