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Eren Sasoglu

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NeurIPS Conference 2024 Conference Paper

Scaling laws for learning with real and surrogate data

Ayush Jain
Andrea Montanari
Eren Sasoglu

Collecting large quantities of high-quality data can be prohibitively expensive or impractical, and a bottleneck in machine learning. One may instead augment a small set of $n$ data points from the target distribution with data from more accessible sources, e. g. data collected under different circumstances or synthesized by generative models. We refer to such data as `surrogate data'. We study a weighted empirical risk minimization (ERM) approach for integrating surrogate data into training. We analyze mathematically this method under several classical statistical models, and validate our findings empirically on datasets from different domains. Our main findings are: $(i)$ Integrating surrogate data can significantly reduce the test error on the original distribution. Surprisingly, this can happen even when the surrogate data is unrelated to the original ones. We trace back this behavior to the classical Stein's paradox. $(ii)$ In order to reap the benefit of surrogate data, it is crucial to use optimally weighted ERM. $(iii)$ The test error of models trained on mixtures of real and surrogate data is approximately described by a scaling law. This scaling law can be used to predict the optimal weighting scheme, and to choose the amount of surrogate data to add.

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STOC Conference 2016 Conference Paper

Reed-Muller codes achieve capacity on erasure channels

Shrinivas Kudekar
Santhosh Kumar
Marco Mondelli
Henry D. Pfister
Eren Sasoglu
Rüdiger L. Urbanke

We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, our method exploits code symmetry. In particular, the technique applies to any sequence of linear codes where the block lengths are strictly increasing, the code rates converge, and the permutation group of each code is doubly transitive. In a nutshell, we show that symmetry alone implies near-optimal performance. An important consequence of this result is that a sequence of Reed-Muller codes with increasing block length and converging rate achieves capacity. This possibility has been suggested previously in the literature, but it has only been proven for cases where the limiting code rate is 0 or 1. Moreover, these results extend naturally to affine-invariant codes and, thus, to all extended primitive narrow-sense BCH codes. This is used to resolve, in the affirmative, the existence question for capacity-achieving sequences of binary cyclic codes. The primary tools used in the proofs are the sharp threshold property for symmetric monotone boolean functions and the area theorem for extrinsic information transfer (EXIT) functions.

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