{"id":"arxiv:2505.24832","title":"How much do language models memorize?","date":"2025-05-30","section":"Data, training, optimization","quality":0.266715,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/","source_url":"https://arxiv.org/abs/2505.24832","text_available":true,"authors":["John X. 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memorize?","offset":0,"level":1,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"Abstract","offset":41,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"1 Introduction","offset":1105,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"2 Memorization, intended and unintended","offset":5964,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"2.1 Warm-up: A statistical view of memorization","offset":7673,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"Proposition 1 (Super-additivity of Unintended Memorization) .","offset":10237,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"2.2 Measuring unintended memorization with Kolmogorov Complexity","offset":11578,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"Definition 2 (Kolmogorov complexity) .","offset":13078,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"Definition 3 (Kolmogorov memorization) .","offset":13839,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"Proposition 4 .","offset":15073,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"2.3 Estimating Kolmogorov with compression","offset":15876,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-1.html#text"},{"title":"Choice of reference model.","offset":18664,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"3 Model Capacity for Memorization","offset":19111,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"3.1 Defining model capacity","offset":19630,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"Definition 5 (Capacity) .","offset":19866,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"3.2 Measuring model capacity with synthetic sequences","offset":20423,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"Experimental details.","offset":22326,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"Results.","offset":23137,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"How does precision affect capacity?","offset":25458,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"4 Disentangling Unintended Memorization from Generalization","offset":26315,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"Experimental 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Membership","offset":30623,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"5.1 Membership in synthetic and text data","offset":31173,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"Synthetic data.","offset":31220,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"Text.","offset":31657,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-2.html#text"},{"title":"5.2 Scaling laws for Membership","offset":32267,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"5.2.1 Functional forms","offset":32598,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Limiting behavior.","offset":33455,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Fitting.","offset":33766,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"5.2.2 Validation on larger models","offset":34199,"level":4,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"6 Related Work","offset":35491,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Language models and compression.","offset":35510,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Language model capacity.","offset":36162,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Information regularization in learning theory.","offset":37373,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Alternative definitions of memorization.","offset":38048,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Prior definitions of memorization.","offset":38276,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"7 Conclusion","offset":39798,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"8 Acknowledgements","offset":40377,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Appendix A Appendix","offset":40557,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"A.1 How reliable are our linear estimates of capacity?","offset":40581,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"A.2 Additional memorization results","offset":41434,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"A.3 Comparison of distributions memorized","offset":42448,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Distribution-level analysis.","offset":42495,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Which datapoints are most memorized?","offset":43235,"level":5,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"A.4 Scaling law fit","offset":45056,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"A.5 Proofs","offset":45387,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"A.6 Proof of Proposition 1","offset":45469,"level":3,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"Proof.","offset":45530,"level":6,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-3.html#text"},{"title":"A.7 Proof of Proposition 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memorization","offset":49035,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-4.html#text"},{"title":"Instructions for reporting errors","offset":53636,"level":2,"url":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/part-4.html#text"}],"text_code_points":54600,"source_markdown":"https://vinnik-dmitry07.github.io/favorite-papers/agents/papers/1d14faeb604373b83ad90ae653998a11cc09492020341f29419e0deed45a300c/source.md"}