%PDF-1.7 %锟斤拷锟斤拷 1 0 obj << /Metadata 3 0 R /Names 4 0 R /OpenAction 5 0 R /Outlines 6 0 R /PageMode /UseOutlines /Pages 7 0 R /Type /Catalog >> endobj 2 0 obj << /Author (Fran锟給is Charton; Ashvni Narayanan) /Creator (arXiv GenPDF \(tex2pdf:4177c2c\)) /DOI (https://doi.org/10.48550/arXiv.2511.10811) /License (http://creativecommons.org/licenses/by/4.0/) /PTEX.Fullbanner (This is pdfTeX, Version 3.141592653-2.6-1.40.28 \(TeX Live 2025\) kpathsea version 6.4.1) /Producer (pikepdf 8.15.1) /Title (Transformers know more than they can tell -- Learning the Collatz sequence) /Trapped /False /arXivID (https://arxiv.org/abs/2511.10811v1) >> endobj 3 0 obj << /Subtype /XML /Type /Metadata /Length 1611 >> stream Transformers know more than they can tell -- Learning the Collatz sequenceFran莽ois ChartonAshvni Narayananhttp://creativecommons.org/licenses/by/4.0/cs.LG endstream endobj 4 0 obj << /Dests 8 0 R >> endobj 5 0 obj << /D [ 9 0 R /Fit ] /S /GoTo >> endobj 6 0 obj << /Count 7 /First 10 0 R /Last 11 0 R /Type /Outlines >> endobj 7 0 obj << /Count 28 /Kids [ 12 0 R 13 0 R 14 0 R 15 0 R 16 0 R ] /Type /Pages >> endobj 8 0 obj << /Kids [ 17 0 R 18 0 R 19 0 R 20 0 R ] /Limits [ (Doc-Start) (theorem.3) ] >> endobj 9 0 obj << /Annots [ 21 0 R 22 0 R 23 0 R 24 0 R 25 0 R 26 0 R 27 0 R 28 0 R 29 0 R 30 0 R 31 0 R 32 0 R 33 0 R 34 0 R 35 0 R 36 0 R 37 0 R 38 0 R 39 0 R 40 0 R 41 0 R 42 0 R 43 0 R 44 0 R 45 0 R 46 0 R 47 0 R 48 0 R 49 0 R 50 0 R 51 0 R 52 0 R 53 0 R 54 0 R 55 0 R ] /Contents [ 56 0 R 57 0 R 58 0 R 59 0 R ] /MediaBox [ 0 0 612 792 ] /Parent 12 0 R /Resources 60 0 R /Type /Page >> endobj 10 0 obj << /A 61 0 R /Next 62 0 R /Parent 6 0 R /Title 63 0 R >> endobj 11 0 obj << /A 64 0 R /Parent 6 0 R /Prev 65 0 R /Title 66 0 R >> endobj 12 0 obj << /Count 6 /Kids [ 9 0 R 67 0 R 68 0 R 69 0 R 70 0 R 71 0 R ] /Parent 7 0 R /Type /Pages >> endobj 13 0 obj << /Count 6 /Kids [ 72 0 R 73 0 R 74 0 R 75 0 R 76 0 R 77 0 R ] /Parent 7 0 R /Type /Pages >> endobj 14 0 obj << /Count 6 /Ki...
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