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Recent studies empirically show that compressing reasoning steps into latent states, or implicit CoT compression, offers a token-efficient alternative. However, the mechanism behind CoT compression remains unclear. In this paper, we provide the first theoretical analysis of the difficulty of learning to internalize intermediate reasoning steps. By introducing Order-r Interaction, we prove that the learning signal for high-order logical dependencies exponentially decays to solve irreducible problem, where skipping intermediate steps inevitably leads to high-order interaction barriers. To empirically validate this, we introduce NatBool-DAG, a challenging benchmark designed to enforce irreducible logical reasoning and eliminate semantic sho","title":"Chain Of Thought Compression: A Theoretical Analysis","url":"https://arxiv.org/abs/2601.21576","vendor":"arxiv_cs_ai"},"summary":"arXiv:2601.21576v2 Announce Type: replace \nAbstract: Chain-of-Thought (CoT) has unlocked advanced reasoning abilities of Large Language Models (LLMs) with intermediate steps, yet incurs prohibitive computational costs due to generation of extra tokens. Recent studies empirically show that compressing reasoning steps into latent states, or implicit CoT compression, offers a token-efficient alternative. However, the mechanism behind CoT compression remains unclear. In this paper, we provide the first theoretical analysis of the difficulty of learning to internalize intermediate reasoning steps. By introducing Order-r Interaction, we prove that the learning signal for high-order logical dependencies exponentially decays to solve irreducible problem, where skipping intermediate steps inevitably leads to high-order interaction barriers. To empirically validate this, we introduce NatBool-DAG, a challenging benchmark designed to enforce irreducible logical reasoning and eliminate semantic sho","title":"Chain Of Thought Compression: A Theoretical Analysis","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-27T04:43:18Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2601.21576"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:680a01eee29b0006507fcc3dd18181b947fe6324100a7112de52b2b7211b864f26db3a07049ea2033760ab6d7d79add736cec5ee4cd5e3b1034924dd567cdb04","signer":"crovia.substrate","subject":{"observed_at":"2026-05-27T04:43:18Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2601.21576"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"28472c43f70624ada46b17f2c25e2945800092a4ed61ebfd76db0b8aa7c9e95a","leaf_index":153825,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"9c65d393a0ac1cf4194e13197fa783134d2b46bfb83810360fc3bae343a50413","side":"left"},{"sibling":"2586f116c0f20fc98fa160def3bfb84ec34b349980242ef3acece83c5295a944","side":"right"},{"sibling":"33908f886055cbc8d90887974d678f2d5af414cad6537d3319a7049e0ae6bf59","side":"right"},{"sibling":"30bdd982a772193c802a8f9960167e19259d9376df1816d7e3579a390d08e8b5","side":"right"},{"sibling":"ef518195cbfeea3233753bde5df87e7a5d44189119d576181d46f875788d5ae8","side":"right"},{"sibling":"3cced4ec86de2a838f3fc9b99ffdf60576ecccfa8bdd6534a0279e9452a4356f","side":"left"},{"sibling":"26b17ab381ecd45e6cdb3b0addf7b75f3dfb0fc0b1c9161c6cec819853787697","side":"left"},{"sibling":"dd15059d2d503b45e928c26e84bea4e5b2d187abeace390e61efd18d39e80f21","side":"left"},{"sibling":"c56e46802f42ead6bcf79619c80428b6dc22e9afc9611a87f0d04a5ef9acadd7","side":"right"},{"sibling":"3165125427a29042fc9d02858a59a68858dbdcb2e19d1afa5f6dd6a95cfbce6a","side":"right"},{"sibling":"04b9a68b8ec6fa37251564383c685c23ce69e5e031df4eae69f79a3a334b68bf","side":"right"},{"sibling":"816f233274bb10f5a122aac086a0c8c697b78fec67a4af55190bb596b7506fab","side":"left"},{"sibling":"d415e6939aee710631f5062799379b547d2c3e3d9a68f263bbb5a693285ab2ca","side":"left"},{"sibling":"374c02d15fb12bd356c179c94766043a982052c6132af8bfc15361b431ffa9f7","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"990705096edf483cc877217308f731dc42d6f6d99f82880167bbdbbfef32560a","side":"right"},{"sibling":"dd265753d95fa2e2fb4f5768e37fab6f691ccff09ad60d0910ff7dc23bac9226","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":154065,"merkle_root":"4993cfdc172e7880b60667f16789dc2e831ff000f81bb1ecba248e73f1510eca","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260527T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-27T05:37:36Z","sig_algorithm":"ed25519","signature":"76ecf118011540405e96506e6219752df04a2850632f2903dc6f10e08b98bc5a42c8d9e1cb5b7c5bf714479806a403df5f34399afa40c23fbb71493a1f77bd0c","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_17b7b1cb1eb5ceb3aab8bcc59902dfc42509b4e3d935d019296586d709b62311"}}