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Recent work shows that sampling from sharpened base-model distributions at test time recovers much of the RL gain, yet existing methods rely solely on output-layer likelihoods and ignore the transformer's internal forward-pass dynamics. We introduce Depth-Entropy Guided Sampling (DEGS), a training-free, test-time method that exploits layer-wise entropy collapse as an intrinsic quality signal. We observe that stronger reasoners -- including RL-posttrained variants -- exhibit a distinctive \"late collapse\": logit-lens decoded entropy stays elevated until deeper layers before converging. We define a per-sequence collapse depth $D(\\mathbf{x})$ and a joint objective $\\pi(\\mathbf{x}) \\propto p(\\mathbf{x})^\\alpha \\exp(\\beta D(\\mathbf{x}))$ that comb","title":"Depth-Entropy Guided Sampling for Training-Free LLM Reasoning","url":"https://arxiv.org/abs/2607.09693","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.09693v1 Announce Type: cross \nAbstract: Reinforcement learning (RL) has become the dominant paradigm for improving the reasoning capabilities of large language models, but it requires expensive training, curated data, and reward signals. Recent work shows that sampling from sharpened base-model distributions at test time recovers much of the RL gain, yet existing methods rely solely on output-layer likelihoods and ignore the transformer's internal forward-pass dynamics. We introduce Depth-Entropy Guided Sampling (DEGS), a training-free, test-time method that exploits layer-wise entropy collapse as an intrinsic quality signal. We observe that stronger reasoners -- including RL-posttrained variants -- exhibit a distinctive \"late collapse\": logit-lens decoded entropy stays elevated until deeper layers before converging. We define a per-sequence collapse depth $D(\\mathbf{x})$ and a joint objective $\\pi(\\mathbf{x}) \\propto p(\\mathbf{x})^\\alpha \\exp(\\beta D(\\mathbf{x}))$ that comb","title":"Depth-Entropy Guided Sampling for Training-Free LLM Reasoning","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-07-14T04:43:37Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2607.09693"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:e5c0df6877179beab89de866351e11bde3576347964f39b318869d2bed254e58f5a0b16b39f7cbf78f9b7ea7fb144588ad6c0cfbb782c3849b6c0b2bb04cd205","signer":"crovia.substrate","subject":{"observed_at":"2026-07-14T04:43:37Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2607.09693"},"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":"6feb7a18f9e18ead17de60c8cdaa846e45023cf85f2d73397a8281d7c7e45de1","leaf_index":312903,"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":"4775f8d6c54257c3eb7fd47ca646ee4c717ae565359c3ed3c424110f6130c629","side":"left"},{"sibling":"8a43d1f59d108fd0c601c353e402f3c16d7e2f24a2115ed425b0c049b4eca820","side":"left"},{"sibling":"0c9036c4df9cada8b71f2d2e86daa1f7da959579015d8759e0109342fe04de38","side":"left"},{"sibling":"c1ea31625ec786e4b967d82636d5f151930f123f04afa63cd614b0ec13742c78","side":"right"},{"sibling":"934dcfbc9d7e52489b7eb56b5845ca7a68ff1130b70aa93381e81333befc34fd","side":"right"},{"sibling":"b55341db964dff97d1f0bdf958511d9a0a5ebb763bd4091e5e5b0920e5f1b249","side":"right"},{"sibling":"fccac03eef6676a6350a95afcd277425f87c0fc8ca6ed34e68a7f13c01eec848","side":"left"},{"sibling":"b6420221ab220053217910d6a61ccf0d6e8ca1f1eb9e0cc40a25723c21042168","side":"right"},{"sibling":"ca17e703a3fca19bfbb090cbed9e2450594a9c237665dd9a566195d3ef3072f7","side":"right"},{"sibling":"8393dc03644000353c5d503b6ec261c022cd2aa85a649223916153bc8af2dc75","side":"left"},{"sibling":"1627ce6908965f2e5fbc7c16bc8e247867478c587014561d0de1359dc2dc0afc","side":"left"},{"sibling":"74e1ba9fd48bdd0f52777dd5b56c10706e73f42629013748eca13ef113cd59db","side":"right"},{"sibling":"682fd39539db5bce908d0ab6f180374728fed6b34a9a8c87c7b4eb5a726e30b8","side":"right"},{"sibling":"184927f71d667ac0c6ebeadb33394626973738b9107c6dc3c0c4949b44acf295","side":"right"},{"sibling":"f302542c38ba7c3aab7c9280dd60259ecec777dca6e6f71b6f0729b0b8791b72","side":"left"},{"sibling":"d8b9143917b539c543cf4448cec00131f8b807bd8004979c54ebe09798748c66","side":"left"},{"sibling":"c4c189d79669979b59d9aa976ee249c54a7e065b4a05bf49463459cc7f37428e","side":"right"},{"sibling":"19475e206bdf2698769a286db2c97c4d3f089741319f9b29a139038c6e511975","side":"right"},{"sibling":"1cecb7f447febd025aac272837c80de218aecc6485d2395a509b2a1f1b9c746e","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":313381,"merkle_root":"5f7d48580373d0ab0bc6bdf34f26de442f9a86d130946f7ee45addd1a55cb9f4","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260714T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-07-14T05:38:23Z","sig_algorithm":"ed25519","signature":"97364224142ed1b2a8925fed1bfba2e0a8a6a15f8ca0999b934846ad83584a78c7f0f5cd09dbc1c938b35383fcc5c8fa4b723118e30916628879d1c5fd3a9908","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_8f2ce9bf7391a4755bf69f1d6f4cf36fd425779332486f8cb643d5a1db4f1e09"}}