{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_4d00795765e309973682b62b29f87a5d674a1f98e3093d83647156dce82fcb35","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_4d00795765e309973682b62b29f87a5d674a1f98e3093d83647156dce82fcb35","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"ea10240d90bfe26b68fec5931cbde5ca41c4283dc723f47d3f4990ea7ad4574b","published":"Thu, 28 May 2026 00:00:00 -0400","receipt_hash":"ea10240d90bfe26b68fec5931cbde5ca41c4283dc723f47d3f4990ea7ad4574b","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"ea10240d90bfe26b68fec5931cbde5ca41c4283dc723f47d3f4990ea7ad4574b","observed_at":"2026-05-28T04:43:38.862500Z","parent_run_hash":"58f8b4a134069e0a15ea3949252489597eb86dd27c9ca3fb15c6fb838ce49ef3","published":"Thu, 28 May 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2605.28388v1 Announce Type: new \nAbstract: Reinforcement Learning with Verifiable Reward (RLVR) is empirically shown to notably enhance the reasoning performance of large language models (LLMs), particularly in mathematics and programming. However, the mechanistic role of Sample Difficulty in RLVR remains poorly understood. In this paper, we investigate RLVR through the lens of difficulty-wise and one-sample analysis. We find that sample difficulty has a non-monotonic effect on RLVR: easy and medium-difficulty problems yield the strongest and most stable reasoning improvements, whereas overly hard problems often provide weak learning signals, induce degenerate behaviors such as answer repetition or skipping necessary computation, and can ultimately degrade the model's pre-existing capabilities. Beyond the obverse of response, we further analyze the model's internal feature dynamics using Temporal Sparse Autoencoders (T-SAE). Easy problems mainly reinforce direct-answer and basic-","title":"Mechanistically Interpreting the Role of Sample Difficulty in RLVR for LLMs","url":"https://arxiv.org/abs/2605.28388","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.28388v1 Announce Type: new \nAbstract: Reinforcement Learning with Verifiable Reward (RLVR) is empirically shown to notably enhance the reasoning performance of large language models (LLMs), particularly in mathematics and programming. However, the mechanistic role of Sample Difficulty in RLVR remains poorly understood. In this paper, we investigate RLVR through the lens of difficulty-wise and one-sample analysis. We find that sample difficulty has a non-monotonic effect on RLVR: easy and medium-difficulty problems yield the strongest and most stable reasoning improvements, whereas overly hard problems often provide weak learning signals, induce degenerate behaviors such as answer repetition or skipping necessary computation, and can ultimately degrade the model's pre-existing capabilities. Beyond the obverse of response, we further analyze the model's internal feature dynamics using Temporal Sparse Autoencoders (T-SAE). Easy problems mainly reinforce direct-answer and basic-","title":"Mechanistically Interpreting the Role of Sample Difficulty in RLVR for LLMs","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-28T04:43:38Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.28388"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:2a8b94cccf833ed09ce2a9fcd93fa7b045c9a94245bc783a2965e659de8f9ce12e010c414bcbea4979e2c585254869feefcb51dc80303354c8cb79aae87ffb05","signer":"crovia.substrate","subject":{"observed_at":"2026-05-28T04:43:38Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.28388"},"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":"1849e2283226bf3c957011eedc668a42091e60043239a9daf10d30b1b0a2a36f","leaf_index":155681,"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":"f7a6b9c8733ece2e5e652738332bbffd9c8a9b50e5c3889243877cdd6f79c510","side":"left"},{"sibling":"470c49e5737a9be7093583a2e82704783cd444d85952ae862f76da24ce5ce2e2","side":"right"},{"sibling":"9650d2a081c143451fcbd1dddfd9400ecc2b8ace50a27da0145335cb2e29cbae","side":"right"},{"sibling":"4212d47318c662a8117fb5075cb416374b3962c4c15c003abe4c3f607890889a","side":"right"},{"sibling":"88a5b09bdd647673190e24d8d4d08a26a0d4adf5c599885cd73097d552e601fb","side":"right"},{"sibling":"5743bc352c06496fc3b58c8a3462f60161d9cae157c0e80c0e29b0772529e640","side":"left"},{"sibling":"36a1078bdcaa003b6d473a09d4271a7c46743ba8b6266a216c903bba5595bb84","side":"right"},{"sibling":"afa86de7d2b39f53748bea8c4274ea857aed4694d034da9da1628457bb87cbe4","side":"right"},{"sibling":"0adb35dd3ad9bfc4a781c02606acf0a3ce1e28e1a88066209cc1a35814e790ad","side":"right"},{"sibling":"f292d3278e493ec60902181b8c0bd5c89c0a1168ef928222fe6161287982f7f0","side":"right"},{"sibling":"2209295faf1a5bf51c97c6fd5a839a8181a4ea44f490420381530f35df7d9b2f","side":"right"},{"sibling":"5784576a15214ea9fc3569e6e1cff1ef443c0b1fc0d036028489088af089de27","side":"right"},{"sibling":"311772ec218efcb2da5a337f9e9f042fe1cc0028643adb0a354787e4ea7911b7","side":"right"},{"sibling":"66331bac84ca0f8983eb09fac7eaf95af234f1b82680b793eabff4ee25caac40","side":"left"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"7b6f0bea4291a5e63574dfca9aa0f9756f450c9478c3d07474d39a7ababb51f9","side":"right"},{"sibling":"1d39fe14b21e2ebbfb87e882423b24ee9469eae1e4c77af5b799ac4db9537467","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":156177,"merkle_root":"c5705a0243d16afd8b1ebfd731b7aa304079c442c2a7906493c5bbed374c69ec","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260528T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-28T05:37:36Z","sig_algorithm":"ed25519","signature":"f087e13febc8bb6a2e0812610de64cebc65be92915518d9c4b230799c3b161839b04c4eb1b02741f938f35545a76ab76555b04c782bdc2f9a44852d171d65909","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_4d00795765e309973682b62b29f87a5d674a1f98e3093d83647156dce82fcb35"}}