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Top-$p$ routing is more adaptive because it selects experts until their cumulative routing probability reaches a threshold, allowing confident tokens to use fewer experts and ambiguous tokens to recruit more. However, we demonstrate that existing naive Top-$p$ implementations with fixed global probability thresholds provide only marginal gains over Top-$k$, suffer from hyperparameter sensitivity, and result in uncontrolled computational costs. In this paper, we propose **DTop-$p$**, a sparsity-controllable dynamic routing mechanism that learns the Top-$p$ probability threshold with a Proportional-Integral controller and uses dynamic routing normalization to support layer-wise expert","title":"DTop-p MoE: Sparsity-Controlled Dynamic Top-p MoE for Foundation Model Pre-training","url":"https://arxiv.org/abs/2512.13996","vendor":"arxiv_cs_ai"},"summary":"arXiv:2512.13996v2 Announce Type: replace \nAbstract: Sparse Mixture-of-Experts architectures are essential for scaling model capacity efficiently, yet the standard Top-$k$ routing imposes a rigid sparsity pattern that ignores the intrinsic variance in token difficulty and layer-specific computational needs. Top-$p$ routing is more adaptive because it selects experts until their cumulative routing probability reaches a threshold, allowing confident tokens to use fewer experts and ambiguous tokens to recruit more. However, we demonstrate that existing naive Top-$p$ implementations with fixed global probability thresholds provide only marginal gains over Top-$k$, suffer from hyperparameter sensitivity, and result in uncontrolled computational costs. In this paper, we propose **DTop-$p$**, a sparsity-controllable dynamic routing mechanism that learns the Top-$p$ probability threshold with a Proportional-Integral controller and uses dynamic routing normalization to support layer-wise expert","title":"DTop-p MoE: Sparsity-Controlled Dynamic Top-p MoE for Foundation Model Pre-training","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-01T04:43:13Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2512.13996"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:4ab921fc9f6c7bb2a8e5117ef5d49ad562c256a6d0b385434867ecef6cdb862f68600a0b7a8ab325096ed7fd440cd1bb7c712407f0d11ae6faa6bc7e75bc1002","signer":"crovia.substrate","subject":{"observed_at":"2026-06-01T04:43:13Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2512.13996"},"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":"6ff2a616bedfb51cd41d50d55f682b7d4ca89f94100672b4a5bd39bb43e885d0","leaf_index":164004,"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":"d509f2306ad31ea7d933a2e5a4c044f6857098276861564ee401cf07f21f4b32","side":"right"},{"sibling":"f92929f728f020c5f3b75182206094667d70bb6b3f29b4686a5e4b14c80b4a34","side":"right"},{"sibling":"801a29fe2d3a4e0bdfd15c62c3ebd62bc60546eb5abb828eb24dc5738d3d8e5d","side":"left"},{"sibling":"55f15a8c1578a5293965661a23dd862f90d71b9e98e657628a684c66a7a5b7ed","side":"right"},{"sibling":"2f465fb071a98a6ea8b6b765aa4b8bf2624470f1f846713514a21bfd02d575e5","side":"right"},{"sibling":"2ed5dc81b48343dc042200ddd691ec7502014cec7a175df1a1ffd9a76812eb3a","side":"left"},{"sibling":"1d23b94e7765a5d6bcc243f4f7ecca5895f450b29cd855b417c9c7111e6b5a45","side":"right"},{"sibling":"c2ed258674acbec09c8c9dbf15c89e6fc50854c6eb5f8d42b378de7db248641a","side":"left"},{"sibling":"86fede29e507d01bfe35484a1579149e8e99b3527ff48559423f6056d11af46a","side":"right"},{"sibling":"fc601f0745c37fc5f7c249300e654db05d61bb9059885eeb0b0a5047b5d28408","side":"right"},{"sibling":"6ed9290cdae063f13bfeb71c4c5440595cabb61fd4b39225b9cc913ffb336dd7","side":"right"},{"sibling":"a0446b923d1ce90021e78edff07f6bfc7cc2a1326a565c5f0786b82a24dd0a2a","side":"right"},{"sibling":"e598fd53912c30e58ca8e58d7d8a338fe0f2ecb63fdd99225bc703c499c948ec","side":"right"},{"sibling":"fc4873333221ec8167697f75b6f6a8a08491a8cf18952defb65fb6d4958fa5e7","side":"right"},{"sibling":"05c8a827da2a05549ee3250310777009120c687885816bf6c7c74801bfaa346d","side":"right"},{"sibling":"5ea2f2dc9f046df723b6bd9932d61a9a3d80a76e79ce1b939b3d93ff79b5a91c","side":"left"},{"sibling":"ce41d9b82f34b16efd653dfb3552acc4e2512939e47903e5fc979fbed00c5764","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":164217,"merkle_root":"a1098816aea1b60b8fe37b62410469bc5024a2c335bbec4f6ef2add7875dbdf2","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260601T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-01T05:37:41Z","sig_algorithm":"ed25519","signature":"d7f91db1d54b9495c499440c2828f4bd53360555391ce6e25adea5183bc1fa0f697d80708a099d0b0429e6f8cb6c71e7fccf82acb3c84481149974fb26074708","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_b856eb734411898b1b228807d00a0e75b2967b4922203681c44a52111ac4772a"}}