Source-linked AI summary
Nemotron-Cascade 2: Post-Training LLMs with Cascade RL and Multi-Domain On-Policy Distillation
Zhuolin Yang, Zihan Liu, Yang Chen, Wenliang Dai, Boxin Wang, Sheng-Chieh Lin, Chankyu Lee, Yangyi Chen, Dongfu Jiang, Jiafan He, Renjie Pi, Grace Lam, Nayeon Lee, Alexander Bukharin, Mohammad Shoeybi, Bryan Catanzaro, Wei Ping
TL;DR
Nemotron-Cascade 2 addresses the challenge of scaling LLM post-training across diverse reasoning and agentic environments. It combines broad SFT with expanded Cascade RL and multi-domain on-policy distillation, achieving best-in-class broad benchmark performance and gold-medal results in major mathematical and coding competitions.
Problem
LLM post-training must incorporate increasingly diverse reasoning and agentic tasks while handling varied rewards and complex environmental feedback without destabilization.
Method
The model combines broad supervised fine-tuning with expanded Cascade RL, multi-domain RL, and on-policy distillation from domain-specific intermediate teachers.
Results
Nemotron-Cascade 2 delivers best-in-class performance across broad benchmarks and gold-medal performance in the IMO, IOI, and ICPC World Finals.
Takeaways & Limitations
The open 30B MoE model demonstrates high intelligence density while releasing model weights, training data, and methodological details for reproduction and extension.
Takeaways & Limitations
IMO 2025 P2 uses an LLM grader because human experts may struggle to verify all intermediate derivation steps.
Abstract
from arXiv · showhide
We introduce Nemotron-Cascade 2, an open 30B MoE model with 3B activated parameters that delivers best-in-class reasoning and strong agentic capabilities. Despite its compact size, its mathematical and coding reasoning performance approaches that of frontier open models. It is the second open-weight LLM, after DeepSeekV3.2-Speciale-671B-A37B, to achieve Gold Medal-level performance in the 2025 International Mathematical Olympiad (IMO), the International Olympiad in Informatics (IOI), and the ICPC World Finals, demonstrating remarkably high intelligence density with 20x fewer parameters. In contrast to Nemotron-Cascade 1, the key technical advancements are as follows. After SFT on a meticulously curated dataset, we substantially expand Cascade RL to cover a much broader spectrum of reasoning and agentic domains. Furthermore, we introduce multi-domain on-policy distillation from the strongest intermediate teacher models for each domain throughout the Cascade RL process, allowing us to efficiently recover benchmark regressions and sustain strong performance gains along the way. We release the collection of model checkpoint and training data.
1. Introduction
Nemotron-Cascade 2 scales Cascade RL to broader reasoning and agentic domains while adding multi-domain on-policy distillation to recover regressions during training. The resulting open 30B MoE model has 3B activated parameters and achieves gold-medal-level performance in major mathematical and coding competitions.
- Reinforcement learning post-training must accommodate diverse reasoning and agentic tasks, reward signals, and environmental feedback without destabilizing training.
- Nemotron-Cascade 2 is an open 30B Mixture-of-Experts model with 3B activated parameters.
- Cascade RL is expanded across high-priority domains, while multi-domain RL jointly trains tasks with similar response formats and verification costs.
- Multi-domain on-policy distillation uses the best-performing intermediate teacher for each domain to recover benchmark regressions arising in increasingly complex RL environments.
- The model achieves gold-medal results in the 2025 IMO and IOI while delivering best-in-class performance across alignment, instruction-following, long-context, and agentic benchmarks.
2. Main Results
Nemotron-Cascade 2 achieves best-in-class results across mathematics, code reasoning, alignment, and instruction following, alongside gold-medal performance in the IMO, IOI, and ICPC World Finals. Its comparisons show broad gains over several released models, while knowledge-intensive and agentic benchmarks remain weaker than Qwen3.5-35B-A3B.
- The evaluation covers mathematical and coding reasoning, knowledge and STEM, alignment, instruction following, long-context understanding, multilingual capabilities, and agentic tasks.
- Nemotron-Cascade 2 achieves gold-medal performance in the 2025 IMO and IOI and is the second open-weight LLM reported to achieve this result in both competitions.
- Nemotron-Cascade 2 outperforms Qwen3.5-35B-A3B and Nemotron-3-Super-120B-A12B across benchmarks in mathematics, code reasoning, general alignment, and instruction following.
- IMO 2025 P2 uses an LLM grader with a ProofBench reference solution and marking schema because human experts may struggle to verify every intermediate derivation step.
- The model achieves gold-medal performance on IMO 2025, IOI 2025, and ICPC World Finals 2025 despite its 30B MoE scale.
- The model outperforms Nemotron-3-Nano-30B-A3B on nearly all benchmarks but underperforms Qwen3.5-35B-A3B on knowledge-intensive and agentic benchmarks.
3. Supervised Fine-Tuning
The SFT stage builds foundational reasoning, conversational, instruction-following, agentic, and software-engineering capabilities from a broad multi-domain corpus. Data curation combines diverse teacher-generated samples, tool-use formats, long-context examples, safety data, and agentic and agentless software-engineering trajectories.
- SFT equips the model with foundational reasoning, conversational, instruction-following, agentic, and software-engineering capabilities.
- The SFT data spans mathematics, coding, science, tool use, agentic tasks, software engineering, dialogue, knowledge-intensive QA, creative writing, role-playing, safety, and instruction following.
- Chat Template: The chat template uses an empty <think></think> block for non-thinking mode, a single <think> followed by a newline for thinking mode, and tagged tool calls.
- Mathematics: Math SFT includes 1.8M Python tool-calling samples, 1.9M non-tool samples, and 816K mathematical proof generation and verification samples.
- Additional Domains: The corpus also includes science, long-context, reasoning-mode, multi-turn dialogue, instruction-following, safety, and conversational tool-use samples from multiple teacher models.
4. Cascade RL and Multi-Domain On-Policy Distillation
Nemotron-Cascade 2 integrates sequential, domain-wise Cascade RL with multi-domain on-policy distillation to expand capabilities while mitigating regressions across specialized stages. Its pipeline improves instruction following, reasoning, alignment, and agentic coding performance through ordered training, stabilization, and dense token-level distillation.
- Cascade RL ordering: The pipeline proceeds from instruction-following RL through multi-domain RL, MOPD, RLHF, long-context RL, and code RL.These stages target instruction adherence, tool use, STEM reasoning, response formatting, unified expertise, alignment, long-context reasoning, and coding.
- Cascade RL ordering: Cascade RL uses sequential, domain-wise training after SFT, with stage ordering adapted to model behaviors and learning trajectories.The ordering aims to reduce interference between domains as the model’s capabilities and training environments change.
- Multi-domain on-policy distillation: MOPD stabilizes Cascade RL by recovering benchmark performance that regressed during specialized stages, producing a more balanced final policy.Its role is to unify specialized expertise after domain-specific training.
- Instruction-following RL: 83.13% accuracy on IFBench demonstrates state-of-the-art instruction adherence from the first Cascade RL stage.The instruction-following stage uses verifiable rewards and precedes later stages that can recover alignment regressions.
- Multi-domain on-policy distillation: MOPD uses dense token-level supervision, reaching stronger performance in fewer optimization steps than sparse outcome-reward RL methods.On AIME25, GRPO rises from 89.9 to 91.0 after 25 steps, while MOPD reaches 92.0 within 30 steps and recovers teacher-level performance.
- Agentless RL: Agentless RL improves both agentless and agentic SWE-bench performance, suggesting code-repair gains generalize across evaluation scaffolds.The evaluation uses Agentless Mini retrieval and SWE-bench Verified with the OpenHands scaffold.
5. International Mathematical Olympiad (IMO)
Nemotron-Cascade-2-30B-A3B is evaluated on IMO 2025 with self-improving generate-verify-refine inference and achieves strong olympiad-level proof performance. Its IMO-ProofBench results are reported across Basic, Advanced, and Overall splits under LLM grading.
- IMO 2025: The model iteratively generates candidate solutions, verifies them, and refines them using its own feedback.
- IMO 2025: The model successfully solves the first five IMO 2025 problems despite its 30B-A3B scale.
- IMO-ProofBench: IMO-ProofBench reports Basic, Advanced, and Overall scores over 30, 30, and 60 problems, respectively.
- IMO-ProofBench: 72.9 on IMO-ProofBench places the model within 8 points of DeepSeek-Math-V2-671B-A37B with 10× fewer active parameters.
- IMO-ProofBench: On IMO-ProofBench Advanced, increasing test-time compute raises the score from 40.7 at round 1 to 53.4 at round 5.
6. Competitive Coding
Nemotron-Cascade-2-30B-A3B is evaluated with multi-round test-time scaling for IOI and large-scale solution generation for ICPC. It achieves gold-medal-level outcomes while showing strong competitive-coding benchmark performance, especially with tool-integrated reasoning.
- IOI 2025: IOI inference uses a multi-round generate-select-submit framework with up to 50 rounds per subtask and 40 candidate solutions per round.
- IOI 2025: 439.28 within at most 2000 model generations yields a gold-medal score, while 507.66 is achievable within 5000 generations.
- ICPC World Finals 2025: The ICPC pipeline generates up to 1000 solutions per problem and successfully solves 10 of 12 problems for the #4 Gold medal placement.
- Benchmark Results: Competitive-coding evaluation covers LiveCodeBench v6, LiveCodeBench Pro, and simulated Codeforces rounds using avg@8 results under a 128K-token thinking budget.
- Benchmark Results: Tool-Integrated Reasoning further boosts performance on hard problems and matches stronger open-source models with more than 300B total parameters.
A.1.1. Non-proof Math
The non-proof mathematics evaluation covers contemporary contest-style benchmarks and uses long-budget reasoning with optional stateful Python tool use. Baselines are taken from official reports or evaluated under recommended settings.
- Benchmarks: Non-proof math evaluation includes AIME 2025, AIME 2026, HMMT February 2025, and IMO-AnswerBench.
- Evaluation Setup: The model uses a 131K-token thinking budget, temperature 1.0, and top-p 1.0 on AIME 2025, AIME 2026, and HMMT February 2025.
- Evaluation Setup: With tools enabled, the model can call a stateful Python executor for up to 100 tool calls.
- Evaluation Setup: Baseline results come from official reports or recommended evaluation settings when official numbers are unavailable.
A.1.2. Math Proof
The math-proof evaluation uses IMO 2025 and IMO-ProofBench, applying generate-verify-refine test-time scaling and repeated LLM grading. The broader appendix also specifies benchmark coverage and inference settings for coding, knowledge, alignment, and long-context tasks.
- Math-Proof Benchmarks: IMO-ProofBench contains 60 proof-based problems split evenly between Basic and Advanced subtasks.
- Proof Evaluation: The generate-verify-refine pipeline uses 128 proof generations, 64 verifications per proof, top-32 proof selection, and four refined proofs.
- Proof Evaluation: For lower-budget IMO-ProofBench cases, the evaluation reduces computation to 32 generations, 16 verifications, top-8 proofs, and two rounds.
- Proof Evaluation: A zero-score judge result forces the final score to zero; otherwise, scores are averaged, reducing DeepSeek-Math-V2’s discrepancy from human ratings from 11.9 to 4.2 points.
- Additional Evaluation: The appendix evaluates coding, knowledge, alignment, and long-context capabilities using dedicated benchmark suites and specified inference configurations.
- Knowledge Reasoning: A boxed-answer prompt improves HLE accuracy by 6–7 points, primarily on the math subset, by matching the answer format used in math SFT data.
A.6. Agentic Tasks
The evaluation suite covers agentic interaction, coding, and multilingual capabilities using task-specific protocols for reasoning traces, context retention, and single-generation accuracy.
- Agentic evaluation: BFCL v4 evaluates web search, memory operations, and function invocation across multiple programming languages and agentic categories.Scores are reported for Agentic, multi-turn, live, and non-live categories using thinking mode and pass@1 accuracy from a single generation.
- Agentic evaluation: SWE-bench Verified uses the OpenHands scaffold with full interaction retention across long-horizon debugging trajectories.The retained history includes tool calls, observations, file views, search results, commands, and intermediate patches.
- Agentic evaluation: τ2-Bench retains reasoning after the latest user turn while discarding earlier-turn reasoning, unlike the official no-thought-carry-over setup.The paper attributes the official setup’s lower scores to train–test mismatch because the SFT data uses latest-turn thought retention.
- Multilingual evaluation: Multilingual evaluation includes MMLU-ProX across 29 languages and WMT24++ across 55 languages.For MMLU-ProX, six languages are selected: English, German, Spanish, French, Italian, and Japanese; evaluation uses thinking mode and pass@1 from one generation.
B. Training Hyperparameters
The paper records training hyperparameters for supervised fine-tuning, Cascade RL stages, and execution-based agentic SWE-RL, alongside structured coding-task prompts and judging criteria.
- Training stages: Training hyperparameters are tabulated separately for SFT, Cascade RL, and execution-based agentic SWE-RL.Cascade RL hyperparameters are split across IF-RL, multi-domain RL, MOPD, RLHF, long-context RL, and code RL tables.
- Coding prompts: The coding prompt requires Python solutions in a specified format and permits accepted solutions with different constraints as references.The prompt also supplies prior incorrect submissions and official verdicts for potential improvement.
D. ELO Rating Analysis
The ELO analysis evaluates Nemotron-Cascade-2-30B-A3B across 40 recent Div.1 and Div.2 Codeforces contests, estimating performance and human-relative ranking under repeated submissions.
- Evaluation setup: 40 recent Div.1 and Div.2 Codeforces contests are used to estimate model performance and relative ranking to human contestants.The evaluation uses LiveCodeBench Pro and allows up to N=8 submissions per contest problem with expected-penalty consideration.
- Evaluation setup: The model uses temperature 1.0, top-p 0.95, and a maximum token budget of 128K during response generation.The analysis follows a rating-estimation approach similar to the prior work cited in the passage.
- Observed performance: The model performs strongly on difficult problems and some Div.1 rounds while remaining stable on easy-to-medium problems.Reported weaknesses involve constructive algorithms, interactive tasks, and hypothesis-driven ideas.
- Results tables: Tables 11 and 12 report Codeforces performance details without and with python-tool use, respectively.They include contest outcomes, estimated human rank, and corresponding Elo scores; each problem is attempted N=8 times.
2. Impossibility: no other value of 𝑘can occur
The impossibility argument proves that a covering of S_n by n lines can have only k∈{0, 1, 3} sunny lines, excluding every other value.
- Boundary counting: A boundary set X contains 3n−3 distinct points on the three sides x=1, y=1, and x+y=n+1.The three corners are counted twice when summing the n points on each side.
- Boundary counting: Any line other than the three special sides contains at most two points of X.A non-side line intersects the triangle boundary in at most two points and cannot contain two points from the same side.
- Forcing a special side: For n≥4, counting boundary coverage forces every n-line covering to contain at least one special side.The proof introduces the number of special sides present and derives this requirement from the coverage bound.
- Induction: Removing a present special side and translating the remaining lines produces an S_{n−1} covering with the same number k of sunny lines.Translation preserves slopes and distinctness, enabling induction on n.
- Base case and conclusion: The base case n=3 excludes k=2, while explicit constructions establish k=0, 1, and 3.Thus induction yields the complete set of possible values {0, 1, 3}.
8. Verification of (3)
The proof verifies equation (3) by substituting explicit expressions and reducing the result to an identical algebraic identity. This establishes the tangency conclusion and completes the coordinate proof.
- Algebraic verification: The explicit substitutions for L and K reduce the left-hand side to d^2(U^2 + V^2 − 2d^2).The expansion cancels the U^2V^2 terms and matches the right-hand side.
- Algebraic verification: The matching expressions prove (3’), and consequently establish equations (3) and (2).The proof explicitly states the equivalence chain from the verified identity.
- Final conclusion: Therefore, the line through H parallel to AP is tangent to the circumcircle of triangle BEF.This is the final geometric consequence of the verified algebraic conditions.
- Proof assessment: The coordinate proof is complete despite several compressed algebraic steps, because those steps follow from previously established formulas.The verification identifies the jumps as routine consequences rather than missing geometric arguments.
- Proof assessment: Under ultra-strict marking, the solution receives full credit because it proves the final tangency condition rather than merely asserting it.The assessment also notes that the coordinate route is denser and less elegant than the reference synthetic proof.
Notation and basic facts
The game’s outcome is determined by comparing λ with √2/2: Alice wins above the threshold, Bazza wins below it, and neither can force a win at equality. The proof analyzes legal moves through slack and a maximal strategy for Bazza.
- Proof framework: The analysis defines slack after each even turn and uses it to determine whether Alice can legally move or exploit a winning threshold.The maximal strategy chooses Bazza’s move to attain the largest permitted even-turn sum of squares.
- Outcome by λ: For λ>√2/2, Alice has a winning strategy that eventually forces Bazza to have no legal move.Alice usually chooses 0, but uses available slack to select a move whose square pushes Q above the next even-turn bound.
- Outcome by λ: At λ=√2/2, neither player has a strategy that forces a win, so the game can continue forever as a draw.Bazza’s maximal strategy prevents Alice from winning while allowing indefinite play, for example when Alice always chooses 0.