arxiv: 2604.08690 · v1 · submitted 2026-04-09 · 💻 cs.LG · cs.CL

Recognition: unknown

Skip-Connected Policy Optimization for Implicit Advantage

Fengwei Teng , Jinyi Bai , Xinhao Yao , Demi Ruohan Wang , Jiahao Zhao , Zhijiang Guo

Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:24 UTC · model grok-4.3

classification 💻 cs.LG cs.CL

keywords skip-connected policy optimizationdense rewardsgroup relative policy optimizationmathematical reasoningreinforcement learninglarge language modelschain of thoughtimplicit advantage

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The pith

Skip-connected policy optimization lets models apply dense rewards to early reasoning steps without the variance that normally makes them worse than outcome-only rewards.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Group-relative policy optimization succeeds with final-answer rewards but dense Monte Carlo estimates for early tokens produce high-variance and sign-inconsistent advantages that degrade performance under practical sampling limits. The paper introduces a decomposition of reasoning into upstream and downstream phases. Upstream steps receive dense rewards estimated from downstream Monte Carlo sampling under single-stream optimization, while downstream steps retain group-relative optimization. A skip connection concatenates the upstream segment directly to the original problem, so the model can still reach the answer even if upstream reasoning contains errors. Experiments report relative gains of 3.91 percent and 6.17 percent over strong baselines on mathematical benchmarks and out-of-domain tasks, together with evidence that generated trajectories contain higher-quality intermediate steps even when the final answer is correct.

Core claim

The paper establishes that Monte Carlo estimation of dense rewards leads to high-variance and sign-inconsistent advantages for early tokens, causing underperformance relative to outcome-only optimization. SKPO addresses this by decomposing the process into upstream and downstream phases, with upstream receiving dense rewards through single-stream optimization based on downstream Monte Carlo sampling, while downstream uses group-relative optimization. The key innovation is a skip connection that concatenates the upstream segment with the original problem, enabling the model to leverage useful upstream reasoning or bypass it entirely. This yields relative improvements of 3.91 percent and 6.17%

What carries the argument

The skip connection that concatenates the upstream reasoning segment with the original problem, allowing downstream optimization to use or ignore the upstream output.

If this is right

Trajectories exhibit higher intermediate-step quality even when final answers match the correctness of baseline trajectories.
Relative performance gains appear on both in-domain mathematical tasks and out-of-domain general reasoning and code-generation tasks.
Single-stream optimization for the upstream phase combined with group-relative optimization for the downstream phase avoids the variance problems observed in pure dense-reward settings.
The model retains the ability to solve the original problem directly when upstream reasoning is flawed.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The upstream-downstream split with skip access may extend to longer multi-hop reasoning chains by inserting additional skip points.
The observed improvement in step quality even on correct final answers suggests the method could aid human inspection or automated verification of reasoning paths.
The approach might reduce the sampling budget required to obtain reliable dense signals in other chain-of-thought domains.

Load-bearing premise

Monte Carlo estimation of dense rewards for early tokens remains beneficial once the skip connection is added and does not introduce new optimization inconsistencies under practical sampling budgets.

What would settle it

Training identical models with dense Monte Carlo rewards but without the skip connection and observing equal or better performance on the same mathematical benchmarks would falsify the necessity of the skip mechanism.

Figures

Figures reproduced from arXiv: 2604.08690 by Demi Ruohan Wang, Fengwei Teng, Jiahao Zhao, Jinyi Bai, Xinhao Yao, Zhijiang Guo.

**Figure 1.** Figure 1: Monte Carlo estimation of token-level rewards under practical sampling budgets (K = 8). Top: true values (left) vs. estimates (right). Bottom: sign accuracy and MAE, showing that early tokens suffer from higher estimation error. By the nature of MC sampling, true token rewards converge to the policy’s average accuracy on the prompt at early positions, and to the trajectory’s binary correctness at late posi… view at source ↗

**Figure 2.** Figure 2: Overview of the SKPO algorithm. We illustrate three components: (1) upstream sampling process and components for upstream advantage computation; (2) downstream sampling process and components for downstream advantage computation; (3) engineering optimization that completes both upstream and downstream sampling within a single GPU batch through KV cache rewriting. their outcome rewards: RMC(ot, a) = 1 K X K… view at source ↗

**Figure 3.** Figure 3: Upstream impact analysis comparing three conditioning strategies across Qwen and Llama models. Top: Diversity (average distinct answers per 8 rollouts); Middle: Advantage zero rate (probability of homogeneous outcomes); Bottom: Response length (excluding prefix). Continual conditioning leads to diversity collapse and elevated advantage zero rate, while Skip maintains properties comparable to Unconditional… view at source ↗

**Figure 4.** Figure 4: Segment-level implicit advantage analysis using GPT-5- nano as external evaluator across both Qwen and Llama models. For each method’s correct responses, we split into 100 segments by relative position and estimate rewards via Monte Carlo continuation sampling. Inter-method relative advantages are computed at each position. SKPO consistently maintains higher advantages in the 20–50% position range, indica… view at source ↗

**Figure 5.** Figure 5: Probability of correct advantage signs for all G = 8 samples across varying group spreads. Reliable credit assignment for narrow spreads requires prohibitive sample counts (N > 512). As claimed in Section 1, directly integrating fine-grained rewards with group-relative advantage estimation leads to a fundamental sign inconsistency problem: with limited Monte Carlo samples, estimated advantages frequently h… view at source ↗

**Figure 6.** Figure 6: Monte Carlo variance analysis. (a) Classification accuracy for individual samples. (b) Distribution shift and sign volatility under sampling noise. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗

**Figure 7.** Figure 7: Advantage estimation accuracy across different correctness distributions. Key observation: Only extreme cases (all correct or all incorrect) achieve reliable sign consistency. Mixed distributions suffer from severe sign errors throughout the trajectory, with accuracy often below 50%. Additional examples (1/8, 2/8, 4/8, 6/8, 7/8) are available in figures/mc/. The results reveal a striking pattern: reliable … view at source ↗

**Figure 8.** Figure 8: MC estimation accuracy across different sampling budgets (K = 8 to K = 8192). Left column shows true token rewards and advantages. Middle columns show MC estimates at each K value. Right column summarizes win rate, variance, and MAE trends. With sufficient samples (K ≥ 512), MC consistently outperforms GRPO, but the required sampling cost (up to 1000×) is impractical for real-world training. This analysis … view at source ↗

**Figure 9.** Figure 9: Mean accuracy at 32 samples across training steps [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗

**Figure 10.** Figure 10: Actor policy entropy throughout training. 0 100 200 300 400 500 Training Step 50 100 150 200 250 Time per Step (seconds) Training Time Per_Step Comparison GSPO SPO Critique DAPO CISPO SKPO [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗

**Figure 11.** Figure 11: Training time per step across different methods. Critique-GRPO exhibits significantly higher per-step time due to its two-batch rollout strategy: first generating 7 direct responses, then spawning 1 self-critique response in a separate GPU batch. Despite the two-phase upstream-downstream architecture, SKPO achieves comparable wall-clock time to single-phase baselines through our engineering optimization t… view at source ↗

read the original abstract

Group Relative Policy Optimization (GRPO) has proven effective in RLVR by using outcome-based rewards. While fine-grained dense rewards can theoretically improve performance, we reveal that under practical sampling budgets, Monte Carlo estimation yields high-variance and sign-inconsistent advantages for early reasoning tokens, paradoxically underperforming outcome-only GRPO. We propose Skip-Connected Optimization (SKPO), which decomposes reasoning into upstream and downstream phases: upstream receives dense rewards from downstream Monte Carlo sampling with single-stream optimization; downstream maintains group-relative optimization, where a skip connection concatenates the upstream segment with the original problem, enabling the model to leverage helpful upstream reasoning while preserving the freedom to bypass flawed reasoning through direct problem access. Experiments demonstrate improvements of 3.91% and 6.17% relative gains over the strongest baselines on Qwen2.5-Math-7B and Llama-3.2-3B respectively across mathematical benchmarks and out-of-domain tasks including general reasoning and code generation. Further analysis reveals an implicit advantage: SKPO generates trajectories with higher intermediate-step quality even when matched for final correctness.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

SKPO adds a skip connection and upstream-downstream split to GRPO to stabilize dense rewards on early tokens, with modest reported gains but an unproven mechanism.

read the letter

The core idea is to split reasoning chains so upstream tokens get dense Monte Carlo rewards from downstream sampling, while a skip connection feeds the original problem plus upstream output to the downstream phase. This is a targeted architectural tweak on top of GRPO that is not just a routine extension of the cited prior work, and the paper shows it produces 3.91% and 6.17% relative gains on Qwen2.5-Math-7B and Llama-3.2-3B across math benchmarks plus some out-of-domain reasoning and code tasks. The intermediate-step quality analysis is also useful, as it suggests the method may improve trajectory quality even on correct final answers. Those are the concrete positives worth noting. The main soft spot is that the skip connection explicitly gives the model a direct path to the original problem, which could let it ignore or bypass the upstream reasoning entirely. Under the same limited sampling budgets that already cause sign-inconsistent advantages in plain GRPO, this risks making the effective advantage for upstream actions even noisier or near zero, so the reported gains might stem from altered conditioning or optimization dynamics rather than the intended dense-reward stabilization. The abstract gives no error bars, no detailed ablation on sampling budgets, and no direct verification that the implicit advantage survives the skip. This leaves the central claim under-supported until those checks are in place. The work is aimed at people doing RLVR on long reasoning chains for math and code agents. Readers who already follow GRPO variants will get the most out of the empirical results and the proposed fix. It is coherent enough on its own terms to deserve a serious referee, who can pressure-test the advantage estimation and the bypass concern with the full experimental details. I would send it to peer review rather than desk reject.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes Skip-Connected Policy Optimization (SKPO) to improve upon Group Relative Policy Optimization (GRPO) in RLVR settings. It decomposes reasoning trajectories into upstream and downstream phases, applies Monte Carlo dense rewards to upstream tokens under single-stream optimization, and uses a skip connection in the downstream phase that concatenates the upstream segment with the original problem. This is claimed to yield an implicit advantage by preserving helpful upstream reasoning while allowing bypass of flawed segments. Experiments report relative gains of 3.91% on Qwen2.5-Math-7B and 6.17% on Llama-3.2-3B across math benchmarks plus out-of-domain reasoning and code tasks, with additional analysis showing higher intermediate-step quality even on trajectories matched for final correctness.

Significance. If the reported mechanism holds, SKPO offers a lightweight architectural modification that stabilizes advantage estimation for early tokens without requiring changes to the reward model or sampling budget. The multi-model, multi-task empirical results and the intermediate-quality observation provide concrete evidence of practical utility in LLM reasoning optimization.

major comments (3)

[§4] §4 (Mechanism and Analysis): The central claim that SKPO produces an implicit advantage via dense upstream rewards depends on upstream tokens receiving informative signals rather than being bypassed. The skip connection explicitly conditions downstream generation on both the problem and the upstream segment, yet no ablation measures the frequency or impact of bypass (e.g., by comparing performance with and without the skip or by correlating upstream token quality with final reward under fixed sampling budgets). Without this, the observed gains and intermediate-step improvements could arise from altered conditioning or optimization dynamics instead of the intended dense-reward mechanism.
[§5] §5 (Experiments): The abstract and experimental tables report relative gains of 3.91% and 6.17% without error bars, standard deviations, or details on the number of random seeds and sampling budgets used for Monte Carlo estimation. Given the paper's own observation that plain GRPO yields sign-inconsistent advantages under practical budgets, the absence of statistical characterization makes it impossible to determine whether the SKPO improvements are robust or could be explained by variance in the evaluation protocol.
[§3.2] §3.2 (Optimization): The upstream phase uses single-stream optimization with Monte Carlo dense rewards while the downstream phase retains group-relative optimization. The manuscript does not analyze whether this split introduces gradient inconsistencies or reward-scale mismatches at the boundary between phases, which could affect convergence under the same practical sampling budgets that already produce noisy advantages in GRPO.

minor comments (2)

The notation for the skip connection (e.g., how the concatenated input is formatted for the policy) is described only at a high level; a concrete example or pseudocode would improve reproducibility.
Figure captions and table footnotes should explicitly state the number of evaluation runs and whether the reported metrics are means or best-of-N.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment point-by-point below, clarifying the intended mechanism, committing to added statistical reporting and analyses, and outlining the revisions that will be incorporated in the next version of the manuscript.

read point-by-point responses

Referee: [§4] The central claim that SKPO produces an implicit advantage via dense upstream rewards depends on upstream tokens receiving informative signals rather than being bypassed. The skip connection explicitly conditions downstream generation on both the problem and the upstream segment, yet no ablation measures the frequency or impact of bypass (e.g., by comparing performance with and without the skip or by correlating upstream token quality with final reward under fixed sampling budgets). Without this, the observed gains and intermediate-step improvements could arise from altered conditioning or optimization dynamics instead of the intended dense-reward mechanism.

Authors: We agree that quantifying bypass behavior would provide stronger direct support for the implicit-advantage interpretation. The skip connection is explicitly introduced so that the downstream policy can ignore unhelpful upstream segments by attending directly to the original problem statement; our existing analysis already shows that SKPO produces higher-quality intermediate steps even on trajectories whose final answer matches the baseline, which is difficult to explain by conditioning changes alone. Nevertheless, the absence of an explicit ablation on bypass frequency or a with/without-skip comparison is a limitation. In the revised manuscript we will add (i) an ablation that removes the skip connection while retaining the upstream dense-reward signal and (ii) a correlation analysis between upstream token quality (measured by step-wise correctness) and final reward under fixed sampling budgets. revision: yes
Referee: [§5] The abstract and experimental tables report relative gains of 3.91% and 6.17% without error bars, standard deviations, or details on the number of random seeds and sampling budgets used for Monte Carlo estimation. Given the paper's own observation that plain GRPO yields sign-inconsistent advantages under practical budgets, the absence of statistical characterization makes it impossible to determine whether the SKPO improvements are robust or could be explained by variance in the evaluation protocol.

Authors: We acknowledge that the lack of error bars and seed information weakens the statistical presentation, especially given the variance issues we ourselves highlight for GRPO. In the revised manuscript we will report all main results with standard deviations computed over at least three independent random seeds, explicitly state the Monte Carlo sampling budgets used for both training and evaluation, and include these details in the experimental tables and abstract where appropriate. revision: yes
Referee: [§3.2] The upstream phase uses single-stream optimization with Monte Carlo dense rewards while the downstream phase retains group-relative optimization. The manuscript does not analyze whether this split introduces gradient inconsistencies or reward-scale mismatches at the boundary between phases, which could affect convergence under the same practical sampling budgets that already produce noisy advantages in GRPO.

Authors: The hybrid optimization is intentional: single-stream dense rewards are applied only to upstream tokens to obtain low-variance signals, while group-relative optimization is retained for the downstream phase to preserve the stable advantage estimation that GRPO already provides. The skip connection ensures that the downstream input always includes the original problem, so the policy gradient at the boundary remains well-defined. We did not observe training divergence or anomalous gradient magnitudes in any of our runs. Still, we agree that an explicit check is warranted. In the revision we will add a short analysis (including gradient-norm and reward-scale statistics at the phase boundary) to confirm the absence of systematic mismatches. revision: yes

Circularity Check

0 steps flagged

Architectural change with empirical validation; no derivation reduces to self-referential inputs

full rationale

The paper defines SKPO via an explicit decomposition into upstream/downstream phases plus a skip connection, then reports experimental gains and intermediate-quality analysis. No equations are shown where a 'prediction' or 'implicit advantage' is mathematically identical to a fitted parameter or input quantity by construction. No load-bearing self-citations or uniqueness theorems are invoked to force the result. The central claims rest on the proposed mechanism being tested against baselines rather than on tautological renaming or fitted-input predictions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard RL assumptions plus the empirical observation that skip connections mitigate variance; no new physical entities or ad-hoc constants are introduced beyond typical RL hyperparameters.

free parameters (1)

RL training hyperparameters
Standard learning rates, batch sizes, and sampling budgets are fitted or chosen during training but are not load-bearing for the architectural claim.

axioms (1)

domain assumption Outcome-based rewards can be extended to dense estimates via Monte Carlo sampling under practical budgets
Invoked when contrasting GRPO with dense-reward attempts in the abstract.

pith-pipeline@v0.9.0 · 5502 in / 1368 out tokens · 46384 ms · 2026-05-10T17:24:02.796916+00:00 · methodology

discussion (0)

Forward citations

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Works this paper leans on

2 extracted references · 2 canonical work pages · cited by 1 Pith paper

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work page doi:10.18653/v1/2025.emnlp-main 2025
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how easy is it to reach a correct answer from this intermediate state

URL https://aclanthology.org/2025. emnlp-main.252/. Li, L., Lu, D., Shao, J., Zhang, C., and Li, X. Scrpo: From errors to insights.arXiv preprint arXiv:2511.06065, 2025c. Li, Z., Xu, T., Zhang, Y ., Lin, Z., Yu, Y ., Sun, R., and Luo, Z.-Q. Remax: A simple, effective, and efficient rein- forcement learning method for aligning large language models. InFort...

work page arXiv 2025