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Reward Models Are Secretly Value Functions: Temporally Coherent Reward Modeling

T0 review · 0 major / 3 minor · reviewed 2026-05-08 · grok-4.3

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Pith's one-line read Reward models can output the conditional expectation of the final reward at every token by adding two regularization terms to the Bradley-Terry loss.

desk verdict TCRM adds two regularizers to the Bradley-Terry loss so the reward model outputs conditional expectations at every token, with reported gains in token accuracy, ProcessBench results from outcome data, and PPO efficiency. read the letter →

arxiv 2604.22981 v1 submitted 2026-04-24 cs.LG

Alex Nikulkov This is my paper · ORCID
classification cs.LG
keywords rewardmodelingRLHFvaluefunctionstemporalcoherenceprocesssupervisionPPOBradley-Terrylossconditionalexpectations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Reward models in RLHF are currently trained to score only the final token of a response. This discards information from intermediate positions and leaves token-level outputs noisy. The paper shows that a reward model's score at any token should instead equal the expected final reward given the response so far. Temporally Coherent Reward Modeling adds two regularization terms to the standard Bradley-Terry loss. These terms correspond to Monte Carlo and temporal-difference value-learning objectives, and their minimizers are provably the desired conditional expectations. The resulting models supply accurate token-level trajectories, strong process-supervision performance from outcome data alone, and lower memory use when reward and value modeling are combined in PPO.

What carries the argument

Temporally Coherent Reward Modeling (TCRM), which augments the Bradley-Terry loss with two regularization terms that enforce consistency with Monte Carlo and TD value-learning objectives.

What would settle it

Train identical reward models on the same data with and without the two TCRM regularizers, then check whether only the regularized version produces token-level outputs whose pairwise accuracy reaches 88.9 percent and whose values match empirical conditional expectations of the final reward.

Watch

Extended reading notes

Core claim

Augmenting the Bradley-Terry ranking loss with Monte Carlo and temporal-difference regularization terms makes the minimizers of the objective exactly equal to the conditional expectations of the terminal reward given any prefix, so that the trained reward model functions as a value function at every token.

Load-bearing premise

Adding the two regularizers will enforce the conditional-expectation property at every token without lowering final-token ranking accuracy or introducing optimization instabilities that erase the claimed efficiency gains.

Editorial extensions

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same regularization principle could supply dense credit-assignment signals in long-horizon tasks where current reward models provide only sparse terminal feedback.
  • Unified reward-value models may simplify other actor-critic algorithms beyond PPO by removing the need for a separate value head.
  • The approach suggests that many ranking-based objectives in machine learning could be regularized to produce temporally consistent predictions without changing model architecture.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. The manuscript argues that reward models trained only on final-token scores in RLHF discard useful intermediate signals and produce noisy token-level outputs. It introduces Temporally Coherent Reward Modeling (TCRM), which augments the standard Bradley-Terry loss with two regularization terms whose forms match Monte Carlo and temporal-difference value-learning objectives. The central theoretical claim is that the global minimizers of the combined objective are exactly the conditional expectations of the final reward given any response prefix. The approach requires no architectural, data, or inference changes and is reported to yield interpretable token-level reward trajectories (middle-token pairwise accuracy rising from 50% to 88.9% while preserving final-token accuracy), state-of-the-art ProcessBench F1 among outcome-supervised models, and a 27% memory / 19% step-time reduction when the same model serves as both reward and value function inside PPO.

Significance. If the equivalence proof is correct and the reported empirical gains prove robust, the work provides a clean, zero-overhead bridge between reward modeling and value functions. The fact that the regularizers are derived directly from standard RL objectives and that the minimizers are parameter-free conditional expectations is a genuine strength. Practical payoffs—better process supervision from outcome data alone and reduced PPO memory footprint—would be attractive to the RLHF community. The manuscript also ships concrete numbers on token-level accuracy and efficiency that can be checked.

minor comments (3)
  1. [Abstract, §4.1] Abstract and §4.1: the middle-token pairwise accuracy figure (50% → 88.9%) is presented without stating the exact evaluation protocol (e.g., whether pairs are drawn from the same response or across responses) or confirming that the 50% baseline is indeed random guessing under the chosen sampling.
  2. [§5.3, Table 4] §5.3 and Table 4: the 27% peak-GPU-memory and 19% step-time reductions are given without reporting the precise model size, batch size, or whether the unified reward/value head shares all parameters or only the backbone; these details are needed to reproduce the efficiency claim.
  3. [Figure 2] Figure 2: the token-level reward trajectories lack variance bands or multiple-run statistics, making it difficult to judge whether the observed coherence is stable across random seeds or data orderings.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and accurate summary of our work, the recognition of its significance as a bridge between reward modeling and value functions, and the recommendation for minor revision. The referee's assessment correctly identifies the core theoretical claim (global minimizers of the TCRM objective are conditional expectations), the zero-overhead nature of the method, and the reported empirical benefits in token-level interpretability, ProcessBench performance, and PPO efficiency. No specific major comments or requested changes were raised in the report.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation is a direct mathematical proof

full rationale

The central claim rests on adding two standard regularization terms (Monte Carlo and TD objectives) to the Bradley-Terry loss and proving that the combined loss has minimizers exactly equal to the conditional expectations E[final reward | prefix]. This follows from the known properties of conditional expectation and value-function objectives in RL, which are external to the paper and not fitted or redefined within it. No steps reduce by construction to the target quantity, no self-citations are load-bearing for the proof, and no ansatz or renaming is invoked. The result is self-contained against external RL theory benchmarks.

Assumptions & free parameters 0 free parameters · 1 assumptions · 1 invented entities

The central claim rests on the standard Bradley-Terry preference model plus the new regularizers; no free parameters are introduced beyond those already present in the base loss, and no new physical or mathematical entities are postulated.

assumptions (1)
  • domain assumption The Bradley-Terry model is an appropriate likelihood for pairwise preference data.
    Standard modeling choice in RLHF reward training; invoked as the base loss before regularization.
invented entities (1)
  • Temporally Coherent Reward Modeling (TCRM) regularizers
    purpose: Enforce that every token-level output equals the conditional expectation of the final reward.
    New regularization terms introduced in the paper; no independent evidence outside this work is provided.

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Cite this review

Pith. "Pith review of Reward Models Are Secretly Value Functions: Temporally Coherent Reward Modeling." pith.science (2026). https://pith.science/paper/2604.22981

@misc{pith2026260422981,
  author       = {Pith},
  title        = {Pith review of: Reward Models Are Secretly Value Functions: Temporally Coherent Reward Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2604.22981}},
  note         = {Machine review of arXiv:2604.22981}
}
read the original abstract

Reward models in RLHF are trained to score only the final token of a response - a choice that discards rich signal from every intermediate position and produces models whose token-level outputs are noise. We argue this is a missed opportunity: a well-trained reward model's output at any token should represent the conditional expectation of the final reward given the response so far. We introduce Temporally Coherent Reward Modeling (TCRM), which induces this property via two regularization terms on top of the standard Bradley-Terry loss, with minimizers provably equal to conditional expectations. The regularizers correspond to Monte Carlo and TD value-learning objectives, establishing a direct connection to RL value functions. TCRM requires zero changes to architecture, data, or inference, yet unlocks three capabilities from one principle: interpretable token-level reward trajectories (middle-token pairwise accuracy improved from 50% to 88.9%, final-token accuracy preserved); state-of-the-art PRM performance on ProcessBench (44.9% average F1) among models trained only on outcome data; and unified reward/value modeling in PPO, reducing peak GPU memory by 27% and step time by 19% with matching LLM quality.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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    cs.CV 2026-08 conditional novelty 6.0 of 10

    SURE learns sample-adaptive variance in a latent reward model and uses that variance to weight dense post-training feedback, improving image and video diffusion alignment in reported experiments.

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages · cited by 1 Pith paper

  1. [1]

    If r(x, y0..k) = E[r(x, y)|x, y0..k], then the average value ofr(x, y0..k) −r (x, y)should be close to 0

    Bias. If r(x, y0..k) = E[r(x, y)|x, y0..k], then the average value ofr(x, y0..k) −r (x, y)should be close to 0

    work page

  2. [2]

    Sincey0..k is more informative thany0..k−1, we should expect to see the mean squared prediction error(r(x, y0..k)−r(x, y)) 2 decrease askincreases

    Decreasing prediction error. Sincey0..k is more informative thany0..k−1, we should expect to see the mean squared prediction error(r(x, y0..k)−r(x, y)) 2 decrease askincreases. 16 Table 10Middle-token accuracy comparison of baseline and TCRM models (a)Baseline Training dataset Evaluation dataset HH Skywork UltraFB HH53.3%50.0% 50.7% Skywork53.8%53.4% 48.9...

    work page

  3. [3]

    What is the capital of Italy?

    Orthogonality principle. Iff(x) = E[Y|X = x], then the residualY−f (x)must be uncorrelated with any function ofX. We will use this principle in a simple form by checking the correlation of the residual with the intermediate score itselfCorr(r(x, y)−r(x, y 0..k), r(x, y0..k)). All metrics will be broken down by relative position within the response (100 bu...

    work page

  4. [4]

    It is Rome

    Correct, with extra prefix. "It is Rome"

    work page

  5. [5]

    Rome, also known as The Eternal City

    Correct, with extra suffix. "Rome, also known as The Eternal City" 17 0 20 40 60 80 100 Relative Position in Response (%) 1.00 0.75 0.50 0.25 0.00 0.25 0.50 0.75 Average (Score at Position - Final Score) Bias: Intermediate vs Final Score Combined Chosen Rejected 0 20 40 60 80 100 Relative Position in Response (%) 0.5 1.0 1.5 2.0 2.5 3.0Average (Score at P...

    work page

  6. [6]

    Rome, GA

    Wrong suffix 1. "Rome, GA"

    work page

  7. [7]

    Rome, also known as The City of Love

    Wrong suffix 2. "Rome, also known as The City of Love" Figure 7 shows the results, which generally follow very intuitive patterns. The most succinct correct answer gets assigned the highest final reward. Adding an extra uninformative prefix to the correct answer in Figure 7b first reduces the reward score (showing that direct answers without filler words ...

    work page 2024

  8. [8]

    \n\n" separator) minus at the end of the previous step was 18 2 1 0 1 2 3 Reward Model Output

    Difference. We classify the step as correct if the difference of reward model scores at the end of the step (at the token corresponding to the "\n\n" separator) minus at the end of the previous step was 18 2 1 0 1 2 3 Reward Model Output "0" "," "1" "," "1" "," "2" "," "3" "," "5" "," "8" "," "1" "3" "," "2" "1" "," "3" "4" "<|im_end|>" (a)Baseline reward...

    work page

Show all 18 references
  1. [9]

    Similar to the previous method, but sigmoid transformation was applied to the reward scores before subtraction

    Sigmoid difference. Similar to the previous method, but sigmoid transformation was applied to the reward scores before subtraction

  2. [10]

    Normalized Difference

    Sigmoid ratio. Similar to the previous method, but we used the ratio of sigmoids instead of difference. Additionally, for reference-free Llama3.1-8B-ImplicitPRM we considered using a "Normalized Difference" method, where the difference between scores was divided by the number ...

    2025

  3. [11]

    This was used to evaluate the checkpoints every 10 training steps to understand training progress

    Reward model scoring. This was used to evaluate the checkpoints every 10 training steps to understand training progress. 21 Hyperparameter Value Batch size 1024 PPO mini batch size 256 Maximum prompt length 1024 tokens Maximum response length 1024 tokens Number of training epo...

  4. [12]

    LLM-as-a-Judge evaluation. This was applied only to generations from 2 final checkpoints (baseline and 1 checkpoint from PPO trained with TCRM RM/VM) To prevent overfitting bias and signal leakage in reward model scoring we used 2 modifications:

  5. [13]

    The prompts for evaluation are also sourced fromDolci-Instruct-RL, but we only used the 10%validation subset with no overlap with the PPO training subset

    Split dataset. The prompts for evaluation are also sourced fromDolci-Instruct-RL, but we only used the 10%validation subset with no overlap with the PPO training subset. A random subset of 1000 prompts from the validation set was used

  6. [14]

    warm start

    Different reward model. We used theSkywork-Reward-V2-Llama-3.1-8BLiu et al. (2025) reward model which was trained on theSkywork-Reward-V2dataset, which has only small overlap with the Skywork-Reward-Preference-80K-v0.2dataset on which the reward models used in PPO were trained...

    2025

  7. [15]

    **Instruction Following:** The response must follow all constraints in the prompt, including negative and formatting constraints

  8. [16]

    **Accuracy:** The response must be accurate, factual and logically consistent

  9. [17]

    **Clarity:** The response must be easy to read and understand

  10. [18]

    A" (Response A is better),

    **Completeness:** The response must fully address all aspects of the prompt. Provide your judgement as: "A" (Response A is better), "B" (Response B is better), or "TIE" (roughly equal quality). ### INPUT DATA **User Query:** <user_query> {prompt} </user_query> **Response A:** ...

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