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arxiv: 2606.25178 · v2 · pith:3O4EQJ5Jnew · submitted 2026-06-23 · 💻 cs.AI

Transferability for General Reasoning: An Automated Curriculum for Multi-Domain RLVR

Yongjin Yang , Jiarui Liu , Yinghui He , Lechen Zhang , Bernhard Sch\"olkopf , Zhijing Jin This is my paper

Pith reviewed 2026-06-30 09:53 UTC · model grok-4.3

classification 💻 cs.AI
keywords reinforcement learningcurriculum learningmulti-domain reasoningtransferabilityRLVRGRPObandit curriculum
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The pith

A curriculum that prioritizes domains by how much their gradients align with others improves macro accuracy in multi-domain RLVR over learnability-only baselines.

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

The paper proposes Transfer-Aware Curriculum (TAC) for RLVR training across six domains that include mathematics, programming, and science. TAC is a bandit-style method that combines local learnability signals from per-domain advantages with a transferability estimate derived from projected gradients computed during each GRPO step. This transfer term measures gradient-geometry alignment to select domains whose updates benefit the full suite rather than only the current domain. On Qwen3-1.7B and Llama3.2-3B, TAC records the highest macro-averaged accuracy, beating proportional random sampling, hand-designed schedules, and a learnability-only bandit by as much as 2.8 points. Removing the transfer term sharply reduces performance, and TAC stays stable under imbalanced domain mixtures where pure learnability methods over-focus on dominant domains.

Core claim

Transfer-Aware Curriculum (TAC) is a bandit-style online curriculum that prioritizes domains whose updates broadly benefit the rest of the training suite. It repurposes signals already produced by RL training: per-domain advantages capture local learnability, and projected gradients, taken from the GRPO step being computed, estimate cross-domain transferability via gradient-geometry alignment, at negligible cost. Across a six-domain reasoning suite, TAC achieves the best macro-averaged accuracy on both Qwen3-1.7B and Llama3.2-3B, outperforming proportional random sampling, a hand-designed schedule, and a learnability-only bandit, and improving over the last of these by up to 2.8 points (10%

What carries the argument

Transfer-Aware Curriculum (TAC), a bandit-style scheduler that augments local learnability advantages with cross-domain transferability estimated from projected gradient alignment during GRPO updates.

If this is right

  • TAC records the highest macro-averaged accuracy across the six-domain suite on two different model sizes.
  • Performance drops sharply when the transferability term is removed from the selection rule.
  • TAC maintains stable behavior on deliberately imbalanced domain mixtures where learnability-only methods over-commit to dominant domains.
  • The added computation for projected gradients incurs less than 1 percent wall-clock overhead.

Where Pith is reading between the lines

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

  • Gradient-alignment signals could be tested as a lightweight transfer proxy in other multi-task RL settings that lack explicit cross-domain evaluation.
  • If the current projection method underestimates certain forms of transfer, richer alignment statistics such as cosine similarity after layer-wise normalization could be substituted.
  • The same selection logic might be applied at the level of individual problems rather than whole domains once per-problem gradient projections become feasible.

Load-bearing premise

Projected gradients computed on one domain during a GRPO step reliably predict whether that update will improve performance on the other domains.

What would settle it

A controlled run in which domains chosen by high projected-gradient alignment produce no measurable accuracy gain on the remaining domains after the same number of updates.

read the original abstract

Reinforcement learning with verifiable rewards (RLVR) has been extended from single-domain training to multi-domain reasoning suites spanning mathematics, programming, and science. However, the training curriculum (how often each domain is sampled) is typically fixed or hand-tuned, even though reasoning skills transfer unevenly across domains. Existing learnability-based curricula adapt to where the policy is currently improving, but are blind to whether a gradient step on the selected domain benefits the remaining domains. In this paper, we propose Transfer-Aware Curriculum (TAC), a bandit-style online curriculum that prioritizes domains whose updates broadly benefit the rest of the training suite. TAC repurposes signals already produced by RL training: per-domain advantages capture local learnability, and projected gradients, taken from the GRPO step being computed, estimate cross-domain transferability via gradient-geometry alignment, at negligible cost (<1% wall-clock overhead). Across a six-domain reasoning suite, TAC achieves the best macro-averaged accuracy on both Qwen3-1.7B and Llama3.2-3B, outperforming proportional random sampling, a hand-designed schedule, and a learnability-only bandit, and improving over the last of these by up to 2.8 points (10% relative). Ablations show performance degrades sharply when the transferability term is removed, and TAC remains robust on imbalanced training mixtures where learnability-only curricula over-commit to dominant domains. Our findings establish cross-domain transferability as a key signal for curriculum design in multi-domain RLVR.

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.

Referee Report

1 major / 1 minor

Summary. The manuscript proposes Transfer-Aware Curriculum (TAC), a bandit-style online curriculum for multi-domain RLVR. TAC combines per-domain advantages (capturing local learnability) with projected gradients from GRPO steps (estimating cross-domain transferability via gradient-geometry alignment at <1% overhead). On a six-domain reasoning suite, TAC reports the highest macro-averaged accuracy on both Qwen3-1.7B and Llama3.2-3B, outperforming proportional random sampling, a hand-designed schedule, and a learnability-only bandit (by up to 2.8 points / 10% relative), while remaining robust on imbalanced mixtures.

Significance. If the gradient-geometry alignment reliably predicts positive cross-domain transfer, TAC offers an efficient, low-overhead method to incorporate transfer signals into multi-domain curricula, addressing a limitation of purely learnability-based approaches. The reported gains across two model scales and the ablation results provide empirical support for the combined signal's utility in reasoning domains.

major comments (1)
  1. [Abstract] Abstract: The central claim that projected gradients yield a reliable proxy for cross-domain transferability (via gradient-geometry alignment) lacks direct supporting evidence such as per-pair correlations, regressions, or transfer-delta statistics linking alignment scores to observed improvements on other domains; the ablation showing degradation when the transfer term is removed does not isolate whether the benefit arises from accurate transfer prediction versus ancillary effects such as increased sampling diversity or regularization.
minor comments (1)
  1. [Abstract] Abstract: No information is provided on statistical significance testing for the accuracy improvements, precise definitions of the six domains, or rules for data exclusion or mixture construction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of TAC's empirical results. We address the concern about direct evidence for the gradient-alignment proxy below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that projected gradients yield a reliable proxy for cross-domain transferability (via gradient-geometry alignment) lacks direct supporting evidence such as per-pair correlations, regressions, or transfer-delta statistics linking alignment scores to observed improvements on other domains; the ablation showing degradation when the transfer term is removed does not isolate whether the benefit arises from accurate transfer prediction versus ancillary effects such as increased sampling diversity or regularization.

    Authors: We agree that the manuscript's support for the proxy is primarily indirect via end-to-end gains and the transfer-term ablation. The ablation isolates the contribution of the transfer signal but does not rule out ancillary effects. In revision we will add a dedicated analysis subsection reporting (i) per-domain-pair alignment scores, (ii) Pearson/Spearman correlations with measured transfer deltas (accuracy lift on target domain after source-domain updates), and (iii) simple linear regressions of transfer delta on alignment. If correlations are moderate we will discuss this limitation explicitly. This addition directly addresses the request for transfer-delta statistics without altering the method or claimed results. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical method with online signals and independent test metrics

full rationale

The paper defines TAC as an online bandit curriculum that reuses per-step RL signals (advantages for learnability, projected gradients for transfer via alignment) already computed during GRPO. The headline results are macro-averaged test accuracies on held-out reasoning benchmarks, compared against baselines including a learnability-only ablation. No equation or claim reduces the reported gains to a post-hoc fit, self-citation chain, or input by construction; the transfer term is an explicit additive component whose removal is ablated. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; the method rests on standard RL assumptions plus the unstated premise that GRPO gradient projections are a faithful proxy for cross-domain benefit. No explicit free parameters or invented entities are named.

axioms (1)
  • domain assumption Projected gradients from a single GRPO step on one domain estimate whether that update benefits other domains
    Central to TAC selection rule; location: abstract description of TAC

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