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arxiv: 2605.28247 · v1 · pith:LLHS5SOInew · submitted 2026-05-27 · 💻 cs.LG · cs.AI

IRDS: Interpretable RLVR Data Selection via Verifier-Coupled Sparse Autoencoder Coverage

Yuhan Li , Mingxu Zhang , Dazhong Shen , Ying Sun This is my paper

Pith reviewed 2026-06-29 14:45 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords data selectionRLVRsparse autoencoderLLM reasoningverifiable rewardsmath benchmarksinterpretabilitycoverage objective
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The pith

IRDS selects RLVR training data on sparse autoencoder clusters using a verifier-coupled coverage objective to raise accuracy on math reasoning benchmarks.

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

The paper presents IRDS as a way to fix data inefficiency in reinforcement learning with verifiable rewards for large language models. It groups problems into sparse autoencoder clusters that correspond to recognizable motifs so selections can be audited by humans. A coverage objective tied to verifier signals then picks instances the model gets wrong but can still improve on, solved via greedy log-determinant maximization. Experiments across three models and six math benchmarks show this yields the top accuracy scores. The method also runs an order of magnitude faster than trajectory-based alternatives.

Core claim

IRDS selects RLVR training instances on a sparse autoencoder cluster basis so the selection itself is auditable on recognizable problem motifs. To select instances the model both fails on and can still learn from, it introduces a verifier-coupled coverage objective on the SAE basis and solves it by greedy log-determinant maximization.

What carries the argument

The verifier-coupled coverage objective on the SAE basis, solved by greedy log-determinant maximization, which ensures both interpretability through motif clusters and effective identification of learnable failures.

If this is right

  • IRDS achieves the highest overall accuracy across six math reasoning benchmarks.
  • It exceeds the strongest baseline by 3.9 and 4.0 percentage points on the two Qwen models.
  • It exceeds the strongest baseline by 0.5 percentage points on Llama-3.1-8B.
  • It runs an order of magnitude cheaper than the trajectory-based baseline.

Where Pith is reading between the lines

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

  • The same cluster-based selection could be tested on non-math domains to check whether problem motifs transfer.
  • If clusters prove stable across model sizes, they might serve as a shared vocabulary for auditing training data in other verifiable-reward settings.

Load-bearing premise

That SAE-derived clusters correspond to recognizable, auditable problem motifs and that the verifier-coupled coverage objective reliably identifies instances the model fails on yet can still learn from.

What would settle it

Applying IRDS to a held-out model and benchmark set and measuring no accuracy gain over the strongest existing baseline would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2605.28247 by Dazhong Shen, Mingxu Zhang, Ying Sun, Yuhan Li.

Figure 1
Figure 1. Figure 1: IRDS overview. 1. Data characterization: train a BatchTopK SAE on frozen residual activations, encode problems into stabilized SAE-cluster coordinates, and derive verifier weights di , ri from base-policy rollouts. 2. Verifier-coupled SAE geometry: form the failure-weighted and trainability-weighted covariances Σd, Σr, combine them into the ridge-regularized metric M, and use its leading directions as the … view at source ↗
Figure 2
Figure 2. Figure 2: BatchTopK-Ortho SAE training: held-out reconstruction loss vs. step, per model and per sparsity [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Full 256-eigenvector feature-amplification scan on QWEN3-1.7B. Left: |∆logit-diff| vs eigenvector rank for α∈ {0.5, 1, 2, 5}. The dashed line at rank 10 marks the named-axis cutoff. Right: logit-shift magnitude at α=5 vs eigenvalue λk. Sensitivity mass is distributed across the full 256-d basis, with |∆|=0.82 and max =2.50 at rank 71 [PITH_FULL_IMAGE:figures/full_fig_p023_3.png] view at source ↗
read the original abstract

Reinforcement learning with verifiable rewards (RLVR) has become a key technique for en- hancing LLM reasoning, yet its data ineffi- ciency remains a major bottleneck. Existing methods address this problem only partially, each missing at least one of subset-level cov- erage, verifier signal use, or interpretability. To address this gap, we present IRDS (Inter- pretable RLVR Data Selection), which selects RLVR training instances on a sparse autoen- coder (SAE) cluster basis so the selection itself is auditable on recognizable problem motifs. To select instances the model both fails on and can still learn from, we introduce a verifier- coupled coverage objective on the SAE basis and solve it by greedy log-determinant max- imization. Experiments on three instruction- tuned models and six math reasoning bench- marks show that IRDS achieves the highest overall accuracy, exceeding the strongest base- line by +3.9/+4.0 pp on the two Qwen models and by +0.5 pp on Llama-3.1-8B, while run- ning an order of magnitude cheaper than the trajectory-based baseline.

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

2 major / 1 minor

Summary. The paper introduces IRDS (Interpretable RLVR Data Selection), a method that selects training instances for reinforcement learning with verifiable rewards (RLVR) on the basis of sparse autoencoder (SAE) clusters. The selection uses a verifier-coupled coverage objective solved via greedy log-determinant maximization, with the goal of choosing instances the model fails on yet can still learn from while keeping the selection auditable via recognizable problem motifs. Experiments on three instruction-tuned models and six math reasoning benchmarks are reported to show IRDS attaining the highest overall accuracy, exceeding the strongest baseline by +3.9/+4.0 pp on the two Qwen models and +0.5 pp on Llama-3.1-8B, at an order of magnitude lower cost than a trajectory-based baseline.

Significance. If the reported gains prove robust under full experimental reporting, the work would be significant for data-efficient RLVR by combining SAE-based interpretability with a coverage objective that incorporates verifier signals. The order-of-magnitude computational saving relative to trajectory baselines and the explicit focus on auditable clusters are concrete strengths that could influence practical data curation pipelines.

major comments (2)
  1. Abstract: performance numbers (+3.9/+4.0 pp on Qwen models, +0.5 pp on Llama-3.1-8B) are stated without any experimental details, error bars, ablation studies, statistical tests, or description of the six benchmarks and three models, rendering the central superiority claim impossible to evaluate from the provided text.
  2. Abstract: the claim that SAE-derived clusters enable selection on 'recognizable problem motifs' and that the verifier-coupled objective 'reliably identifies instances the model fails on yet can still learn from' is presented as a core contribution, yet no cluster examples, motif validation, or failure-mode analysis is supplied, leaving the interpretability and selection reliability assumptions untested.
minor comments (1)
  1. Abstract: hyphenation artifacts appear in 'en- hancing' and 'in- efficiency'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below. The full manuscript supplies the experimental details and supporting analyses referenced in the abstract; we agree the abstract itself can be strengthened for standalone clarity.

read point-by-point responses

  1. Referee: [—] Abstract: performance numbers (+3.9/+4.0 pp on Qwen models, +0.5 pp on Llama-3.1-8B) are stated without any experimental details, error bars, ablation studies, statistical tests, or description of the six benchmarks and three models, rendering the central superiority claim impossible to evaluate from the provided text.

    Authors: We agree that the abstract, constrained by length, omits these details. The full paper specifies the three models and six benchmarks in Section 4.1, reports results with error bars across three random seeds in Table 1, presents ablations in Section 5, and includes paired statistical tests in Section 4.3. We will revise the abstract to include a concise description of the experimental setup. revision: yes

  2. Referee: [—] Abstract: the claim that SAE-derived clusters enable selection on 'recognizable problem motifs' and that the verifier-coupled objective 'reliably identifies instances the model fails on yet can still learn from' is presented as a core contribution, yet no cluster examples, motif validation, or failure-mode analysis is supplied, leaving the interpretability and selection reliability assumptions untested.

    Authors: The abstract summarizes the claims; the full manuscript supplies the supporting material in Section 3.2 (cluster examples with recognizable motifs and human validation) and Section 4.4 (failure-mode analysis linking verifier signals to learnable instances). If additional examples or quantitative motif validation metrics are desired, we can expand these sections. revision: partial

Circularity Check

0 steps flagged

No significant circularity; method uses external verifier and standard SAE optimization

full rationale

The abstract and provided context describe IRDS as selecting data via SAE clusters with a verifier-coupled coverage objective solved by greedy log-determinant maximization. No equations, fitted parameters renamed as predictions, or self-citation chains are shown that reduce the central claim to its inputs by construction. The reported accuracy gains are presented as empirical outcomes on external benchmarks, not forced by definition or internal fitting. This matches the default expectation of a non-circular paper; the reader's score of 2.0 is consistent with minor self-citation potential but no load-bearing reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no information available on free parameters, axioms, or invented entities. Full paper required for ledger audit.

pith-pipeline@v0.9.1-grok · 5748 in / 1071 out tokens · 43777 ms · 2026-06-29T14:45:03.384761+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

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    task feature

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