Decompose Sparsely Where You Should, Absorb Densely Where You Should No

Sparse autoencoders (SAEs) are typically trained to reconstruct the \textbf{entire} residual stream through a sparse dictionary, implicitly assuming that all activation content is amenable to sparse, monosemantic decomposition. We question this assumption and hypothesize that activations contain a low-rank, dense component that is computationally important to the model yet inherently unsuitable for sparse representation, which serves as a major source of the persistent dense latents widely observed in trained SAEs. To test this, we add a small rank-$r$ linear bottleneck in parallel with standard SAEs (BatchTopK and Matryoshka), allowing dense structure to be absorbed before sparse reconstruction. On Gemma-2-2B layer 12, a rank-24 bottleneck reduces dense latent count by up to 84\% while improving sparse probing and targeted probe perturbation on both architectures at matched sparsity. The absorbed component is (i) \textbf{structurally identifiable} as the top principal components and outlier dimensions; (ii) \textbf{causally necessary}, with removing it raising next-token cross-entropy by 7.5$\times$, far exceeding the 2.8$\times$ from removing the geometrically near-identical top-24 PCA directions; and (iii) \textbf{redundantly encoded by sparse dictionaries}, with ablating 787 maximally aligned sparse features raising cross-entropy by only 2.9$\times$ and ablating 2,048 topic-aligned features leaving MMLU topic classification virtually unchanged, whereas removing the scaffold drops it from 98.7\% to chance. Together, our findings identify a compact, semantically informative and causally important component of residual stream activations (which we term a \textbf{computational scaffold}) that standard sparse dictionaries represent inefficiently, suggesting that the scope of sparsity-based interpretability methods warrants careful re-examination.

RUBRIC-ARROW: Alternating Pointwise Rubric Reward Modeling for LLM Post-training in Non-verifiable Domains

Pointwise reward modeling offers critical signals for LLM post-training, yet struggles with absolute scoring in subjective, non-verifiable settings. Rubric-based methods address this by decomposing evaluation into explicit criteria, but existing approaches typically depend on frontier LLMs and suffer from ties caused by hard Boolean aggregation. We present RUBRIC-ARROW, an alternating framework that jointly trains a rubric generator and a rubric-conditioned judge, with its RL stage using only pairwise preference data. Our method couples a probability-based scoring rule that reduces ties with phase-specific preference-based rewards and an alternating GRPO scheme that together train the pointwise evaluator. Extensive experiments show that RUBRIC-ARROW achieves competitive reward-modeling accuracy and yields consistent gains for downstream policy post-training.

AutoResearchClaw: Self-Reinforcing Autonomous Research with Human-AI Collaboration

Automating scientific discovery requires more than generating papers from ideas. Real research is iterative: hypotheses are challenged from multiple perspectives, experiments fail and inform the next attempt, and lessons accumulate across cycles. Existing autonomous research systems often model this process as a linear pipeline: they rely on single-agent reasoning, stop when execution fails, and do not carry experience across runs. We present AutoResearchClaw, a multi-agent autonomous research pipeline built on five mechanisms: structured multi-agent debate for hypothesis generation and result analysis, a self-healing executor with a \textsc{Pivot}/\textsc{Refine} decision loop that transforms failures into information, verifiable result reporting that prevents fabricated numbers and hallucinated citations, human-in-the-loop collaboration with seven intervention modes spanning full autonomy to step-by-step oversight, and cross-run evolution that converts past mistakes into future safeguards. On ARC-Bench, a 25-topic experiment-stage benchmark, AutoResearchClaw outperforms AI Scientist v2 by 54.7%. A human-in-the-loop ablation across seven intervention modes reveals that precise, targeted collaboration at high-leverage decision points consistently outperforms both full autonomy and exhaustive step-by-step oversight. We position AutoResearchClaw as a research amplifier that augments rather than replaces human scientific judgment. Code is available at https://github.com/aiming-lab/AutoResearchClaw.

Evidence Over Plans: Online Trajectory Verification for Skill Distillation

Agent skills can remarkably improve task success rates by using human-written procedural documents, but their quality is difficult to assess without environment-grounded verification. Existing skill generation methods heavily rely on preference logs rather than direct environment interaction, often yielding negligible or even degraded gains. We identify that it is a fundamental timing bottleneck: robust skills should be posterior-based, distilled from empirical environment interaction rather than prior plans. In this study, we introduce the Posterior Distillation Index (PDI), a trajectory-level metric that quantifies how well a distilled skill is grounded in the task-environment evidence. To operationalize PDI, we present SPARK (Structured Pipelines for Autonomous Runnable tasKs and sKill generation) for preserving task execution evidence towards full trajectory-level analysis. SPARK generates environment-verified trajectories used to compute PDI, and it applies PDI as an online diagnostic and intervention signal to ensure posterior skill formation. Across 86 runnable tasks, SPARK-generated skills consistently surpass no-skill baselines and outperform human-written skills on student models (inference cost up to 1,000x cheaper than teacher models). These findings show that PDI-guided distillation produces efficient and transferable skills grounded in the task-environment interaction. We release our code at https://github.com/EtaYang10th/spark-skills .

DARE: Difficulty-Adaptive Reinforcement Learning with Co-Evolved Difficulty Estimation

Reinforcement learning improves the reasoning ability of large language models but remains costly and sample-inefficient, as many rollouts provide weak learning signals. Difficulty-aware data selection methods attempt to address this by prioritizing moderately difficult prompts, yet our analysis reveals three limitations: difficulty estimates become inaccurate under policy drift, data selection alone yields limited final-performance gains, and inference efficiency remains largely unchanged. These findings suggest that efficient and effective RL requires more than filtering by difficulty: the policy should learn to solve hard tasks while producing concise responses for easy ones. To this end, we propose **Dare**, a unified framework that co-evolves difficulty estimation with the policy via self-normalized importance sampling, maintains diverse difficulty coverage through a symmetric Beta sampling distribution, and applies tailored training strategies across difficulty tiers with adaptive compute allocation. Extensive experiments across multiple models and domains demonstrate that **Dare** consistently outperforms existing methods in training efficiency, final effectiveness, and inference efficiency, producing more concise responses on easy tasks while improving correctness on hard ones. Code is available at https://github.com/EtaYang10th/DARE.

LUCID-SAE: Learning Unified Vision-Language Sparse Codes for Interpretable Concept Discovery

Sparse autoencoders (SAEs) offer a natural path toward comparable explanations across different representation spaces. However, current SAEs are trained per modality, producing dictionaries whose features are not directly understandable and whose explanations do not transfer across domains. In this study, we introduce LUCID (Learning Unified vision-language sparse Codes for Interpretable concept Discovery), a unified vision-language sparse autoencoder that learns a shared latent dictionary for image patch and text token representations, while reserving private capacity for modality-specific details. We achieve feature alignment by coupling the shared codes with a learned optimal transport matching objective without the need of labeling. LUCID yields interpretable shared features that support patch-level grounding, establish cross-modal neuron correspondence, and enhance robustness against the concept clustering problem in similarity-based evaluation. Leveraging the alignment properties, we develop an automated dictionary interpretation pipeline based on term clustering without manual observations. Our analysis reveals that LUCID's shared features capture diverse semantic categories beyond objects, including actions, attributes, and abstract concepts, demonstrating a comprehensive approach to interpretable multimodal representations.

Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals

Evaluating mathematical reasoning in LLMs is constrained by limited benchmark sizes and inherent model stochasticity, yielding high-variance accuracy estimates and unstable rankings across platforms. On difficult problems, an LLM may fail to produce a correct final answer, yet still provide reliable pairwise comparison signals indicating which of two candidate solutions is better. We leverage this observation to design a statistically efficient evaluation framework that combines standard labeled outcomes with pairwise comparison signals obtained by having models judge auxiliary reasoning chains. Treating these comparison signals as control variates, we develop a semiparametric estimator based on the efficient influence function (EIF) for the setting where auxiliary reasoning chains are observed. This yields a one-step estimator that achieves the semiparametric efficiency bound, guarantees strict variance reduction over naive sample averaging, and admits asymptotic normality for principled uncertainty quantification. Across simulations, our one-step estimator substantially improves ranking accuracy, with gains increasing as model output noise grows. Experiments on GPQA Diamond, AIME 2025, and GSM8K further demonstrate more precise performance estimation and more reliable model rankings, especially in small-sample regimes where conventional evaluation is pretty unstable.

Alternating Reinforcement Learning for Rubric-Based Reward Modeling in Non-Verifiable LLM Post-Training

Standard reward models typically predict scalar scores that fail to capture the multifaceted nature of response quality in non-verifiable domains, such as creative writing or open-ended instruction following. To address this limitation, we propose Rubric-ARM, a framework that jointly optimizes a rubric generator and a judge using reinforcement learning from preference feedback. Unlike existing methods that rely on static rubrics or disjoint training pipelines, our approach treats rubric generation as a latent action learned to maximize judgment accuracy. We introduce an alternating optimization strategy to mitigate the non-stationarity of simultaneous updates, providing theoretical analysis that demonstrates how this schedule reduces gradient variance during training. Extensive experiments show that Rubric-ARM achieves state-of-the-art performance among baselines on multiple benchmarks and significantly improves downstream policy alignment in both offline and online reinforcement learning settings.

Labels or Preferences? Budget-Constrained Learning with Human Judgments over AI-Generated Outputs

The increasing reliance on human preference feedback to judge AI-generated pseudo labels has created a pressing need for principled, budget-conscious data acquisition strategies. We address the crucial question of how to optimally allocate a fixed annotation budget between ground-truth labels and pairwise preferences in AI. Our solution, grounded in semi-parametric inference, casts the budget allocation problem as a monotone missing data framework. Building on this formulation, we introduce Preference-Calibrated Active Learning (PCAL), a novel method that learns the optimal data acquisition strategy and develops a statistically efficient estimator for functionals of the data distribution. Theoretically, we prove the asymptotic optimality of our PCAL estimator and establish a key robustness guarantee that ensures robust performance even with poorly estimated nuisance models. Our flexible framework applies to a general class of problems, by directly optimizing the estimator's variance instead of requiring a closed-form solution. This work provides a principled and statistically efficient approach for budget-constrained learning in modern AI. Simulations and real-data analysis demonstrate the practical benefits and superior performance of our proposed method.

Students' Perceptions and Preferences of Generative Artificial Intelligence Feedback for Programming

The rapid evolution of artificial intelligence (AI), specifically large language models (LLMs), has opened opportunities for various educational applications. This paper explored the feasibility of utilizing ChatGPT, one of the most popular LLMs, for automating feedback for Java programming assignments in an introductory computer science (CS1) class. Specifically, this study focused on three questions: 1) To what extent do students view LLM-generated feedback as formative? 2) How do students see the comparative affordances of feedback prompts that include their code, vs. those that exclude it? 3) What enhancements do students suggest for improving AI-generated feedback? To address these questions, we generated automated feedback using the ChatGPT API for four lab assignments in the CS1 class. The survey results revealed that students perceived the feedback as aligning well with formative feedback guidelines established by Shute. Additionally, students showed a clear preference for feedback generated by including the students' code as part of the LLM prompt, and our thematic study indicated that the preference was mainly attributed to the specificity, clarity, and corrective nature of the feedback. Moreover, this study found that students generally expected specific and corrective feedback with sufficient code examples, but had diverged opinions on the tone of the feedback. This study demonstrated that ChatGPT could generate Java programming assignment feedback that students perceived as formative. It also offered insights into the specific improvements that would make the ChatGPT-generated feedback useful for students.