Two of the most fundamental questions in statistical learning theory are the following: which prediction problems are learnable, and how should they be learned? For the former, elegant answers often take the form of combinatorial dimensions. The latter question, however, has proved considerably more elusive: all known general-purpose multiclass learners rely on intricate orientations of exponentially large one-inclusion structures, and familiar algorithmic principles such as proper learning and regularization remain poorly understood. Motivated by prior work, we ask whether learning reduces to proper learning---possibly over a larger hypothesis class---and whether proper or improper multiclass learning can ultimately be captured by suitable regularizers. Our primary results answer both questions negatively, resolving three open problems from prior work. First, we exhibit a learnable multiclass problem that cannot be embedded in any properly learnable class, meaning learning cannot be reduced to proper learning by enlarging the hypothesis class. Second, we demonstrate that proper learning can require training error and characterize this phenomenon precisely: every properly learnable class admits a proper learner making $o(m)$ errors on samples of size $m$, but every prescribed sublinear scale $a_m=o(m)$ is necessary for some properly learnable problem. Third, regularization is not a general learner: we exhibit a properly learnable class that cannot be learned by any Structural Risk Minimization (SRM) learner, and a learnable class that cannot be learned by any local regularizer. We complement these impossibility results with a positive theory that gives two sufficient conditions for SRM learnability and characterizes SRM representability through integrability of revealed preferences.
Pretrained models are typically viewed as generalists, requiring bespoke post-training to achieve task-specific expertise. Gan & Isola (2026) recently proposed a striking alternative: that pretrained models lie in a dense neural thicket of task specialists, which can be surfaced with simple Gaussian weight perturbations. We examine this neural thicket of task-specific experts and identify several key findings that question this perspective. First, we find that the apparent lift of the best-of-N selected perturbation decays quickly with selection-set size m, strongly suggesting overfitting to the selection questions. In fact, for 10 of the 12 model-task pairs we study, a simple null model of pure selection noise predicts more than 75 percent of the top expert's reward lift. Second, the top experts' advantage often vanishes on held-out questions or remains within the run-to-run variability of the unperturbed pretrained model. Third, we find that majority voting over the top-K selected perturbations, termed RandOpt(N, K) by Gan & Isola (2026), is often matched or outperformed by majority voting over K samples from the base model. Overall, our results suggest that random weight perturbations may be ineffective at uncovering task experts around pretrained models, and that task adaptation requires more sophistication than random search. Code and artifacts are available at github.com/asil012/RevisitingNeuralThickets.
Woody Haosheng Gan, Deqing Fu University of Southern California, Julian Asilis, Ollie Liu University of Southern California, Vatsal Sharan University of Southern California, Robin Jia University of Southern California, Willie Neiswanger University of Southern California
Steering methods have emerged as effective tools for guiding large language models’ behavior, yet multimodal large language models (MLLMs) lack comparable techniques due to architectural diversity and limited availability of multimodal steering vectors. Inspired by this gap, we demonstrate that steering vectors derived solely from text-only LLM backbones can effectively guide and enhance their multimodal counterparts, revealing a novel cross-modal transfer that enables reuse of existing interpretability tools. Using community-standard methods—Sparse Autoencoders (SAE), Mean Shift, and Linear Probing—we validate this transfer effect across diverse MLLM architectures and visual reasoning tasks. Text-derived steering consistently enhances multimodal performance, with Mean Shift achieving up to +7.3% improvement in spatial relationship accuracy and +3.3% in counting accuracy on CV-Bench, and exhibits strong generalization to out-of-distribution datasets, for example reaching +34.2% on CLEVR counting tasks. This reveals that textual representations alone can effectively enhance visual grounding in MLLMs, bridging the mature ecosystem of text-based steering to MLLMs with minimal additional data collection or computational overhead.
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cs.CL · cs.CV
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表