arXiv:2510.03638v4 Announce Type: replace-cross Abstract: Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing memory needs for the same level of performance compared to explicit models. While it is empirically known that these compact models can often match or even exceed the accuracy of larger explicit networks by allocating more test-time compute, the underlying mechanism remains poorly understood. We study this gap through a nonparametric analysis of expressive power. We provide a strict mathematical characterization, showing that a simple and regular implicit operator can, through iteration, progressively express more complex mappings. We prove that for a broad class of implicit models, this process lets the model's expressive power scale with test-time compute, ultimately matching a much richer function class. The theory is validated across four domains: image reconstruction, scientific computing, operations research, and LLM reasoning, demonstrating that as test-time iterations increase, the complexity of the learned mapping rises, while the solution quality simultaneously improves and stabilizes.

Background: Stroke is a leading cause of long-term upper limb disability, severely impacting patients’ independence and quality of life. Robot-assisted therapy (RAT) has emerged as a promising, high-intensity rehabilitation alternative. However, conclusions from existing systematic reviews on its efficacy are inconsistent and often lack a holistic framework, limiting their use for guiding personalized clinical decisions. Objective: This study aims to systematically synthesize recent evidence on RAT for upper limb rehabilitation after stroke. Guided by the International Classification of Functioning, Disability and Health framework, it moves beyond singular outcomes to provide a multidimensional evaluation across body function, activity, and participation levels. The review aims to provide stratified guidance for clinical decision-making based on patient- and intervention-specific characteristics, thereby supporting evidence-based practice and informing future research. Methods: This study included systematic reviews and meta-analyses published from January 1, 2019, to December 26, 2025, comparing RAT with conventional therapy for upper limb rehabilitation after stroke. Overall, 6 databases, including PubMed, Web of Science, and Embase, were searched. Two reviewers (XZ and LZ) independently performed study selection, data extraction, and quality assessment using the AMSTAR 2 tool. The synthesis integrated outcome measures and subgroup analyses derived from the included studies. Results: This umbrella review included 21 meta-analyses encompassing 535 randomized controlled trials and 27,598 patients across acute, subacute, and chronic stroke stages. According to AMSTAR 2, 17 reviews were high quality, 3 moderate, and 1 critically low. The synthesis demonstrated that RAT was superior in improving upper limb motor function, but no statistically significant advantages were observed in activities of daily living compared to conventional therapy. Subgroup analyses revealed that treatment effects were influenced by stroke stage, upper limb motor impairment level, and robot type. Conclusions: RAT is an effective intervention for improving upper limb motor function after stroke. However, its benefits are primarily observed at the level of body function, with limited evidence for long-term maintenance. The current evidence is constrained by significant outcome heterogeneity and methodological limitations inherent to umbrella reviews. Future research should validate these findings in broader clinical practice, focus on translating functional gains into sustained improvements in daily activities and participation, and include cost-effectiveness evaluations. Trial Registration: PROSPERO CRD42024497183; https://www.crd.york.ac.uk/PROSPERO/view/CRD42024497183