AMUSE: Anytime Muon with Stable Gradient Evaluation

Modern deep learning commonly relies on AdamW with prescribed learning rate schedules, but recent works challenge both components: Schedule-Free optimization removes explicit schedules via iterate averaging, and Muon improves the update geometry by orthogonalizing momentum for matrix parameters. Despite Muon's strong empirical performance, its underlying mechanism remains partially understood. We study Muon through the river-valley loss landscape, where useful training progress occurs along a flat, low-curvature bulk subspace (the river), while high-curvature dominant directions form steep valley walls that induce oscillations. We empirically show that while Muon's orthogonalization accelerates river progress by increasing the bulk component, it also amplifies dominant-direction noise, causing oscillatory trajectories. Building on this, we propose Anytime MUon with Stable gradient Evaluation (AMUSE), which integrates Muon's rapid bulk progress with the stabilizing effect of Schedule-Free averaging. AMUSE uses a time-varying interpolation coefficient that initially evaluates gradients near the fast Muon sequence for rapid adaptation, then gradually shifts toward the stable averaged sequence to suppress valley-wall oscillations. As a result, AMUSE requires no learning rate schedules and supports anytime training. Across vision tasks and large language model pretraining, AMUSE consistently improves the performance-iteration Pareto frontier over (Schedule-Free) AdamW and Muon.

SPARTA: Scalable and Principled Benchmark of Tree-Structured Multi-hop QA over Text and Tables

Real-world Table-Text question answering (QA) tasks require models that can reason across long text and source tables, traversing multiple hops and executing complex operations such as aggregation. Yet existing benchmarks are small, manually curated - and therefore error-prone - and contain shallow questions that seldom demand more than two hops or invoke aggregations, grouping, or other advanced analytical operations expressible in natural-language queries. We present SPARTA, an end-to-end construction framework that automatically generates large-scale Table-Text QA benchmarks with lightweight human validation, requiring only one quarter of the annotation time of HybridQA. The framework first constructs a reference fact database by enriching each source table with grounding tables whose tuples are atomic facts automatically extracted from the accompanying unstructured passages, then synthesizes nested queries whose number of nested predicates matches the desired hop count. To ensure that every SQL statement is executable and that its verbalization yields a fluent, human-sounding question, we propose two novel techniques: provenance-based refinement, which rewrites any syntactically valid query that returns a non-empty result, and realistic-structure enforcement, which confines generation to post-order traversals of the query graph. The resulting pipeline produces thousands of high-fidelity question-answer pairs covering aggregations, grouping, and deep multi-hop reasoning across text and tables. On SPARTA, state-of-the-art models that reach over 70 F1 on HybridQA or over 50 F1 on OTT-QA drop by more than 30 F1 points, exposing fundamental weaknesses in current cross-modal reasoning. Our benchmark, construction code, and baseline models are available at https://github.com/pshlego/SPARTA/tree/main.