Abstract:Force/torque feedback can substantially improve Vision-Language-Action (VLA) models on contact-rich manipulation, but most existing approaches fuse all modalities at a single operating frequency. This design ignores the mismatched sampling rates of real robot sensors, forcing downsampling of the high-frequency contact cues needed for reactive correction. Combined with common VLM-action-expert (AE) pipelines that execute action chunks largely open loop between expensive VLM updates, unified-frequency fusion often yields delayed responses to impacts, stick-slip, and force spikes. We propose FAVLA, a force-adaptive fast-slow VLA that decouples slow perception planning from fast contact-aware control. FAVLA runs a slow VLM at a fixed low frequency to encode modalities to produce latent representations and to predict near-future force variation. A fast AE then executes at a variable high frequency, conditioning on the latest force sequence data to generate reactive actions. We further introduce a force adapter that injects high-frequency force features into multiple AE layers, and adaptively schedules the AE's execution frequency based on the VLM's predicted force variation. Extensive experiments on contact-rich tasks demonstrate that FAVLA significantly outperforms baselines, achieving superior reactivity and success rates, especially with a smaller contact force during manipulation.
Abstract:Motivated by the prevalence of prediction problems in the economy, we study markets in which firms sell models to a consumer to help improve their prediction. Firms decide whether to enter, choose models to train on their data, and set prices. The consumer can purchase multiple models and use a weighted average of the models bought. Market outcomes can be expressed in terms of the bias-variance decompositions of the models that firms sell. We show that market structure can depend in subtle and nonmonotonic ways on the statistical properties of available models. Moreover, firms may choose inefficiently biased models to deter entry by competitors or to obtain larger profits.