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Tactile sensing is an indispensable modality for contact-rich dexterous manipulation, a capability that hints at the ultimate frontiers of embodied intelligence. However, commercially available tactile sensors are still at a relatively early stage of development, with each type of sensor offering irreplaceable strengths alongside its own drawbacks. A key challenge is thus to free tactile understanding from sensor-specific physics, so that embodied models can effectively leverage heterogeneous tactile data. To this end, we develop LingBot-Touch, a tactile foundation model characterized by the following properties. (i) Our model yields a unified representation across different tactile sensors (i.e., piezoresistive, magnetic, and visuotactile sensors), and is easily extensible to new sensor types. (ii) The resulting tactile tokens are plug-and-play: they can be seamlessly integrated into policy models across paradigms, from diffusion policy to vision-language-action (VLA) models such as $π_{0.5}$ and LingBot-VLA, consistently enhancing manipulation dexterity. (iii) Extensive experiments, spanning simulation and real-robot deployments across multiple hardware platforms, demonstrate that our tactile representation substantially benefits complex manipulation tasks while maintaining strong computational efficiency. We believe the findings in this work demonstrate the potential of leveraging cross-sensor data to scale tactile learning, and offer encouraging insights for the design of future hardware and embodied models.

The phenomenon of implicit bias has attracted interest in recent years as a fundamental aspect of the remarkable generalizing ability of neural networks. In a nutshell, it entails that gradient descent dynamics in many neural nets, even without any explicit regularizer in the loss function, converges to the solution of a regularized learning problem. In this work, we show that this phenomenon extends to non-linear spectral parameterizations in matrix sensing. More precisely, we propose a matrix network architecture called Spectral Neural Networks (abbrv. SNN) where each neuron applies nonlinear activation to the singular values of the input matrix. Conceptually, this entails coordinatizing the space of matrices by their singular values and singular vectors, as opposed to by their entries, a potentially fruitful perspective for matrix learning. We prove the exponentially fast decay of squared loss during the training dynamics of an SNN parameterized matrix sensing model under gradient flow (which is a continuous approximation of the discrete gradient descent), and also that the training implicitly selects an approximate solution that minimizes nuclear norm. We also demonstrate the effectiveness of the SNN architecture in the context of matrix sensing by empirical investigations. We believe that the SNN architecture has the potential to be of wide applicability in a broad class of matrix learning scenarios.