Deep learning practice is increasingly driven by powerful foundation models (FM), pre-trained at scale and then fine-tuned for specific tasks of interest. A key property of this workflow is the efficacy of performing sparse or parameter-efficient finetuning, meaning that by updating only a tiny fraction of the whole FM parameters on a downstream task can lead to surprisingly good performance, often even superior to a full model update. However, it is not clear what is the optimal and principled way to select which parameters to update. Although a growing number of sparse fine-tuning ideas have been proposed, they are mostly not satisfactory, relying on hand-crafted heuristics or heavy approximation. In this paper we propose a novel Bayesian sparse fine-tuning algorithm: we place a (sparse) Laplace prior for each parameter of the FM, with the mean equal to the initial value and the scale parameter having a hyper-prior that encourages small scale.

Deep learning practice is increasingly driven by powerful foundation models (FM), pre-trained at scale and then fine-tuned for specific tasks of interest.

Membership in Ris already proven by Abrahamsen, Kleist and Miltzow in [3]. Thealgorithm then needs to verify that the neural network described byΘ fits all data points inD with a total error at mostγ. The goal of this appendix is to build a geometric understanding off(,Θ). We point the interested reader to these articles [6, 26, 49, 66, 92] investigating the set of functions exactly represented by different architecturesofReLUnetworks. To see that this observation is true, consider the following construction.

Calibration of multi-camera systems is a key task for accurate object tracking. However, it remains a challenging problem in real-world conditions, where traditional methods are not applicable due to the lack of accurate floor plans, physical access to place calibration patterns, or synchronized video streams. This paper presents a novel two-stage calibration method that overcomes these limitations. In the first stage, partial calibration of individual cameras is performed based on an operator's annotation of natural geometric primitives (parallel, perpendicular, and vertical lines, or line segments of equal length). This allows estimating key parameters (roll, pitch, focal length) and projecting the camera's Effective Field of View (EFOV) onto the horizontal plane in a base 3D coordinate system. In the second stage, precise system calibration is achieved through interactive manipulation of the projected EFOV polygons. The operator adjusts their position, scale, and rotation to align them with the floor plan or, in its absence, using virtual calibration elements projected onto all cameras in the system. This determines the remaining extrinsic parameters (camera position and yaw). Calibration requires only a static image from each camera, eliminating the need for physical access or synchronized video. The method is implemented as a practical web service. Comparative analysis and demonstration videos confirm the method's applicability, accuracy, and flexibility, enabling the deployment of precise multi-camera tracking systems in scenarios previously considered infeasible.

F or each line ℓ L the change of the gradient of f when crossing ℓ is constant along ℓ. Then there is a fully connected two-layer neural network with m hidden neurons computing f . To see that this observation is true, consider the following construction. Describing all gadgets purely by their data points is tedious and obscures the relatively simple geometry enforced by these data points. A weak data point relaxes a regular data point and prescribes only a lower bound on the value of the label.

Primitives are expressions in typed lambda calculus.