Function Spaces
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Related Articles from SNS
Flow-Transformed Implicit Processes for Function-Space Variational Inference
Announce Type: new Abstract: Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling. However, performing posterior inference with such priors is challenging because their induced function-space distributions are typically not available in closed form. One practical strategy is to approximate the prior using a finite collection of sampled functions, and then represent posterior functions...
Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces
arXiv:2603.14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime. Based on one-step generative transport, the method learns an amortized neural operator whose pushforward of a Gaussian source approximates the posterior distribution conditioned on each new observation. We show that white-noise sources are incompatible with the function-space limit, and therefore adopt a prior-aligned GRF as the source.
Curvature-Guided LoRA: Matching Full Fine-Tuning in Function Space
arXiv:2603.29824v2 Announce Type: replace Abstract: Parameter-efficient fine-tuning methods such as LoRA enable efficient adaptation of large pretrained models, but often lag behind full fine-tuning in both convergence speed and final performance. Recent approaches aim to reduce this gap by aligning LoRA parameter updates with those of full fine-tuning, but such parameter-space alignment only indirectly controls model predictions. Instead, we adopt a function-space perspective and formulate...
Function-Space Priors for Bayesian Neural ODEs with Application to Vessel Trajectory Prediction
arXiv:2606.06351v1 Announce Type: cross Abstract: Vessel trajectory prediction from Automatic Identification System (AIS) data is essential for maritime situational awareness, yet it remains challenging due to irregular sampling, missing reports, and complex dynamics. Beyond accurate point forecasts, maritime applications also demand well-calibrated uncertainty estimates for reliable decision-making. Bayesian Neural Ordinary Differential Equations (ODEs) offer a principled framework for...
What Objects Enable, Not What They Are: Functional Latent Spaces for Affordance Reasoning
arXiv:2606.05533v1 Announce Type: new Abstract: Existing robot planning systems rely on appearance-based reasoning, where visual observations are encoded into latent spaces organized around object appearances (e.g., recognizing a "cart" based on how it looks). However, planning requires reasoning about task-relevant functionalities of objects (e.g., whether an object is "movable"), which appearance-based latent spaces do not capture. As a result, existing approaches struggle to generalize to...
From Hazard Functions to Language Space: Cox-Supervised Distillation of Survival Risk into a Large Language Model
new Abstract: We investigate whether information about time-to-event risk estimated by a Cox proportional hazards model can be transferred into a generative large language model. We propose a text-based survival modelling pipeline in which structured clinical covariates are converted into text prompts and a Qwen-based large language model is fine-tuned to generate patient-specific survival risk using Cox model predictions as a training target. Across GBSG2, ACTG320, and WHAS500, the model...
Understanding the Parameter Space Geometry of Transformers Encoding Boolean Functions
arXiv:2606.08768v1 Announce Type: new Abstract: Transformers consistently fail to learn certain simple functions that are provably expressible with specific parameter settings. This gap between learnability and expressivity is particularly prominent for sensitive functions -- functions whose output is likely to change if a single bit of the input is flipped -- for example, PARITY. While prior work has established that transformers exhibit a bias toward functions with low average sensitivity,...
Limitations of Taylor hypothesis in a forest clearcut flow
arXiv:2507.12069v3 Announce Type: replace Abstract: Taylor's hypothesis (TH) converts temporal observations to spatial information of the flow while carrying out measurements on a micrometeorological tower. Other than TH, there exists a more general elliptic model, which converts time to space by focusing on the geometry of the space-time correlation function. In elliptic model, TH is recovered when the space-time correlation functions are straight lines and when TH is invalid, they are...
Kernel Neural Operators (KNOs) for Scalable, Memory-efficient, Geometrically-flexible Operator Learning
Announce Type: replace Abstract: This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from functions to functions). The KNO decouples the choice of kernel from the numerical integration scheme (quadrature), thereby naturally allowing for operator learning with explicitly-chosen trainable kernels on irregular geometries....
Dynamical local Fr\'echet curve regression in manifolds
Announce Type: replace-cross Abstract: Under mild conditions, this paper derives a least-squares local linear Fr\'echet curve predictor for response and regressor evaluated in a separable Hilbert space. We obtain the conditions allowing the implementation of this local linear Fr\'echet functional predictor in the ambient L^{2}-space of vector functions, with values in the time-varying tangent space on a compact Riemannian manifold. An intrinsic local linear Fr\'echet curve predictor...