Pan-sharpening aims to generate a spatially and spectrally enriched multi-spectral image by integrating information from low-resolution multi-spectral image and texture-rich panchromatic counterpart. In this work, we propose a WKVsharing embraced random shuffle RWKV high-order modeling paradigm for pansharpening from Bayesian perspective, coupled with random weight manifold distribution training strategy derived from Functional theory to regularize the solution space adhering to the following principles: 1) Random-shuffle RWKV. Recently, the Vision RWKV model, with its inherent linear complexity in global modeling, has inspired us to explore its untapped potential in pan-sharpening tasks. However, its attention mechanism, relying on a recurrent bidirectional scanning strategy, suffers from biased effects and demands significant processing time. To address this, we propose a novel Bayesian-inspired scanning strategy called Random Shuffle, complemented by a theoretically-sound inverse shuffle to preserve information coordination invariance, effectively eliminating biases associated with fixed sequence scanning.

Performative prediction is a framework accounting for the shift in the data distribution induced by the prediction of a model deployed in the real world. Ensuring convergence to a stable solution--one at which the post-deployment data distribution no longer changes--is crucial in settings where model predictions can influence future data. This paper, for the first time, extends the Repeated Risk Minimization (RRM) algorithm class by utilizing historical datasets from previous retraining snapshots, yielding a class of algorithms that we call Affine Risk Minimizers that converges to a performatively stable point for a broader class of problems. We introduce a new upper bound for methods that use only the final iteration of the dataset and prove for the first time the tightness of both this new bound and the previous existing bounds within the same regime. We also prove that our new algorithm class can surpass the lower bound for standard RRM, thus breaking the prior lower bound, and empirically observe faster convergence to the stable point on various performative prediction benchmarks. We offer at the same time the first lower bound analysis for RRM within the class of Affine Risk Minimizers, quantifying the potential improvements in convergence speed that could be achieved with other variants in our scheme.

Machine unlearning algorithms aim to efficiently remove data from a model without retraining it from scratch, in order to remove corrupted or outdated data or respect a user's "right to be forgotten." Certified machine unlearning is a strong theoretical guarantee based on differential privacy that quantifies the extent to which an algorithm erases data from the model weights. In contrast to existing works in certified unlearning for convex or strongly convex loss functions, or nonconvex objectives with limiting assumptions, we propose the first, first-order, black-box (i.e., can be applied to models pretrained with vanilla gradient descent) algorithm for unlearning on general nonconvex loss functions, which unlearns by "rewinding" to an earlier step during the learning process before performing gradient descent on the loss function of the retained data points. We prove (ϵ,δ) certified unlearning and performance guarantees that establish the privacy-utility-complexity tradeoff of our algorithm, and we prove generalization guarantees for functions that satisfy the Polyak-Lojasiewicz inequality. Finally, we demonstrate the superior performance of our algorithm compared to existing methods, within a new experimental framework that more accurately reflects unlearning user data in practice.

Compound AI systems, comprising multiple interacting components such as LLMs, foundation models, and external tools, have demonstrated remarkable improvements compared to single models in various tasks. To ensure their effective deployment in real-world applications, aligning these systems with human preferences is crucial. However, aligning the compound system via policy optimization, unlike the alignment of a single model, is challenging for two main reasons: (i) nondifferentiable interactions between components make end-to-end gradient-based optimization methods inapplicable, and (ii) system-level preferences cannot be directly transformed into component-level preferences. To address these challenges, we first formulate compound AI systems as Directed Acyclic Graphs (DAGs), explicitly modeling both component interactions and the associated data flows. Building on this formulation, we introduce SysDPO, a framework that extends Direct Preference Optimization (DPO) to enable joint system-level alignment. We propose two variants, SysDPO-Direct and SysDPO-Sampling, tailored for scenarios depending on whether we construct a system-specific preference dataset. We empirically demonstrate the effectiveness of our approach across two applications: the joint alignment of a language model and a diffusion model, and the joint alignment of an LLM collaboration system.

Training deep learning models for point cloud prediction tasks such as shape completion and generation depends critically on loss functions that measure discrepancies between predicted and ground-truth point sets. Commonly used functions such as Chamfer Distance (CD), HyperCD, InfoCD and Density-aware CD rely on nearest-neighbor assignments, which often induce many-to-one correspondences, leading to point congestion in dense regions and poor coverage in sparse regions. These losses also involve non-differentiable operations due to index selection, which may affect gradient-based optimization. Earth Mover Distance (EMD) enforces one-to-one correspondences and captures structural similarity more effectively, but its cubic computational complexity limits its practical use. We propose the Adaptive Probabilistic Matching Loss (APML), a fully differentiable approximation of one-to-one matching that leverages Sinkhorn iterations on a temperature-scaled similarity matrix derived from pairwise distances. We analytically compute the temperature to guarantee a minimum assignment probability, eliminating manual tuning. APML achieves near-quadratic runtime, comparable to Chamfer-based losses, and avoids non-differentiable operations.

One of the chronic problems of deep-learning models is shortcut learning. In a case where the majority of training data are dominated by a certain feature, neural networks prefer to learn such a feature even if the feature is not generalizable outside the training set. Based on the framework of Neural Tangent Kernel (NTK), we analyzed the case of linear neural networks to derive some important properties of shortcut learning. We defined a "feature" of a neural network as an eigenfunction of NTK. Then, we found that shortcut features correspond to features with larger eigenvalues when the shortcuts stem from the imbalanced number of samples in the clustered distribution. We also showed that the features with larger eigenvalues still have a large influence on the neural network output even after training, due to data variances in the clusters. Such a preference for certain features remains even when a margin of a neural network output is controlled, which shows that the max-margin bias is not the only major reason for shortcut learning. These properties of linear neural networks are empirically extended for more complex neural networks as a two-layer fully-connected ReLU network and a ResNet-18.

Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solvers for integer linear programming (ILP) problems. Yet, they lack scalability for tackling nonlinear challenges. To handle nonlinearities, state-of-the-art Branch-and-Cut solvers employ linear relaxations, leading to exponential growth in auxiliary variables and severe computation limitations. To overcome these limitations, we propose BIPNN (Binary Integer Programming Neural Network), an unsupervised learning framework to solve nonlinear BIP problems via hypergraph neural networks (HyperGNN). Specifically, (I) BIPNN reformulates BIPs-constrained, discrete, and nonlinear (sin, log, exp) optimization problems-into unconstrained, differentiable, and polynomial loss functions.

Recent advances in diffusion models have enabled high-quality synthesis of specific subjects, such as identities or objects. This capability, while unlocking new possibilities in content creation, also introduces significant privacy risks, as personalization techniques can be misused by malicious users to generate unauthorized content. Although several studies have attempted to counter this by generating adversarially perturbed samples designed to disrupt personalization, they rely on unrealistic assumptions and become ineffective in the presence of even a few clean images or under simple image transformations. To address these challenges, we shift the protection target from the images to the diffusion model itself to hinder the personalization of specific subjects, through our novel framework called AntiPersonalized Diffusion Models (APDM). We first provide a theoretical analysis demonstrating that a naive approach of existing loss functions to diffusion models is inherently incapable of ensuring convergence for robust anti-personalization. Motivated by this finding, we introduce Direct Protective Optimization (DPO), a novel loss function that effectively disrupts subject personalization in the target model without compromising generative quality. Moreover, we propose a new dual-path optimization strategy, coined Learning to Protect (L2P). By alternating between personalization and protection paths, L2P simulates future personalization trajectories and adaptively reinforces protection at each step. Experimental results demonstrate that our framework outperforms existing methods, achieving state-of-the-art performance in preventing unauthorized personalization. The code is available at https://github.com/KU-VGI/APDM.

The meta-task of obtaining and aligning representations through contrastive pretraining is steadily gaining importance since its introduction in CLIP and ALIGN. In this paper we theoretically explain the advantages of synchronizing with trainable inverse temperature and bias under the sigmoid loss, as implemented in the recent SigLIP and SigLIP2 models of Google DeepMind. Temperature and bias can drive the loss function to zero for a rich class of configurations that we call (m,brel)-Constellations. (m,brel)-Constellations are a novel combinatorial object related to spherical codes and are parametrized by a margin mand relative bias brel. We use our characterization of constellations to theoretically justify the success of SigLIP on retrieval, to explain the modality gap present in SigLIP, and to identify the necessary dimension for producing high-quality representations. Finally, we propose a reparameterization of the sigmoid loss with explicit relative bias, which improves training dynamics in experiments with synthetic data.

We consider binary classification restricted to a class of continuous piecewise linear functions whose decision boundaries are (possibly nonconvex) starshaped polyhedral sets, supported on a fixed polyhedral simplicial fan. We investigate the expressivity of these function classes and describe the combinatorial and geometric structure of the loss landscape, most prominently the sublevel sets, for two loss-functions: the 0/1-loss (discrete loss) and a log-likelihood loss function. In particular, we give explicit bounds on the VC dimension of this model, and concretely describe the sublevel sets of the discrete loss as chambers in a hyperplane arrangement. For the log-likelihood loss, we give sufficient conditions for the optimum to be unique, and describe the geometry of the optimum when varying the rate parameter of the underlying exponential probability distribution.