Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Sampling in turn enables learning.

--Diffusion models (DMs) have recently achieved significant success in wireless communications systems due to their denoising capabilities. The broadcast nature of wireless signals makes them susceptible not only to Gaussian noise, but also to unaware interference. This raises the question of whether DMs can effectively mitigate interference in wireless semantic communication systems. In this paper, we model the interference cancellation problem as a maximum a posteriori (MAP) problem over the joint posterior probability of the signal and interference, and theoretically prove that the solution provides excellent estimates for the signal and interference. T o solve this problem, we develop an interference cancellation diffusion model (ICDM), which decomposes the joint posterior into independent prior probabilities of the signal and interference, along with the channel transition probablity. The log-gradients of these distributions at each time step are learned separately by DMs and accurately estimated through deriving. ICDM further integrates these gradients with advanced numerical iteration method, achieving accurate and rapid interference cancellation. Extensive experiments demonstrate that ICDM significantly reduces the mean square error (MSE) and enhances perceptual quality compared to schemes without ICDM. For example, on the CelebA dataset under the Rayleigh fading channel with a signal-to-noise ratio (SNR) of 20 dB and signal to interference plus noise ratio (SINR) of 0 dB, ICDM reduces the MSE by 4 . Diffusion models (DMs) [1]-[4], which utilize a score function to model the gradient of the conditional data distribution, have recently achieved remarkable success in the field of artificial intelligence generated content (AIGC). These models are capable of generating controllable and high-quality content in various domains, including long-form text generation, controllable image generation, and consistent video generation. They have also become a fundamental technology for large language models (LLMs) such as GPT -4o. The inherent controllability of the content generated by diffusion models has significantly driven their application across diverse fields [5]-[7].

Ensuring that generative AI systems align with human values is essential but challenging, especially when considering multiple human values and their potential trade-offs. Since human values can be personalized and dynamically change over time, the desirable levels of value alignment vary across different ethnic groups, industry sectors, and user cohorts. Within existing frameworks, it is hard to define human values and align AI systems accordingly across different directions simultaneously, such as harmlessness, helpfulness, and positiveness. To address this, we develop a novel, first-principle approach called Multi-Human-Value Alignment Palette (MAP), which navigates the alignment across multiple human values in a structured and reliable way. MAP formulates the alignment problem as an optimization task with user-defined constraints, which define human value targets. It can be efficiently solved via a primal-dual approach, which determines whether a user-defined alignment target is achievable and how to achieve it. We conduct a detailed theoretical analysis of MAP by quantifying the trade-offs between values, the sensitivity to constraints, the fundamental connection between multi-value alignment and sequential alignment, and proving that linear weighted rewards are sufficient for multi-value alignment. Extensive experiments demonstrate MAP's ability to align multiple values in a principled manner while delivering strong empirical performance across various tasks. Recent advancements in artificial intelligence (AI) have highlighted the critical need for aligning AI systems with human values, a concept known as human value alignment (Griffith et al., 2013; Arumugam et al., 2019; Gabriel, 2020). The alignment can serve the purpose of generating outcomes that are better suited for human ethics (Griffith et al., 2013), personalized needs (Kirk et al., 2024), or reduced harmful content (Bai et al., 2022). This alignment has traditionally been pursued by adjusting AI behavior to adhere to specific attributes via preference datasets or reward functions. This formulation has deep conceptual roots in the Bayesian decision theoretic framework (Bissiri et al., 2016).

We study the problem of reconstructing low-rank matrices from their noisy observations. We formulate the problem in the Bayesian framework, which allows us to exploit structural properties of matrices in addition to low-rankedness, such as sparsity. We propose an efficient approximate message passing algorithm, derived from the belief propagation algorithm, to perform the Bayesian inference for matrix reconstruction. We have also successfully applied the proposed algorithm to a clustering problem, by reformulating it as a low-rank matrix reconstruction problem with an additional structural property. Numerical experiments show that the proposed algorithm outperforms Lloyd's K-means algorithm.

Computing the MAP assignment in graphical models is generally intractable. As a result, for discrete graphical models, the MAP problem is often approximated using linear programming relaxations. Much research has focused on characterizing when these LP relaxations are tight, and while they are relatively well-understood in the discrete case, only a few results are known for their continuous analog. In this work, we use graph covers to provide necessary and sufficient conditions for continuous MAP relaxations to be tight. We use this characterization to give simple proofs that the relaxation is tight for log-concave decomposable and logsupermodular decomposable models. We conclude by exploring the relationship between these two seemingly distinct classes of functions and providing specific conditions under which the MAP relaxation can and cannot be tight.