Recent advances in diffusion-based generative models have achieved remarkable visual fidelity, yet a detailed understanding of how specific perceptual attributes - such as color and shape - are internally represented remains limited. This work explores how color is encoded in a generative model through a systematic analysis of the latent representations in Stable Diffusion. Through controlled synthetic datasets, principal component analysis (PCA) and similarity metrics, we reveal that color information is encoded along circular, opponent axes predominantly captured in latent channels c_3 and c_4, whereas intensity and shape are primarily represented in channels c_1 and c_2. Our findings indicate that the latent space of Stable Diffusion exhibits an interpretable structure aligned with a efficient coding representation. These insights provide a foundation for future work in model understanding, editing applications, and the design of more disentangled generative frameworks.

We study discrete diffusion for language and other categorical data and focus on a common limitation of masked denoisers: reverse transitions typically factorize across positions, which can weaken joint structure and degrade quality in few-step generation. We propose \emph{Latent Discrete Diffusion Models} (LDDMs), which couple a masked discrete diffusion over tokens with a continuous diffusion over latent embeddings. The latent channel provides a softer signal and carries cross-token dependencies that help resolve ambiguities. We present two instantiations: (i) FUJI-LDDMs, which perform fully joint denoising of tokens and latents, and (ii) SEQ-LDDMs, which sequentially resolve the latent and then the discrete chain conditionally on it. For both variants we derive ELBO-style objectives and discuss design choices to learn informative latents yet amenable to diffusoin modeling. In experiments, LDDMs yield improvements on unconditional generation metrics as compared to state-of-the-art masked discrete diffusion baselines, and are effective at lower sampling budgets, where unmasking many tokens per step is desirable.

Neural audio codecs and autoencoders have emerged as versatile models for audio compression, transmission, feature-extraction, and latent-space generation. However, a key limitation is that most are trained to maximize reconstruction fidelity, often neglecting the specific latent structure necessary for optimal performance in diverse downstream applications. We propose a simple, post-hoc framework to address this by modifying the bottleneck of a pre-trained autoencoder. Our method introduces a "Re-Bottleneck", an inner bottleneck trained exclusively through latent space losses to instill user-defined structure. We demonstrate the framework's effectiveness in three experiments. First, we enforce an ordering on latent channels without sacrificing reconstruction quality. Second, we align latents with semantic embeddings, analyzing the impact on downstream diffusion modeling. Third, we introduce equivariance, ensuring that a filtering operation on the input waveform directly corresponds to a specific transformation in the latent space. Ultimately, our Re-Bottleneck framework offers a flexible and efficient way to tailor representations of neural audio models, enabling them to seamlessly meet the varied demands of different applications with minimal additional training.

The large-scale structure of the Universe provides one of the most stringent tests of gravity on cosmological scales. Over the past decades, the ΛCDM cosmological model has emerged as the standard framework for understanding our cosmos, where Λ represents the cosmological constant (associated with dark energy) and CDM denotes cold dark matter--which together comprise approximately 95% of the Universe's energy budget. Theoretical predictions of ΛCDM can now be implemented with remarkable precision in numerical simulations, which capture the formation of the cosmic web: an intricate network where galaxies reside in dense clusters, connected by filamen-tary structures and separated by vast cosmic voids. This success, however, presents cosmology with a new challenge. High-resolution simulations like AbacusSummit generate datasets exceeding 2000 TB, severely constraining our ability to scale training datasets for machine learning applications. Moreover, extracting meaningful insights from these high-dimensional datasets requires models that can effectively navigate the curse of dimensionality.

--We introduce V ariational Latent Mode Decomposition (VLMD), a new algorithm for extracting oscillatory modes and associated connectivity structures from multivariate signals. VLMD addresses key limitations of existing Multivariate Mode Decomposition (MMD) techniques--including high computational cost, sensitivity to parameter choices, and weak modeling of interchannel dependencies. Its improved performance is driven by a novel underlying model, Latent Mode Decomposition (LMD), which blends sparse coding and mode decomposition to represent multichannel signals as sparse linear combinations of shared latent components composed of AM-FM oscillatory modes. This formulation enables VLMD to operate in a lower-dimensional latent space, enhancing robustness to noise, scalability, and interpretability. The algorithm solves a constrained variational optimization problem that jointly enforces reconstruction fidelity, sparsity, and frequency regularization. Experiments on synthetic and real-world datasets demonstrate that VLMD outperforms state-of-the-art MMD methods in accuracy, efficiency, and the interpretability of extracted structures. ONST A TIONARY signal decomposition techniques constitute an essential tool in Signal Processing for analyzing complex signals. Among them, Mode Decomposition (MD) has emerged as a fundamental framework, enabling the extraction of meaningful intrinsic oscillatory components [1]. Over the last couple of decades, a wide range of MD methods and algorithms have been developed and successfully applied across a wide range of interdisciplinary applications, such as biomedical signal analysis, structural health monitoring, and financial time-series analysis. This particular trend dates back to the late nineties with the introduction of Empirical Mode Decomposition (EMD) [1], which was followed by the development of other similar alternatives, such as Synchro-squeezed Transform (SST) [2], V ariational Mode Decomposition (VMD) [3] and Sliding-window Singular Spectrum Analysis (SSA) [4]. Originally designed for single-channel time series analysis, some of these methods were later extended to handle multivariate time series. Notable multivariate algorithms include Multivariate Empirical Mode Decomposition (MEMD) [5], multivariate nonlinear chirp mode decomposition [6], iterative filtering [7], as well as Multivariate V ariational Mode Decomposition (MVMD) [8].

For the efficient inference of Large Language Models (LLMs), the effective compression of key-value (KV) cache is essential. Three main types of KV cache compression techniques, namely sparsity, channel compression, and quantization, have been identified. This study presents SVDq, a Singular Value Decomposition (SVD) - based mixed precision quantization method for K cache. Initially, K cache is transformed into latent channels using SVD basis representations. Since the values in latent channels decay rapidly and become negligible after only a few latent channels, our method then incorporates importance-aware quantization and compression for latent channels. This enables the effective allocation of higher precision to more significant channels. Theoretically, we prove that SVDq results in quantization errors (x0.1 or even lower) that are much lower than those of per-channel key quantization in the original space. Our findings based on RULER and LongBench benchmarks demonstrate that SVDq can achieve an equivalent key cache precision as low as 1.25-bit. When combined with key sparsity, it can reach a key compression ratio of up to 410x for attention computation, all while maintaining comparable model performance. Notably, our method is nearly lossless for LongBench datasets. This indicates that SVDq enables high-precision low-bit quantization, providing a more efficient solution for KV cache compression in LLMs.

The brain-computer interface (BCI) enables individuals with severe physical impairments to communicate with the world. BCIs offer computational neuroscience opportunities and challenges in converting real-time brain activities to computer commands and are typically framed as a classification problem. This article focuses on the P300 BCI that uses the event-related potential (ERP) BCI design, where the primary challenge is classifying target/non-target stimuli. We develop a novel Gaussian latent group model with sparse time-varying effects (GLASS) for making Bayesian inferences on the P300 BCI. GLASS adopts a multinomial regression framework that directly addresses the dataset imbalance in BCI applications. The prior specifications facilitate i) feature selection and noise reduction using soft-thresholding, ii) smoothing of the time-varying effects using global shrinkage, and iii) clustering of latent groups to alleviate high spatial correlations of EEG data. We develop an efficient gradient-based variational inference (GBVI) algorithm for posterior computation and provide a user-friendly Python module available at https://github.com/BangyaoZhao/GLASS. The application of GLASS identifies important EEG channels (PO8, Oz, PO7, Pz, C3) that align with existing literature. GLASS further reveals a group effect from channels in the parieto-occipital region (PO8, Oz, PO7), which is validated in cross-participant analysis.