Large language model (LLM) routers improve the efficiency of multi-model systems by directing each query to the most appropriate model while leveraging the diverse strengths of heterogeneous LLMs. Most existing approaches frame routing as a classification problem based solely on the input query. While this reduces overhead by avoiding inference across all models, it overlooks valuable information that could be gleaned from potential outputs and fails to capture implicit intent or contextual nuances that often emerge only during response generation. These limitations can result in suboptimal routing decisions, particularly for complex or ambiguous queries that require deeper semantic understanding. To address this challenge, we propose Lookahead, a routing framework that "foresees" potential model outputs by predicting their latent representations and uses these predictions to guide model selection, thus enabling more informed routing without full inference. Within this framework, we implement two approaches based on causal and masked language models. Empirical evaluations across seven public benchmarks--spanning instruction following, mathematical reasoning, and code generation--show that Lookahead consistently outperforms existing routing baselines, achieving an average performance gain of 7.7% over the state-of-the-art.

Many modeling tasks from disparate domains can be framed in the same way, computing spherical signals from geometric inputs, for example, computing the radar response of different objects or navigating through an environment. This paper introduces G2Sphere, a general method for mapping object geometries to spherical signals. G2Sphere operates entirely in Fourier space, encoding geometric structure into latent Fourier features using equivariant neural networks and outputting the Fourier coefficients of the continuous target signal, which can be evaluated at any resolution. By utilizing a hybrid GNN-spherical CNN architecture, our method achieves a much higher frequency output signal than comparable equivariant GNNs and avoids hand-engineered geometry features used previously by purely spherical methods. We perform experiments on various challenging domains, including radar response modeling, aerodynamic drag prediction, and policy learning for manipulation and navigation. We find that G2Sphere outperforms competitive baselines in terms of accuracy and inference time, and we demonstrate that equivariance and Fourier features lead to improved sample efficiency and generalization.

Learning disentangled representations in sequential data is a key goal in deep learning, with broad applications in vision, audio, and time series. While realworld data involves multiple interacting semantic factors over time, prior work has mostly focused on simpler two-factor static and dynamic settings, primarily because such settings make data collection easier, thereby overlooking the inherently multifactor nature of real-world data. We introduce the first standardized benchmark for evaluating multi-factor sequential disentanglement across six diverse datasets spanning video, audio, and time series. Our benchmark includes modular tools for dataset integration, model development, and evaluation metrics tailored to multi-factor analysis. We additionally propose a post-hoc Latent Exploration Stage to automatically align latent dimensions with semantic factors, and introduce a Koopman-inspired model that achieves state-of-the-art results. Moreover, we show that Vision-Language Models can automate dataset annotation and serve as zeroshot disentanglement evaluators, removing the need for manual labels and human intervention. Together, these contributions provide a robust and scalable foundation for advancing multi-factor sequential disentanglement. Our code is available on GitHub, and the datasets and trained models are available on Hugging Face.

Diffusion models have achieved impressive performance in generating high-quality and diverse synthetic data. However, their success typically assumes a classbalanced training distribution. In real-world settings, multi-class data often follow a long-tailed distribution, where standard diffusion models struggleproducing lowdiversity and lower-quality samples for tail classes. While this degradation is well-documented, its underlying cause remains poorly understood. In this work, we investigate the behavior of diffusion models trained on long-tailed datasets and identify a key issue: the latent representations (from the bottleneck layer of the U-Net) for tail class subspaces exhibit significant overlap with those of head classes, leading to feature borrowing and poor generation quality. Importantly, we show that this is not merely due to limited data per class, but that the relative class imbalance significantly contributes to this phenomenon. To address this, we propose COntrastive Regularization for Aligning Latents (CORAL), a contrastive latent alignment framework that leverages supervised contrastive losses to encourage well-separated latent class representations. Experiments demonstrate that CORAL significantly improves both the diversity and visual quality of samples generated for tail classes relative to state-of-the-art methods.

We present Prototypical Pair Network (ProtoPairNet), a novel interpretable architecture that combines deep learning with case-based reasoning to predict continuous targets. While prototype-based models have primarily addressed image classification with discrete outputs, extending these methods to continuous targets, such as regression, poses significant challenges. Existing architectures which rely heavily on one-to-one comparison with prototypes lack the directional information necessary for continuous predictions.

Incomplete multi-view deep clustering is an emerging research hot-pot to incorporate data information of multiple sources or modalities when parts of them are missing. Most of existing approaches encode the available data observations into multiple view-specific latent representations and subsequently integrate them for the next clustering task. However, they ignore that the latent representations are unique to a fixed set of data samples in all views. Meanwhile, the pair-wise similarities of missing data observations are also failed to utilize in latent representation learning sufficiently, leading to unsatisfactory clustering performance. To address these issues, we propose an incomplete multi-view deep clustering method with data imputation and alignment.

The multi-view Gaussian process latent variable model (MV-GPLVM) aims to learn a unified representation from multi-view data but is hindered by challenges such as limited kernel expressiveness and low computational efficiency. To overcome these issues, we first introduce a new duality between the spectral density and the kernel function. By modeling the spectral density with a bivariate Gaussian mixture, we then derive a generic and expressive kernel termed Next-Gen Spectral Mixture (NG-SM) for MV-GPLVMs. To address the inherent computational inefficiency of the NG-SM kernel, we design a new form of random Fourier feature approximation. Combined with a tailored reparameterization trick, this approximation enables scalable variational inference for both the model and the unified latent representations. Numerical evaluations across a diverse range of multi-view datasets demonstrate that our proposed method consistently outperforms state-of-the-art models in learning meaningful latent representations.

While latent diffusion models (LDMs), such as Stable Diffusion, are designed for high-resolution (HR) image generation, they often struggle with significant structural one. Instead distortions of relying when generating on extensiv images e retraining, at resolutions a more resource-ef higher than ficient their approach training is to reprogram the pretrained model for HR image generation; however, existing methods often result in poor image quality and long inference time. We introduce RepLDM, high-quality a, no high-ef vel reprogramming ficiency, high-r frame esolution work image for pretrained generation; LDMs see that Fig. enables 1. RepLDM consists of two stages: (i) an attention guidance stage, which generates a latent training-free representa self-attention tion of a higher mechanism -quality to training-resolution enhance the structural image consistenc using a y; no and vel (ii) a progressive upsampling stage, which progressively performs upsampling in pixel space to mitigate the severe artifacts caused by latent space upsampling.

Cross-modal representation learning aims to extract semantically aligned representations from heterogeneous modalities such as images and text. Existing multimodal VAE-based models often suffer from limited capability to align heterogeneous modalities or lack sufficient structural constraints to clearly separate the modality-specific and shared factors. In this work, we propose a novel framework, termed Disentangled Cross-Modal Representation Learning with Enhanced Mutual Supervision (DCMEM). Specifically, our model disentangles the common and distinct information across modalities and regularizes the shared representation learned from each modality in a mutually supervised manner. Moreover, we incorporate the information bottleneck principle into our model to ensure that the shared and modality-specific factors encode exclusive yet complementary information. Notably, our model is designed to be trainable on both complete and partial multimodal datasets with a valid Evidence Lower Bound. Extensive experimental results demonstrate significant improvements of our model over existing methods on various tasks including cross-modal generation, clustering and classification.

Naive DDIM inversion process usually suffers from a trajectory deviation issue, i.e., the latent trajectory during reconstruction deviates from the one during inversion. To alleviate this issue, previous methods either learn to mitigate the deviation or design a cumbersome compensation strategy to reduce the mismatch error, exhibiting substantial time and computation cost. In this work, we present a nearly free-lunch method (named FreeInv) to address the issue more effectively and efficiently. In FreeInv, we randomly transform the latent representation and keep the transformation the same between the corresponding inversion and reconstruction time-step. It is motivated from a statistical perspective that an ensemble of DDIM inversion processes for multiple trajectories yields a smaller trajectory mismatch error on expectation. Moreover, through theoretical analysis and empirical study, we show that FreeInv performs an efficient ensemble of multiple trajectories. FreeInv can be freely integrated into existing inversion-based image and video editing techniques. Especially for inverting video sequences, it brings more significant fidelity and efficiency improvements. Comprehensive quantitative and qualitative evaluation on PIE benchmark and DAVIS dataset shows that FreeInv remarkably outperforms conventional DDIM inversion, and is competitive among previous state-of-the-art inversion methods, with superior computation efficiency.