Daily Papers

Knowledge distillation (KD) has been widely adopted to compress large language models (LLMs). Existing KD methods investigate various divergence measures including the Kullback-Leibler (KL), reverse Kullback-Leibler (RKL), and Jensen-Shannon (JS) divergences. However, due to limitations inherent in their assumptions and definitions, these measures fail to deliver effective supervision when few distribution overlap exists between the teacher and the student. In this paper, we show that the aforementioned KL, RKL, and JS divergences respectively suffer from issues of mode-averaging, mode-collapsing, and mode-underestimation, which deteriorates logits-based KD for diverse NLP tasks. We propose the Sinkhorn Knowledge Distillation (SinKD) that exploits the Sinkhorn distance to ensure a nuanced and precise assessment of the disparity between teacher and student distributions. Besides, profit by properties of the Sinkhorn metric, we can get rid of sample-wise KD that restricts the perception of divergence in each teacher-student sample pair. Instead, we propose a batch-wise reformulation to capture geometric intricacies of distributions across samples in the high-dimensional space. Comprehensive evaluation on GLUE and SuperGLUE, in terms of comparability, validity, and generalizability, highlights our superiority over state-of-the-art methods on all kinds of LLMs with encoder-only, encoder-decoder, and decoder-only architectures.

Recent advances in 3D Gaussian Splatting (3DGS) have revolutionized scene reconstruction, opening new possibilities for 3D steganography by hiding 3D secrets within 3D covers. The key challenge in steganography is ensuring imperceptibility while maintaining high-fidelity reconstruction. However, existing methods often suffer from detectability risks and utilize only suboptimal 3DGS features, limiting their full potential. We propose a novel end-to-end key-secured 3D steganography framework (KeySS) that jointly optimizes a 3DGS model and a key-secured decoder for secret reconstruction. Our approach reveals that Gaussian features contribute unequally to secret hiding. The framework incorporates a key-controllable mechanism enabling multi-secret hiding and unauthorized access prevention, while systematically exploring optimal feature update to balance fidelity and security. To rigorously evaluate steganographic imperceptibility beyond conventional 2D metrics, we introduce 3D-Sinkhorn distance analysis, which quantifies distributional differences between original and steganographic Gaussian parameters in the representation space. Extensive experiments demonstrate that our method achieves state-of-the-art performance in both cover and secret reconstruction while maintaining high security levels, advancing the field of 3D steganography. Code is available at https://github.com/RY-Paper/KeySS

Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix scaling and guarantees an approximated solution with near-linear runtime. Despite the success of the Sinkhorn algorithm, its runtime may still be slow due to the potentially large number of iterations needed for convergence. To achieve possibly super-exponential convergence, we present Sinkhorn-Newton-Sparse (SNS), an extension to the Sinkhorn algorithm, by introducing early stopping for the matrix scaling steps and a second stage featuring a Newton-type subroutine. Adopting the variational viewpoint that the Sinkhorn algorithm maximizes a concave Lyapunov potential, we offer the insight that the Hessian matrix of the potential function is approximately sparse. Sparsification of the Hessian results in a fast O(n^2) per-iteration complexity, the same as the Sinkhorn algorithm. In terms of total iteration count, we observe that the SNS algorithm converges orders of magnitude faster across a wide range of practical cases, including optimal transportation between empirical distributions and calculating the Wasserstein W_1, W_2 distance of discretized densities. The empirical performance is corroborated by a rigorous bound on the approximate sparsity of the Hessian matrix.

Graph Edit Distance (GED) measures the (dis-)similarity between two given graphs, in terms of the minimum-cost edit sequence that transforms one graph to the other. However, the exact computation of GED is NP-Hard, which has recently motivated the design of neural methods for GED estimation. However, they do not explicitly account for edit operations with different costs. In response, we propose GRAPHEDX, a neural GED estimator that can work with general costs specified for the four edit operations, viz., edge deletion, edge addition, node deletion and node addition. We first present GED as a quadratic assignment problem (QAP) that incorporates these four costs. Then, we represent each graph as a set of node and edge embeddings and use them to design a family of neural set divergence surrogates. We replace the QAP terms corresponding to each operation with their surrogates. Computing such neural set divergence require aligning nodes and edges of the two graphs. We learn these alignments using a Gumbel-Sinkhorn permutation generator, additionally ensuring that the node and edge alignments are consistent with each other. Moreover, these alignments are cognizant of both the presence and absence of edges between node-pairs. Experiments on several datasets, under a variety of edit cost settings, show that GRAPHEDX consistently outperforms state-of-the-art methods and heuristics in terms of prediction error.

In this study, we propose Feature-aligned N-BEATS as a domain generalization model for univariate time series forecasting problems. The proposed model is an extension of the doubly residual stacking architecture of N-BEATS (Oreshkin et al. [34]) into a representation learning framework. The model is a new structure that involves marginal feature probability measures (i.e., pushforward measures of multiple source domains) induced by the intricate composition of residual operators of N-BEATS in each stack and aligns them stack-wise via an entropic regularized Wasserstein distance referred to as the Sinkhorn divergence (Genevay et al. [14]). The loss function consists of a typical forecasting loss for multiple source domains and an alignment loss calculated with the Sinkhorn divergence, which allows the model to learn invariant features stack-wise across multiple source data sequences while retaining N-BEATS's interpretable design. We conduct a comprehensive experimental evaluation of the proposed approach and the results demonstrate the model's forecasting and generalization capabilities in comparison with methods based on the original N-BEATS.

Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. In this work, we (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. We show that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. Our theoretical results provide new insight in understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, we provide an algorithm to compute the metric by leveraging Sinkhorn divergences and validate our findings through a simulation study.

3D Gaussian Splatting (3DGS) has demonstrated its potential in reconstructing scenes from unposed images. However, optimization-based 3DGS methods struggle with sparse views due to limited prior knowledge. Meanwhile, feed-forward Gaussian approaches are constrained by input formats, making it challenging to incorporate more input views. To address these challenges, we propose RegGS, a 3D Gaussian registration-based framework for reconstructing unposed sparse views. RegGS aligns local 3D Gaussians generated by a feed-forward network into a globally consistent 3D Gaussian representation. Technically, we implement an entropy-regularized Sinkhorn algorithm to efficiently solve the optimal transport Mixture 2-Wasserstein (MW_2) distance, which serves as an alignment metric for Gaussian mixture models (GMMs) in Sim(3) space. Furthermore, we design a joint 3DGS registration module that integrates the MW_2 distance, photometric consistency, and depth geometry. This enables a coarse-to-fine registration process while accurately estimating camera poses and aligning the scene. Experiments on the RE10K and ACID datasets demonstrate that RegGS effectively registers local Gaussians with high fidelity, achieving precise pose estimation and high-quality novel-view synthesis. Project page: https://3dagentworld.github.io/reggs/.

Optimal transport (OT) theory has been been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another. Recent works have drawn inspiration from Brenier's theorem, which states that when the ground cost is the squared-Euclidean distance, the ``best'' map to morph a continuous measure in P(Rd) into another must be the gradient of a convex function. To exploit that result, [Makkuva+ 2020, Korotin+2020] consider maps T=nabla f_theta, where f_theta is an input convex neural network (ICNN), as defined by Amos+2017, and fit theta with SGD using samples. Despite their mathematical elegance, fitting OT maps with ICNNs raises many challenges, due notably to the many constraints imposed on theta; the need to approximate the conjugate of f_theta; or the limitation that they only work for the squared-Euclidean cost. More generally, we question the relevance of using Brenier's result, which only applies to densities, to constrain the architecture of candidate maps fitted on samples. Motivated by these limitations, we propose a radically different approach to estimating OT maps: Given a cost c and a reference measure rho, we introduce a regularizer, the Monge gap M^c_{rho}(T) of a map T. That gap quantifies how far a map T deviates from the ideal properties we expect from a c-OT map. In practice, we drop all architecture requirements for T and simply minimize a distance (e.g., the Sinkhorn divergence) between Tsharpmu and nu, regularized by M^c_rho(T). We study M^c_{rho}, and show how our simple pipeline outperforms significantly other baselines in practice.