Many few-shot segmentation (FSS) methods use cross attention to fuse support foreground (FG) into query features, regardless of the quadratic complexity. A recent advance Mamba can also well capture intra-sequence dependencies, yet the complexity is only linear. Hence, we aim to devise a cross (attention-like) Mamba to capture inter-sequence dependencies for FSS. A simple idea is to scan on support features to selectively compress them into the hidden state, which is then used as the initial hidden state to sequentially scan query features. Nevertheless, it suffers from (1) support forgetting issue: query features will also gradually be compressed when scanning on them, so the support features in hidden state keep reducing, and many query pixels cannot fuse sufficient support features; (2) intra-class gap issue: query FG is essentially more similar to itself rather than to support FG, i.e., query may prefer not to fuse support features but their own ones from the hidden state, yet the success of FSS relies on the effective use of support information. To tackle them, we design a hybrid Mamba network (HMNet), including (1) a support recapped Mamba to periodically recap the support features when scanning query, so the hidden state can always contain rich support information; (2) a query intercepted Mamba to forbid the mutual interactions among query pixels, and encourage them to fuse more support features from the hidden state. Consequently, the support information is better utilized, leading to better performance. Extensive experiments have been conducted on two public benchmarks, showing the superiority of HMNet. The code is available at https://github.com/Sam1224/HMNet.

Probabilistic circuits (PCs) have emerged as a powerful framework to compactly represent probability distributions for efficient and exact probabilistic inference. It has been shown that PCs with a general directed acyclic graph (DAG) structure can be understood as a mixture of exponentially (in its height) many components, each of which is a product distribution over univariate marginals. However, existing structure learning algorithms for PCs often generate tree-structured circuits or use tree-structured circuits as intermediate steps to compress them into DAGstructured circuits. This leads to the intriguing question of whether there exists an exponential gap between DAGs and trees for the PC structure.

When a user contributes more data points, more information can be collected to improve the algorithm's performance. But at the same time, more noise might need to be added to the algorithm in order to keep the algorithm differentially private and this might hurt the algorithm's performance.

When a user contributes more data points, more information can be collected to improve the algorithm's performance. But at the same time, more noise might need to be added to the algorithm in order to keep the algorithm differentially private and this might hurt the algorithm's performance.

Optimal transportation, or computing the Wasserstein or "earth mover's" distance between two n-dimensional distributions, is a fundamental primitive which arises in many learning and statistical settings.

Although humans inherently have diverse values, current large language model (LLM) alignment methods often assume that aligning LLMs with the general public's preferences is optimal. A major challenge in adopting a more individualized approach to LLM alignment is its lack of scalability, as it involves repeatedly acquiring preference data and training new reward models and LLMs for each individual's preferences. To address these challenges, we propose a new paradigm where users specify what they value most within the system message, steering the LLM's generation behavior to better align with the user's intentions. However, a naive application of such an approach is non-trivial since LLMs are typically trained on a uniform system message (e.g., "You are a helpful assistant"), which limits their ability to generalize to diverse, unseen system messages.

Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate estimator for a task such as least square regression. We show that these limitations can be circumvented in the distributed setting by designing sketching methods that minimize the bias of the estimator, rather than its error. In particular, we give a sparse sketching method running in optimal space and current matrix multiplication time, which recovers a nearly-unbiased least squares estimator using two passes over the data. This leads to new communication-efficient distributed averaging algorithms for least squares and related tasks, which directly improve on several prior approaches. Our key novelty is a new bias analysis for sketched least squares, giving a sharp characterization of its dependence on the sketch sparsity. The techniques include new higher-moment restricted Bai-Silverstein inequalities, which are of independent interest to the non-asymptotic analysis of deterministic equivalents for random matrices that arise from sketching.

Surprisingly, however, the optimal rate in terms of Bellman error for the VI setup was not known, and finding a general acceleration mechanism has been an open problem. In this paper, we present the first accelerated VI for both the Bellman consistency and optimality operators. Our method, called Anc-VI, is based on an anchoring mechanism (distinct from Nesterov's acceleration), and it reduces the Bellman error faster than standard VI. In particular, Anc-VI exhibits a O(1/k)-rate for γ 1 or even γ = 1, while standard VI has rate O(1) for γ 1 1/k, where k is the iteration count. We also provide a complexity lower bound matching the upper bound up to a constant factor of 4, thereby establishing optimality of the accelerated rate of Anc-VI. Finally, we show that the anchoring mechanism provides the same benefit in the approximate VI and Gauss-Seidel VI setups as well.

Tensor Train (TT) decomposition is widely used in the machine learning and quantum physics communities as a popular tool to efficiently compress high-dimensional tensor data. In this paper, we propose an efficient algorithm to accelerate computing the TT decomposition with the Alternating Least Squares (ALS) algorithm relying on exact leverage scores sampling. For this purpose, we propose a data structure that allows us to efficiently sample from the tensor with time complexity logarithmic in the tensor size.

The aim of this paper is to address the challenge of gradual domain adaptation within a class of manifold-constrained data distributions.