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Matroid intersection is a classical optimization problem where, given two matroids over the same ground set, the goal is to find the largest common independent set. In this paper, we show that there exists a certain "sparsifer": a subset of elements, of size $O(|S^{opt}| \cdot 1/\varepsilon)$, where $S^{opt}$ denotes the optimal solution, that is guaranteed to contain a $3/2 + \varepsilon$ approximation, while guaranteeing certain robustness properties. We call such a small subset a Density Constrained Subset (DCS), which is inspired by the Edge-Degree Constrained Subgraph (EDCS) [Bernstein and Stein, 2015], originally designed for the maximum cardinality matching problem in a graph. Our proof is constructive and hinges on a greedy decomposition of matroids, which we call the density-based decomposition. We show that this sparsifier has certain robustness properties that can be used in one-way communication and random-order streaming models.

This paper proposes a method to estimate the class separability of an unlabeled text dataset by inspecting the topological characteristics of sentence-transformer embeddings of the text. Experiments conducted involve both binary and multi-class cases, with balanced and imbalanced scenarios. The results demonstrate a clear correlation and a better consistency between the proposed method and other separability and classification metrics, such as Thornton's method and the AUC score of a logistic regression classifier, as well as unsupervised methods. Finally, we empirically show that the proposed method can be part of a stopping criterion for fine-tuning language-model classifiers. By monitoring the class separability of the embedding space after each training iteration, we can detect when the training process stops improving the separability of the embeddings without using additional labels.

Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the marginals of this variable in the two joint distributions may not be the same. In such settings, standard OT variants cannot be employed, and novel estimation techniques are necessary. Since the main challenge is that the conditional distributions are not explicitly available, the key idea in our OT formulation is to employ kernelized-least-squares terms computed over the joint samples, which implicitly match the transport plan's marginals with the empirical conditionals. Under mild conditions, we prove that our estimated transport plans, as a function of the conditioned variable, are asymptotically optimal. For finite samples, we show that the deviation in terms of our regularized objective is bounded by $O(1/m^{1/4})$, where $m$ is the number of samples. We also discuss how the conditional transport plan could be modelled using explicit probabilistic models as well as using implicit generative ones. We empirically verify the consistency of our estimator on synthetic datasets, where the optimal plan is analytically known. When employed in applications like prompt learning for few-shot classification and conditional-generation in the context of predicting cell responses to treatment, our methodology improves upon state-of-the-art methods.

In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear functional approximation for policy evaluation in discounted Markov Decision Processes. We show that a simple algorithm with a universal and instance-independent step size together with Polyak-Ruppert tail averaging is sufficient to obtain near-optimal variance and bias terms. We also provide the respective sample complexity bounds. Our proof technique is based on refined error bounds for linear stochastic approximation together with the novel stability result for the product of random matrices that arise from the TD-type recurrence.

This paper explores a fine-grained version of the Watrous conjecture, including the randomized and quantum algorithms with success probabilities arbitrarily close to $1/2$. Our contributions include the following: i) An analysis of the optimal success probability of quantum and randomized query algorithms of two fundamental partial symmetric Boolean functions given a fixed number of queries. We prove that for any quantum algorithm computing these two functions using $T$ queries, there exist randomized algorithms using $\mathsf{poly}(T)$ queries that achieve the same success probability as the quantum algorithm, even if the success probability is arbitrarily close to 1/2. ii) We establish that for any total symmetric Boolean function $f$, if a quantum algorithm uses $T$ queries to compute $f$ with success probability $1/2+\beta$, then there exists a randomized algorithm using $O(T^2)$ queries to compute $f$ with success probability $1/2+\Omega(\delta\beta^2)$ on a $1-\delta$ fraction of inputs, where $\beta,\delta$ can be arbitrarily small positive values. As a corollary, we prove a randomized version of Aaronson-Ambainis Conjecture for total symmetric Boolean functions in the regime where the success probability of algorithms can be arbitrarily close to 1/2. iii) We present polynomial equivalences for several fundamental complexity measures of partial symmetric Boolean functions. Specifically, we first prove that for certain partial symmetric Boolean functions, quantum query complexity is at most quadratic in approximate degree for any error arbitrarily close to 1/2. Next, we show exact quantum query complexity is at most quadratic in degree. Additionally, we give the tight bounds of several complexity measures, indicating their polynomial equivalence.

This letter proposes a scheme assisted by a reconfigurable intelligent surface (RIS) for efficient uplink traffic multiplexing between enhanced mobile broadband (eMBB) and ultra-reliable-low-latency communication (URLLC). The scheme determines two RIS configurations based only on the eMBB channel state information (CSI) available at the base station (BS). The first optimizes eMBB quality of service, while the second reduces eMBB interference in URLLC traffic by temporarily silencing the eMBB traffic. Numerical results demonstrate that this approach, relying solely on eMBB CSI and without BS coordination, can outperform the state-of-the-art preemptive puncturing by 4.9 times in terms of URLLC outage probability.

CRYSTALS-Dilithium is a lattice-based signature scheme to be standardized by NIST as the primary post-quantum signature algorithm. In this work, we make a thorough study of optimizing the implementations of Dilithium by utilizing the Advanced Vector Extension (AVX) instructions, specifically AVX2 and the latest AVX-512. We first present an improved parallel small polynomial multiplication with tailored early evaluation (PSPM-TEE) to further speed up the signing procedure. Our PSPM algorithm outperform the NTT by 47%-66% in AVX2 and AVX-512 implementation. We then present a tailored reduction method that is simpler and faster than Montgomery reduction. We minimize the CPU cycles of tailored reduction AVX-512 implementation by using AVX-512IFMA. Finally, we propose a fully and highly vectorized implementation of Dilithium using AVX-512. This is achieved by carefully vectorizing most of Dilithium functions with the AVX-512 instructions in order to improve efficiency both for time and for space simultaneously. With all the optimization efforts, our AVX-512 implementation improves the performance by 43.2%/39.3%/45.6% in key generation, 36.6%/41.6%/43.7% in signing, and 45.3%/46.5%/47.4% in verification for the parameter sets of Dilithium2/3/5 respectively. To the best of our knowledge, our AVX-512 implementation has the best performance for Dilithium on the Intel x86-64 CPU platform to date.

This work presents an algorithm for tracking the shape of multiple entangling Deformable Linear Objects (DLOs) from a sequence of RGB-D images. This algorithm runs in real-time and improves on previous single-DLO tracking approaches by enabling tracking of multiple objects. This is achieved using Global-Local Topology Preservation (GLTP). This work uses the geodesic distance in GLTP to define the distance between separate objects and the distance between different parts of the same object. Tracking multiple entangling DLOs is demonstrated experimentally. The source code is publicly released.

Automatically creating the description of an image using any natural languages sentence like English is a very challenging task. It requires expertise of both image processing as well as natural language processing. This paper discuss about different available models for image captioning task. We have also discussed about how the advancement in the task of object recognition and machine translation has greatly improved the performance of image captioning model in recent years. In addition to that we have discussed how this model can be implemented. In the end, we have also evaluated the performance of model using standard evaluation matrices.

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.