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Variational inference (VI) is a technique to approximate difficult to compute posteriors by optimization. In contrast to MCMC, VI scales to many observations. In the case of complex posteriors, however, state-of-the-art VI approaches often yield unsatisfactory posterior approximations. This paper presents Bernstein flow variational inference (BF-VI), a robust and easy-to-use method, flexible enough to approximate complex multivariate posteriors. BF-VI combines ideas from normalizing flows and Bernstein polynomial-based transformation models. In benchmark experiments, we compare BF-VI solutions with exact posteriors, MCMC solutions, and state-of-the-art VI methods including normalizing flow based VI. We show for low-dimensional models that BF-VI accurately approximates the true posterior; in higher-dimensional models, BF-VI outperforms other VI methods. Further, we develop with BF-VI a Bayesian model for the semi-structured Melanoma challenge data, combining a CNN model part for image data with an interpretable model part for tabular data, and demonstrate for the first time how the use of VI in semi-structured models.

We examine the possibility of approximating Maximum Vertex-Disjoint Shortest Paths. In this problem, the input is an edge-weighted (directed or undirected) $n$-vertex graph $G$ along with $k$ terminal pairs $(s_1,t_1),(s_2,t_2),\ldots,(s_k,t_k)$. The task is to connect as many terminal pairs as possible by pairwise vertex-disjoint paths such that each path is a shortest path between the respective terminals. Our work is anchored in the recent breakthrough by Lochet [SODA '21], which demonstrates the polynomial-time solvability of the problem for a fixed value of $k$. Lochet's result implies the existence of a polynomial-time $ck$-approximation for Maximum Vertex-Disjoint Shortest Paths, where $c \leq 1$ is a constant. Our first result suggests that this approximation algorithm is, in a sense, the best we can hope for. More precisely, assuming the gap-ETH, we exclude the existence of an $o(k)$-approximations within $f(k) \cdot $poly($n$) time for any function $f$ that only depends on $k$. Our second result demonstrates the infeasibility of achieving an approximation ratio of $n^{\frac{1}{2}-\varepsilon}$ in polynomial time, unless P = NP. It is not difficult to show that a greedy algorithm selecting a path with the minimum number of arcs results in a $\lceil\sqrt{\ell}\rceil$-approximation, where $\ell$ is the number of edges in all the paths of an optimal solution. Since $\ell \leq n$, this underscores the tightness of the $n^{\frac{1}{2}-\varepsilon}$-inapproximability bound. Additionally, we establish that Maximum Vertex-Disjoint Shortest Paths is fixed-parameter tractable when parameterized by $\ell$ but does not admit a polynomial kernel. Our hardness results hold for undirected graphs with unit weights, while our positive results extend to scenarios where the input graph is directed and features arbitrary (non-negative) edge weights.

With the incorporation of the UNet architecture, diffusion probabilistic models have become a dominant force in image generation tasks. One key design in UNet is the skip connections between the encoder and decoder blocks. Although skip connections have been shown to improve training stability and model performance, we reveal that such shortcuts can be a limiting factor for the complexity of the transformation. As the sampling steps decrease, the generation process and the role of the UNet get closer to the push-forward transformations from Gaussian distribution to the target, posing a challenge for the network's complexity. To address this challenge, we propose Skip-Tuning, a simple yet surprisingly effective training-free tuning method on the skip connections. Our method can achieve 100% FID improvement for pretrained EDM on ImageNet 64 with only 19 NFEs (1.75), breaking the limit of ODE samplers regardless of sampling steps. Surprisingly, the improvement persists when we increase the number of sampling steps and can even surpass the best result from EDM-2 (1.58) with only 39 NFEs (1.57). Comprehensive exploratory experiments are conducted to shed light on the surprising effectiveness. We observe that while Skip-Tuning increases the score-matching losses in the pixel space, the losses in the feature space are reduced, particularly at intermediate noise levels, which coincide with the most effective range accounting for image quality improvement.

We explore the cryptographic power of arbitrary shared physical resources. The most general such resource is access to a fresh entangled quantum state at the outset of each protocol execution. We call this the Common Reference Quantum State (CRQS) model, in analogy to the well-known Common Reference String (CRS). The CRQS model is a natural generalization of the CRS model but appears to be more powerful: in the two-party setting, a CRQS can sometimes exhibit properties associated with a Random Oracle queried once by measuring a maximally entangled state in one of many mutually unbiased bases. We formalize this notion as a Weak One-Time Random Oracle (WOTRO), where we only ask of the $m$-bit output to have some randomness when conditioned on the $n$-bit input. We show that when $n-m\in\omega(\lg n)$, any protocol for WOTRO in the CRQS model can be attacked by an (inefficient) adversary. Moreover, our adversary is efficiently simulatable, which rules out the possibility of proving the computational security of a scheme by a fully black-box reduction to a cryptographic game assumption. On the other hand, we introduce a non-game quantum assumption for hash functions that implies WOTRO in the CRQS model (where the CRQS consists only of EPR pairs). We first build a statistically secure WOTRO protocol where $m=n$, then hash the output. The impossibility of WOTRO has the following consequences. First, we show the fully-black-box impossibility of a quantum Fiat-Shamir transform, extending the impossibility result of Bitansky et al. (TCC 2013) to the CRQS model. Second, we show a fully-black-box impossibility result for a strenghtened version of quantum lightning (Zhandry, Eurocrypt 2019) where quantum bolts have an additional parameter that cannot be changed without generating new bolts. Our results also apply to $2$-message protocols in the plain model.

We study the extent to which it is possible to approximate the optimal value of a Unique Games instance in Fixed-Point Logic with Counting (FPC). Formally, we prove lower bounds against the accuracy of FPC-interpretations that map Unique Games instances (encoded as relational structures) to rational numbers giving the approximate fraction of constraints that can be satisfied. We prove two new FPC-inexpressibility results for Unique Games: the existence of a $(1/2, 1/3 + \delta)$-inapproximability gap, and inapproximability to within any constant factor. Previous recent work has established similar FPC-inapproximability results for a small handful of other problems. Our construction builds upon some of these ideas, but contains a novel technique. While most FPC-inexpressibility results are based on variants of the CFI-construction, ours is significantly different. We start with a graph of very large girth and label the edges with random affine vector spaces over $\mathbb{F}_2$ that determine the constraints in the two structures. Duplicator's strategy involves maintaining a partial isomorphism over a minimal tree that spans the pebbled vertices of the graph.

Self-supervised learning, dubbed the dark matter of intelligence, is a promising path to advance machine learning. Yet, much like cooking, training SSL methods is a delicate art with a high barrier to entry. While many components are familiar, successfully training a SSL method involves a dizzying set of choices from the pretext tasks to training hyper-parameters. Our goal is to lower the barrier to entry into SSL research by laying the foundations and latest SSL recipes in the style of a cookbook. We hope to empower the curious researcher to navigate the terrain of methods, understand the role of the various knobs, and gain the know-how required to explore how delicious SSL can be.

In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.

Visual recognition is currently one of the most important and active research areas in computer vision, pattern recognition, and even the general field of artificial intelligence. It has great fundamental importance and strong industrial needs. Deep neural networks (DNNs) have largely boosted their performances on many concrete tasks, with the help of large amounts of training data and new powerful computation resources. Though recognition accuracy is usually the first concern for new progresses, efficiency is actually rather important and sometimes critical for both academic research and industrial applications. Moreover, insightful views on the opportunities and challenges of efficiency are also highly required for the entire community. While general surveys on the efficiency issue of DNNs have been done from various perspectives, as far as we are aware, scarcely any of them focused on visual recognition systematically, and thus it is unclear which progresses are applicable to it and what else should be concerned. In this paper, we present the review of the recent advances with our suggestions on the new possible directions towards improving the efficiency of DNN-related visual recognition approaches. We investigate not only from the model but also the data point of view (which is not the case in existing surveys), and focus on three most studied data types (images, videos and points). This paper attempts to provide a systematic summary via a comprehensive survey which can serve as a valuable reference and inspire both researchers and practitioners who work on visual recognition problems.

Deep neural networks (DNNs) are successful in many computer vision tasks. However, the most accurate DNNs require millions of parameters and operations, making them energy, computation and memory intensive. This impedes the deployment of large DNNs in low-power devices with limited compute resources. Recent research improves DNN models by reducing the memory requirement, energy consumption, and number of operations without significantly decreasing the accuracy. This paper surveys the progress of low-power deep learning and computer vision, specifically in regards to inference, and discusses the methods for compacting and accelerating DNN models. The techniques can be divided into four major categories: (1) parameter quantization and pruning, (2) compressed convolutional filters and matrix factorization, (3) network architecture search, and (4) knowledge distillation. We analyze the accuracy, advantages, disadvantages, and potential solutions to the problems with the techniques in each category. We also discuss new evaluation metrics as a guideline for future research.

Commonsense knowledge and commonsense reasoning are some of the main bottlenecks in machine intelligence. In the NLP community, many benchmark datasets and tasks have been created to address commonsense reasoning for language understanding. These tasks are designed to assess machines' ability to acquire and learn commonsense knowledge in order to reason and understand natural language text. As these tasks become instrumental and a driving force for commonsense research, this paper aims to provide an overview of existing tasks and benchmarks, knowledge resources, and learning and inference approaches toward commonsense reasoning for natural language understanding. Through this, our goal is to support a better understanding of the state of the art, its limitations, and future challenges.