OpenRaiser/Intern-Atlas huggingface dataset:
MMD-Regularized Unbalanced Optimal Transport
Venue: arXiv cs.LG 2024
Year: 2024

We study the unbalanced optimal transport (UOT) problem, where the marginal constraints are enforced using Maximum Mean Discrepancy (MMD) regularization. Our work is motivated by the observation that the literature on UOT is focused on regularization based on $ϕ$-divergence (e.g., KL divergence). Despite the popularity of MMD, its role as a regularizer in the context of UOT seems less understood. We begin by deriving a specific dual of MMD-regularized UOT (MMD-UOT), which helps us prove several useful properties. One interesting outcome of this duality result is that MMD-UOT induces novel metrics, which not only lift the ground metric like the Wasserstein but are also sample-wise efficient to estimate like the MMD. Further, for real-world applications involving non-discrete measures, we present an estimator for the transport plan that is supported only on the given ($m$) samples. Under certain conditions, we prove that the estimation error with this finitely-supported transport plan is also $\mathcal{O}(1/\sqrt{m})$. As far as we know, such error bounds that are free from the curse of dimensionality are not known for $ϕ$-divergence regularized UOT. Finally, we discuss how the proposed estimator can be computed efficiently using accelerated gradient descent. Our experiments show that MMD-UOT consistently outperforms popular baselines, including KL-regularized UOT and MMD, in diverse machine learning applications.
P1AC: Revisiting Absolute Pose From a Single Affine Correspondence
Venue: arXiv cs.CV 2024
Year: 2024

Affine correspondences have traditionally been used to improve feature matching over wide baselines. While recent work has successfully used affine correspondences to solve various relative camera pose estimation problems, less attention has been given to their use in absolute pose estimation. We introduce the first general solution to the problem of estimating the pose of a calibrated camera given a single observation of an oriented point and an affine correspondence. The advantage of our approach (P1AC) is that it requires only a single correspondence, in comparison to the traditional point-based approach (P3P), significantly reducing the combinatorics in robust estimation. P1AC provides a general solution that removes restrictive assumptions made in prior work and is applicable to large-scale image-based localization. We propose a minimal solution to the P1AC problem and evaluate our novel solver on synthetic data, showing its numerical stability and performance under various types of noise. On standard image-based localization benchmarks we show that P1AC achieves more accurate results than the widely used P3P algorithm. Code for our method is available at https://github.com/jonathanventura/P1AC/ .
An Experimental Study of Semantic Continuity for Deep Learning Models
Venue: arXiv cs.LG 2024
Year: 2024

Deep learning models suffer from the problem of semantic discontinuity: small perturbations in the input space tend to cause semantic-level interference to the model output. We argue that the semantic discontinuity results from these inappropriate training targets and contributes to notorious issues such as adversarial robustness, interpretability, etc. We first conduct data analysis to provide evidence of semantic discontinuity in existing deep learning models, and then design a simple semantic continuity constraint which theoretically enables models to obtain smooth gradients and learn semantic-oriented features. Qualitative and quantitative experiments prove that semantically continuous models successfully reduce the use of non-semantic information, which further contributes to the improvement in adversarial robustness, interpretability, model transfer, and machine bias.
On the Overlooked Pitfalls of Weight Decay and How to Mitigate Them: A Gradient-Norm Perspective
Venue: arXiv cs.LG 2024
Year: 2024

Weight decay is a simple yet powerful regularization technique that has been very widely used in training of deep neural networks (DNNs). While weight decay has attracted much attention, previous studies fail to discover some overlooked pitfalls on large gradient norms resulted by weight decay. In this paper, we discover that, weight decay can unfortunately lead to large gradient norms at the final phase (or the terminated solution) of training, which often indicates bad convergence and poor generalization. To mitigate the gradient-norm-centered pitfalls, we present the first practical scheduler for weight decay, called the Scheduled Weight Decay (SWD) method that can dynamically adjust the weight decay strength according to the gradient norm and significantly penalize large gradient norms during training. Our experiments also support that SWD indeed mitigates large gradient norms and often significantly outperforms the conventional constant weight decay strategy for Adaptive Moment Estimation (Adam).
A Tractable Online Learning Algorithm for the Multinomial Logit Contextual Bandit
Venue: arXiv cs.LG 2024
Year: 2024

In this paper, we consider the contextual variant of the MNL-Bandit problem. More specifically, we consider a dynamic set optimization problem, where a decision-maker offers a subset (assortment) of products to a consumer and observes the response in every round. Consumers purchase products to maximize their utility. We assume that a set of attributes describe the products, and the mean utility of a product is linear in the values of these attributes. We model consumer choice behavior using the widely used Multinomial Logit (MNL) model and consider the decision maker problem of dynamically learning the model parameters while optimizing cumulative revenue over the selling horizon $T$. Though this problem has attracted considerable attention in recent times, many existing methods often involve solving an intractable non-convex optimization problem. Their theoretical performance guarantees depend on a problem-dependent parameter which could be prohibitively large. In particular, existing algorithms for this problem have regret bounded by $O(\sqrt{κd T})$, where $κ$ is a problem-dependent constant that can have an exponential dependency on the number of attributes. In this paper, we propose an optimistic algorithm and show that the regret is bounded by $O(\sqrt{dT} + κ)$, significantly improving the performance over existing methods. Further, we propose a convex relaxation of the optimization step, which allows for tractable decision-making while retaining the favourable regret guarantee.
Decomposition, Compression, and Synthesis (DCS)-based Video Coding: A Neural Exploration via Resolution-Adaptive Learning
Venue: arXiv cs.CV 2024
Year: 2024

Inspired by the facts that retinal cells actually segregate the visual scene into different attributes (e.g., spatial details, temporal motion) for respective neuronal processing, we propose to first decompose the input video into respective spatial texture frames (STF) at its native spatial resolution that preserve the rich spatial details, and the other temporal motion frames (TMF) at a lower spatial resolution that retain the motion smoothness; then compress them together using any popular video coder; and finally synthesize decoded STFs and TMFs for high-fidelity video reconstruction at the same resolution as its native input. This work simply applies the bicubic resampling in decomposition and HEVC compliant codec in compression, and puts the focus on the synthesis part. For resolution-adaptive synthesis, a motion compensation network (MCN) is devised on TMFs to efficiently align and aggregate temporal motion features that will be jointly processed with corresponding STFs using a non-local texture transfer network (NL-TTN) to better augment spatial details, by which the compression and resolution resampling noises can be effectively alleviated with better rate-distortion efficiency. Such "Decomposition, Compression, Synthesis (DCS)" based scheme is codec agnostic, currently exemplifying averaged $\approx$1 dB PSNR gain or $\approx$25% BD-rate saving, against the HEVC anchor using reference software. In addition, experimental comparisons to the state-of-the-art methods and ablation studies are conducted to further report the efficiency and generalization of DCS algorithm, promising an encouraging direction for future video coding.
A Decentralised Digital Token Architecture for Public Transport
Venue: arXiv cs.CY 2024
Year: 2024

Digitisation is often viewed as beneficial to a user. Whereas traditionally, people would physically have to identify to a service, pay for a ticket in cash, or go into a library to access a book, people can now achieve all of this through a click of a button. Such actions may seem functionally identical to their analogue counterparts, but in the digital case, a user's actions are automatically recorded. The recording of user's interactions presents a problem because once the information is collected, it is outside of the control of the person whom it concerns. This issue is only exacerbated by the centralisation of the authentication mechanisms underpinning the aforementioned services, permitting the aggregation and analysis of even more data. This work aims to motivate the need and establish the feasibility of the application of a privacy-enhancing digital token management service to public transit. A proof-of-concept implementation is developed, building upon a design proposed by Goodell and Aste. This implementation was optimised for the public transport use case. Its performance is tested in a local environment to better understand the technical challenges and assess the technical feasibility of the system in a production setting. It was observed that for loads between one and five requests per second the proof-of-concept performs comparably to other contactless payment systems, with a maximum median response time less than two seconds. Due to hardware bottlenecks, reliable throughput in our test environment was limited to five requests per second. The demonstrated throughput and latency indicate that the system can feasibly compete with solutions currently in use. Yet, further work is needed to demonstrate their performance characteristics in an environment similar to that experienced in production.
Shrinkage under Random Projections, and Cubic Formula Lower Bounds for $\mathsf{AC}^0$
Venue: arXiv cs.CC 2024
Year: 2024

$\newcommand{\ACz}{\mathbf{AC}^0}$ Håstad showed that any De Morgan formula (composed of AND, OR and NOT gates) shrinks by a factor of $\tilde{O}(p^{2})$ under a random restriction that leaves each variable alive independently with probability $p$ [SICOMP, 1998]. Using this result, he gave an $\widetildeΩ(n^{3})$ formula size lower bound for the Andreev function, which, up to lower order improvements, remains the state-of-the-art lower bound for any explicit function. In this paper, we extend the shrinkage result of Håstad to hold under a far wider family of random restrictions and their generalization -- random projections. Based on our shrinkage results, we obtain an $\widetildeΩ(n^{3})$ formula size lower bound for an explicit function computable in $\ACz$. This improves upon the best known formula size lower bounds for $\ACz$, that were only quadratic prior to our work. In addition, we prove that the KRW conjecture [Karchmer et al., Computational Complexity 5(3/4), 1995] holds for inner functions for which the unweighted quantum adversary bound is tight. In particular, this holds for inner functions with a tight Khrapchenko bound. Our random projections are tailor-made to the function's structure so that the function maintains structure even under projection -- using such projections is necessary, as standard random restrictions simplify $\ACz$ circuits. In contrast, we show that any De Morgan formula shrinks by a quadratic factor under our random projections, allowing us to prove the cubic lower bound. Our proof techniques build on Håstad's proof for the simpler case of balanced formulas. This allows for a significantly simpler proof at the cost of slightly worse parameters. As such, when specialized to the case of $p$-random restrictions, our proof can be used as an exposition of Håstad's result.
Improved Digital Therapy for Developmental Pediatrics Using Domain-Specific Artificial Intelligence: Machine Learning Study
Venue: arXiv cs.CV 2024
Year: 2024

Background: Automated emotion classification could aid those who struggle to recognize emotions, including children with developmental behavioral conditions such as autism. However, most computer vision emotion recognition models are trained on adult emotion and therefore underperform when applied to child faces. Objective: We designed a strategy to gamify the collection and labeling of child emotion-enriched images to boost the performance of automatic child emotion recognition models to a level closer to what will be needed for digital health care approaches. Methods: We leveraged our prototype therapeutic smartphone game, GuessWhat, which was designed in large part for children with developmental and behavioral conditions, to gamify the secure collection of video data of children expressing a variety of emotions prompted by the game. Independently, we created a secure web interface to gamify the human labeling effort, called HollywoodSquares, tailored for use by any qualified labeler. We gathered and labeled 2155 videos, 39,968 emotion frames, and 106,001 labels on all images. With this drastically expanded pediatric emotion-centric database (>30 times larger than existing public pediatric emotion data sets), we trained a convolutional neural network (CNN) computer vision classifier of happy, sad, surprised, fearful, angry, disgust, and neutral expressions evoked by children. Results: The classifier achieved a 66.9% balanced accuracy and 67.4% F1-score on the entirety of the Child Affective Facial Expression (CAFE) as well as a 79.1% balanced accuracy and 78% F1-score on CAFE Subset A, a subset containing at least 60% human agreement on emotions labels. This performance is at least 10% higher than all previously developed classifiers evaluated against CAFE, the best of which reached a 56% balanced accuracy even when combining "anger" and "disgust" into a single class.
Variational Transport: A Convergent Particle-BasedAlgorithm for Distributional Optimization
Venue: arXiv cs.LG 2024
Year: 2024

We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises widely in machine learning and statistics, with Monte-Carlo sampling, variational inference, policy optimization, and generative adversarial network as examples. For this problem, we propose a novel particle-based algorithm, dubbed as variational transport, which approximately performs Wasserstein gradient descent over the manifold of probability distributions via iteratively pushing a set of particles. Specifically, we prove that moving along the geodesic in the direction of functional gradient with respect to the second-order Wasserstein distance is equivalent to applying a pushforward mapping to a probability distribution, which can be approximated accurately by pushing a set of particles. Specifically, in each iteration of variational transport, we first solve the variational problem associated with the objective functional using the particles, whose solution yields the Wasserstein gradient direction. Then we update the current distribution by pushing each particle along the direction specified by such a solution. By characterizing both the statistical error incurred in estimating the Wasserstein gradient and the progress of the optimization algorithm, we prove that when the objective function satisfies a functional version of the Polyak-Łojasiewicz (PL) (Polyak, 1963) and smoothness conditions, variational transport converges linearly to the global minimum of the objective functional up to a certain statistical error, which decays to zero sublinearly as the number of particles goes to infinity.
Pit30M: A Benchmark for Global Localization in the Age of Self-Driving Cars
Venue: arXiv cs.CV 2024
Year: 2024

We are interested in understanding whether retrieval-based localization approaches are good enough in the context of self-driving vehicles. Towards this goal, we introduce Pit30M, a new image and LiDAR dataset with over 30 million frames, which is 10 to 100 times larger than those used in previous work. Pit30M is captured under diverse conditions (i.e., season, weather, time of the day, traffic), and provides accurate localization ground truth. We also automatically annotate our dataset with historical weather and astronomical data, as well as with image and LiDAR semantic segmentation as a proxy measure for occlusion. We benchmark multiple existing methods for image and LiDAR retrieval and, in the process, introduce a simple, yet effective convolutional network-based LiDAR retrieval method that is competitive with the state of the art. Our work provides, for the first time, a benchmark for sub-metre retrieval-based localization at city scale. The dataset, its Python SDK, as well as more information about the sensors, calibration, and metadata, are available on the project website: https://pit30m.github.io/
An FPT algorithm for Matching Cut and d-cut
Venue: arXiv cs.DS 2024
Year: 2024

Given a positive integer $d$, the d-CUT is the problem of deciding if an undirected graph $G=(V,E)$ has a cut $(A,B)$ such that every vertex in $A$ (resp. $B$) has at most $d$ neighbors in $B$ (resp. $A$). For $d=1$, the problem is referred to as MATCHING CUT. Gomes and Sau, in IPEC 2019, gave the first fixed parameter tractable algorithm for d-CUT parameterized by maximum number of the crossing edges in the cut (i.e. the size of edge cut). However, their paper doesn't provide an explicit bound on the running time, as it indirectly relies on a MSOL formulation and Courcelle's Theorem. Motivated by this, we design and present an FPT algorithm for d-CUT for general graphs with running time $2^{O(k\log k)}n^{O(1)}$ where $k$ is the maximum size of the edge cut. This is the first FPT algorithm for the d-CUT and MATCHING CUT with an explicit dependence on this parameter. We also observe that there is no algorithm solving MATCHING CUT in time $2^{o(k)}n^{O(1)}$ where $k$ is the maximum size of the edge cut unless ETH fails.
Fair Asynchronous Session Subtyping
Venue: arXiv cs.PL 2024
Year: 2024

Session types are widely used as abstractions of asynchronous message passing systems. Refinement for such abstractions is crucial as it allows improvements of a given component without compromising its compatibility with the rest of the system. In the context of session types, the most general notion of refinement is asynchronous session subtyping, which allows message emissions to be anticipated w.r.t. a bounded amount of message consumptions. In this paper we investigate the possibility to anticipate emissions w.r.t. an unbounded amount of consumptions: to this aim we propose to consider fair compliance over asynchronous session types and fair refinement as the relation that preserves it. This allows us to propose a novel variant of session subtyping that leverages the notion of controllability from service contract theory and that is a sound characterisation of fair refinement. In addition, we show that both fair refinement and our novel subtyping are undecidable. We also present a sound algorithm which deals with examples that feature potentially unbounded buffering. Finally, we present an implementation of our algorithm and an empirical evaluation of it on synthetic benchmarks.
A Matrix-based Distance of Pythagorean Fuzzy Set and its Application in Medical Diagnosis
Venue: arXiv cs.AI 2024
Year: 2024

The pythagorean fuzzy set (PFS) which is developed based on intuitionistic fuzzy set, is more efficient in elaborating and disposing uncertainties in indeterminate situations, which is a very reason of that PFS is applied in various kinds of fields. How to measure the distance between two pythagorean fuzzy sets is still an open issue. Mnay kinds of methods have been proposed to present the of the question in former reaserches. However, not all of existing methods can accurately manifest differences among pythagorean fuzzy sets and satisfy the property of similarity. And some other kinds of methods neglect the relationship among three variables of pythagorean fuzzy set. To addrees the proplem, a new method of measuring distance is proposed which meets the requirements of axiom of distance measurement and is able to indicate the degree of distinction of PFSs well. Then some numerical examples are offered to to verify that the method of measuring distances can avoid the situation that some counter? intuitive and irrational results are produced and is more effective, reasonable and advanced than other similar methods. Besides, the proposed method of measuring distances between PFSs is applied in a real environment of application which is the medical diagnosis and is compared with other previous methods to demonstrate its superiority and efficiency. And the feasibility of the proposed method in handling uncertainties in practice is also proved at the same time.
Learning with Density Matrices and Random Features
Venue: arXiv cs.LG 2024
Year: 2024

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement, system combination and expectations as linear algebra operations. This paper explores how density matrices can be used as a building block for machine learning models exploiting their ability to straightforwardly combine linear algebra and probability. One of the main results of the paper is to show that density matrices coupled with random Fourier features could approximate arbitrary probability distributions over $\mathbb{R}^n$. Based on this finding the paper builds different models for density estimation, classification and regression. These models are differentiable, so it is possible to integrate them with other differentiable components, such as deep learning architectures and to learn their parameters using gradient-based optimization. In addition, the paper presents optimization-less training strategies based on estimation and model averaging. The models are evaluated in benchmark tasks and the results are reported and discussed.