OpenRaiser/Intern-Atlas huggingface dataset:
Probabilistic Query Evaluation with Bag Semantics
Venue: arXiv cs.DB 2023
Year: 2023

We study the complexity of evaluating queries on probabilistic databases under bag semantics. We focus on self-join free conjunctive queries, and probabilistic databases where occurrences of different facts are independent, which is the natural generalization of tuple-independent probabilistic databases to the bag semantics setting. For set semantics, the data complexity of this problem is well understood, even for the more general class of unions of conjunctive queries: it is either in polynomial time, or #P-hard, depending on the query (Dalvi & Suciu, JACM 2012). A reasonably general model of bag probabilistic databases may have unbounded multiplicities. In this case, the probabilistic database is no longer finite, and a careful treatment of representation mechanisms is required. Moreover, the answer to a Boolean query is a probability distribution over (possibly all) non-negative integers, rather than a probability distribution over { true, false }. Therefore, we discuss two flavors of probabilistic query evaluation: computing expectations of answer tuple multiplicities, and computing the probability that a tuple is contained in the answer at most k times for some parameter k. Subject to mild technical assumptions on the representation systems, it turns out that expectations are easy to compute, even for unions of conjunctive queries. For query answer probabilities, we obtain a dichotomy between solvability in polynomial time and #P-hardness for self-join free conjunctive queries.
Coded Caching with Private Demands and Caches
Venue: arXiv cs.IT 2023
Year: 2023

Recently it was shown that the seminal Maddah-Ali and Niesen (MAN) coded caching scheme leaks the demand information of each user to the others. Many works have considered coded caching with demand privacy, while each non-trivial existing coded caching scheme with private demands was built on the fact that the cache information of each user is private to the others. However, most of these schemes leak the users' cache information. Consequently, in most realistic settings (e.g., video streaming), where the system is used over time with multiple sequential transmission rounds, these schemes leak demand privacy beyond the first round. This observation motivates our new formulation of coded caching with simultaneously private demands and caches. The main contribution of this paper is a new construction that generates private coded caching schemes by leveraging two-server private information retrieval (PIR) schemes. We show that if in the PIR scheme the demand is uniform over all files and the queries are independent, the resulting caching scheme is private on both the demands and on the caches. Interestingly, we propose a new construction of two-server PIR schemes in this class by leveraging coded caching schemes. By applying the seminal MAN coded caching scheme into our construction, the resulting two-server PIR scheme is proved to be order optimal. This is a second new structural result, somehow closing the loop in the relation between coded caching and PIR. Finally, to explore a broader tradeoff between cache privacy and transmission load, we relax the cache privacy constraint and introduce the definition of leakage on cache information. Then, again as a by-product of our new construction, we propose new schemes with perfect demand privacy and imperfect cache privacy that achieve an order-gain in load with respect to the scheme with perfect privacy on both demands and caches.
Positive First-order Logic on Words and Graphs
Venue: arXiv cs.FL 2023
Year: 2023

We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This provides a simple proof that Lyndon's preservation theorem fails on finite structures. We lift this example language to finite graphs, thereby providing a new result of independent interest for FO-definable graph classes: negation might be needed even when the class is closed under addition of edges. We finally show that the problem of whether a given regular language of finite words is definable in FO+ is undecidable.
New results on the robust coloring problem
Venue: arXiv cs.DM 2023
Year: 2023

Many variations of the classical graph coloring model have been intensively studied due to their multiple applications; scheduling problems and aircraft assignments, for instance, motivate the robust coloring problem. This model gets to capture natural constraints of those optimization problems by combining the information provided by two colorings: a vertex coloring of a graph and the induced edge coloring on a subgraph of its complement; the goal is to minimize, among all proper colorings of the graph for a fixed number of colors, the number of edges in the subgraph with the endpoints of the same color. The study of the robust coloring model has been focused on the search for heuristics due to its NP-hard character when using at least three colors, but little progress has been made in other directions. We present a new approach on the problem obtaining the first collection of non-heuristic results for general graphs; among them, we prove that robust coloring is the model that better approaches the equitable partition of the vertex set, even when the graph does not admit a so-called \emph{equitable coloring}. We also show the NP-completeness of its decision problem for the unsolved case of two colors, obtain bounds on the associated robust coloring parameter, and solve a conjecture on paths that illustrates the complexity of studying this coloring model.
Generalizing similarity in noisy setups: the DIBS phenomenon
Venue: arXiv cs.LG 2023
Year: 2023

This work uncovers an interplay among data density, noise, and the generalization ability in similarity learning. We consider Siamese Neural Networks (SNNs), which are the basic form of contrastive learning, and explore two types of noise that can impact SNNs, Pair Label Noise (PLN) and Single Label Noise (SLN). Our investigation reveals that SNNs exhibit double descent behaviour regardless of the training setup and that it is further exacerbated by noise. We demonstrate that the density of data pairs is crucial for generalization. When SNNs are trained on sparse datasets with the same amount of PLN or SLN, they exhibit comparable generalization properties. However, when using dense datasets, PLN cases generalize worse than SLN ones in the overparametrized region, leading to a phenomenon we call Density-Induced Break of Similarity (DIBS). In this regime, PLN similarity violation becomes macroscopical, corrupting the dataset to the point where complete interpolation cannot be achieved, regardless of the number of model parameters. Our analysis also delves into the correspondence between online optimization and offline generalization in similarity learning. The results show that this equivalence fails in the presence of label noise in all the scenarios considered.
Compositionality as Lexical Symmetry
Venue: arXiv cs.CL 2023
Year: 2023

In tasks like semantic parsing, instruction following, and question answering, standard deep networks fail to generalize compositionally from small datasets. Many existing approaches overcome this limitation with model architectures that enforce a compositional process of sentence interpretation. In this paper, we present a domain-general and model-agnostic formulation of compositionality as a constraint on symmetries of data distributions rather than models. Informally, we prove that whenever a task can be solved by a compositional model, there is a corresponding data augmentation scheme -- a procedure for transforming examples into other well formed examples -- that imparts compositional inductive bias on any model trained to solve the same task. We describe a procedure called LEXSYM that discovers these transformations automatically, then applies them to training data for ordinary neural sequence models. Unlike existing compositional data augmentation procedures, LEXSYM can be deployed agnostically across text, structured data, and even images. It matches or surpasses state-of-the-art, task-specific models on COGS semantic parsing, SCAN and ALCHEMY instruction following, and CLEVR-COGENT visual question answering datasets.
Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer
Venue: arXiv cs.LG 2023
Year: 2023

Several problems in stochastic analysis are defined through their geometry, and preserving that geometric structure is essential to generating meaningful predictions. Nevertheless, how to design principled deep learning (DL) models capable of encoding these geometric structures remains largely unknown. We address this open problem by introducing a universal causal geometric DL framework in which the user specifies a suitable pair of metric spaces $\mathscr{X}$ and $\mathscr{Y}$ and our framework returns a DL model capable of causally approximating any ``regular'' map sending time series in $\mathscr{X}^{\mathbb{Z}}$ to time series in $\mathscr{Y}^{\mathbb{Z}}$ while respecting their forward flow of information throughout time. Suitable geometries on $\mathscr{Y}$ include various (adapted) Wasserstein spaces arising in optimal stopping problems, a variety of statistical manifolds describing the conditional distribution of continuous-time finite state Markov chains, and all Fréchet spaces admitting a Schauder basis, e.g. as in classical finance. Suitable spaces $\mathscr{X}$ are compact subsets of any Euclidean space. Our results all quantitatively express the number of parameters needed for our DL model to achieve a given approximation error as a function of the target map's regularity and the geometric structure both of $\mathscr{X}$ and of $\mathscr{Y}$. Even when omitting any temporal structure, our universal approximation theorems are the first guarantees that Hölder functions, defined between such $\mathscr{X}$ and $\mathscr{Y}$ can be approximated by DL models.
CoTV: Cooperative Control for Traffic Light Signals and Connected Autonomous Vehicles using Deep Reinforcement Learning
Venue: arXiv cs.AI 2023
Year: 2023

The target of reducing travel time only is insufficient to support the development of future smart transportation systems. To align with the United Nations Sustainable Development Goals (UN-SDG), a further reduction of fuel and emissions, improvements of traffic safety, and the ease of infrastructure deployment and maintenance should also be considered. Different from existing work focusing on the optimization of the control in either traffic light signal (to improve the intersection throughput), or vehicle speed (to stabilize the traffic), this paper presents a multi-agent Deep Reinforcement Learning (DRL) system called CoTV, which Cooperatively controls both Traffic light signals and Connected Autonomous Vehicles (CAV). Therefore, our CoTV can well balance the achievement of the reduction of travel time, fuel, and emissions. In the meantime, CoTV can also be easy to deploy by cooperating with only one CAV that is the nearest to the traffic light controller on each incoming road. This enables more efficient coordination between traffic light controllers and CAV, thus leading to the convergence of training CoTV under the large-scale multi-agent scenario that is traditionally difficult to converge. We give the detailed system design of CoTV and demonstrate its effectiveness in a simulation study using SUMO under various grid maps and realistic urban scenarios with mixed-autonomy traffic.
Score vs. Winrate in Score-Based Games: which Reward for Reinforcement Learning?
Venue: arXiv cs.AI 2023
Year: 2023

In the last years, the DeepMind algorithm AlphaZero has become the state of the art to efficiently tackle perfect information two-player zero-sum games with a win/lose outcome. However, when the win/lose outcome is decided by a final score difference, AlphaZero may play score-suboptimal moves because all winning final positions are equivalent from the win/lose outcome perspective. This can be an issue, for instance when used for teaching, or when trying to understand whether there is a better move. Moreover, there is the theoretical quest for the perfect game. A naive approach would be training an AlphaZero-like agent to predict score differences instead of win/lose outcomes. Since the game of Go is deterministic, this should as well produce an outcome-optimal play. However, it is a folklore belief that "this does not work". In this paper, we first provide empirical evidence for this belief. We then give a theoretical interpretation of this suboptimality in general perfect information two-player zero-sum game where the complexity of a game like Go is replaced by the randomness of the environment. We show that an outcome-optimal policy has a different preference for uncertainty when it is winning or losing. In particular, when in a losing state, an outcome-optimal agent chooses actions leading to a higher score variance. We then posit that when approximation is involved, a deterministic game behaves like a nondeterministic game, where the score variance is modeled by how uncertain the position is. We validate this hypothesis in AlphaZero-like software with a human expert.
Fenrir: Physics-Enhanced Regression for Initial Value Problems
Venue: arXiv cs.LG 2023
Year: 2023

We show how probabilistic numerics can be used to convert an initial value problem into a Gauss--Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in ordinary differential equations is reduced to hyperparameter estimation in Gauss--Markov regression, which tends to be considerably easier. The method's relation and benefits in comparison to classical numerical integration and gradient matching approaches is elucidated. In particular, the method can, in contrast to gradient matching, handle partial observations, and has certain routes for escaping local optima not available to classical numerical integration. Experimental results demonstrate that the method is on par or moderately better than competing approaches.
ExPoSe: Combining State-Based Exploration with Gradient-Based Online Search
Venue: arXiv cs.AI 2023
Year: 2023

Online tree-based search algorithms iteratively simulate trajectories and update action-values for a set of states stored in a tree structure. It works reasonably well in practice but fails to effectively utilise the information gathered from similar states. Depending upon the smoothness of the action-value function, one approach to overcoming this issue is through online learning, where information is interpolated among similar states; Policy Gradient Search provides a practical algorithm to achieve this. However, Policy Gradient Search lacks an explicit exploration mechanism, which is a key feature of tree-based online search algorithms. In this paper, we propose an efficient and effective online search algorithm called Exploratory Policy Gradient Search (ExPoSe), which leverages information sharing among states by updating the search policy parameters directly, while incorporating a well-defined exploration mechanism during the online search process. We evaluate ExPoSe on a range of decision-making problems, including Atari games, Sokoban, and Hamiltonian cycle search in sparse graphs. The results demonstrate that ExPoSe consistently outperforms other popular online search algorithms across all domains. The ExPoSe source code is available at \textit{\url{https://github.com/dixantmittal/ExPoSe}}.
Automatic Identification of Self-Admitted Technical Debt from Four Different Sources
Venue: arXiv cs.SE 2023
Year: 2023

Technical debt refers to taking shortcuts to achieve short-term goals while sacrificing the long-term maintainability and evolvability of software systems. A large part of technical debt is explicitly reported by the developers themselves; this is commonly referred to as Self-Admitted Technical Debt or SATD. Previous work has focused on identifying SATD from source code comments and issue trackers. However, there are no approaches available for automatically identifying SATD from other sources such as commit messages and pull requests, or by combining multiple sources. Therefore, we propose and evaluate an approach for automated SATD identification that integrates four sources: source code comments, commit messages, pull requests, and issue tracking systems. Our findings show that our approach outperforms baseline approaches and achieves an average F1-score of 0.611 when detecting four types of SATD (i.e., code/design debt, requirement debt, documentation debt, and test debt) from the four aforementioned sources. Thereafter, we analyze 23.6M code comments, 1.3M commit messages, 3.7M issue sections, and 1.7M pull request sections to characterize SATD in 103 open-source projects. Furthermore, we investigate the SATD keywords and relations between SATD in different sources. The findings indicate, among others, that: 1) SATD is evenly spread among all sources; 2) issues and pull requests are the two most similar sources regarding the number of shared SATD keywords, followed by commit messages, and then followed by code comments; 3) there are four kinds of relations between SATD items in the different sources.
On the predictability in reversible steganography
Venue: arXiv cs.CV 2023
Year: 2023

Artificial neural networks have advanced the frontiers of reversible steganography. The core strength of neural networks is the ability to render accurate predictions for a bewildering variety of data. Residual modulation is recognised as the most advanced reversible steganographic algorithm for digital images. The pivot of this algorithm is predictive analytics in which pixel intensities are predicted given some pixel-wise contextual information. This task can be perceived as a low-level vision problem and hence neural networks for addressing a similar class of problems can be deployed. On top of the prior art, this paper investigates predictability of pixel intensities based on supervised and unsupervised learning frameworks. Predictability analysis enables adaptive data embedding, which in turn leads to a better trade-off between capacity and imperceptibility. While conventional methods estimate predictability by the statistics of local image patterns, learning-based frameworks consider further the degree to which correct predictions can be made by a designated predictor. Not only should the image patterns be taken into account but also the predictor in use. Experimental results show that steganographic performance can be significantly improved by incorporating the learning-based predictability analysers into a reversible steganographic system.
Message Passing Neural PDE Solvers
Venue: arXiv cs.LG 2023
Year: 2023

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards fully end-to-end learned systems. Most works so far can only generalize over a subset of properties to which a generic solver would be faced, including: resolution, topology, geometry, boundary conditions, domain discretization regularity, dimensionality, etc. In this work, we build a solver, satisfying these properties, where all the components are based on neural message passing, replacing all heuristically designed components in the computation graph with backprop-optimized neural function approximators. We show that neural message passing solvers representationally contain some classical methods, such as finite differences, finite volumes, and WENO schemes. In order to encourage stability in training autoregressive models, we put forward a method that is based on the principle of zero-stability, posing stability as a domain adaptation problem. We validate our method on various fluid-like flow problems, demonstrating fast, stable, and accurate performance across different domain topologies, equation parameters, discretizations, etc., in 1D and 2D.
New Bounds on the Size of Binary Codes with Large Minimum Distance
Venue: arXiv cs.IT 2023
Year: 2023

Let $A(n, d)$ denote the maximum size of a binary code of length $n$ and minimum Hamming distance $d$. Studying $A(n, d)$, including efforts to determine it as well to derive bounds on $A(n, d)$ for large $n$'s, is one of the most fundamental subjects in coding theory. In this paper, we explore new lower and upper bounds on $A(n, d)$ in the large-minimum distance regime, in particular, when $d = n/2 - Ω(\sqrt{n})$. We first provide a new construction of cyclic codes, by carefully selecting specific roots in the binary extension field for the check polynomial, with length $n= 2^m -1$, distance $d \geq n/2 - 2^{c-1}\sqrt{n}$, and size $n^{c+1/2}$, for any $m\geq 4$ and any integer $c$ with $0 \leq c \leq m/2 - 1$. These code parameters are slightly worse than those of the Delsarte--Goethals (DG) codes that provide the previously known best lower bound in the large-minimum distance regime. However, using a similar and extended code construction technique we show a sequence of cyclic codes that improve upon DG codes and provide the best lower bound in a narrower range of the minimum distance $d$, in particular, when $d = n/2 - Ω(n^{2/3})$. Furthermore, by leveraging a Fourier-analytic view of Delsarte's linear program, upper bounds on $A(n, n/2 - ρ\sqrt{n})$ with $ρ\in (0.5, 9.5)$ are obtained that scale polynomially in $n$. To the best of authors' knowledge, the upper bound due to Barg and Nogin \cite{barg2006spectral} is the only previously known upper bound that scale polynomially in $n$ in this regime. We numerically demonstrate that our upper bound improves upon the Barg-Nogin upper bound in the specified high-minimum distance regime.
MAML and ANIL Provably Learn Representations
Venue: arXiv cs.LG 2023
Year: 2023

Recent empirical evidence has driven conventional wisdom to believe that gradient-based meta-learning (GBML) methods perform well at few-shot learning because they learn an expressive data representation that is shared across tasks. However, the mechanics of GBML have remained largely mysterious from a theoretical perspective. In this paper, we prove that two well-known GBML methods, MAML and ANIL, as well as their first-order approximations, are capable of learning common representation among a set of given tasks. Specifically, in the well-known multi-task linear representation learning setting, they are able to recover the ground-truth representation at an exponentially fast rate. Moreover, our analysis illuminates that the driving force causing MAML and ANIL to recover the underlying representation is that they adapt the final layer of their model, which harnesses the underlying task diversity to improve the representation in all directions of interest. To the best of our knowledge, these are the first results to show that MAML and/or ANIL learn expressive representations and to rigorously explain why they do so.