A package query returns a package -- a multiset of tuples -- that maximizes or minimizes a linear objective function subject to linear constraints, thereby enabling in-database decision support. Prior work has established the equivalence of package queries to Integer Linear Programs (ILPs) and developed the SketchRefine algorithm for package query processing. While this algorithm was an important first step toward supporting prescriptive analytics scalably inside a relational database, it struggles when the data size grows beyond a few hundred million tuples or when the constraints become very tight. In this paper, we present Progressive Shading, a novel algorithm for processing package queries that can scale efficiently to billions of tuples and gracefully handle tight constraints. Progressive Shading solves a sequence of optimization problems over a hierarchy of relations, each resulting from an ever-finer partitioning of the original tuples into homogeneous groups until the original relation is obtained. This strategy avoids the premature discarding of high-quality tuples that can occur with SketchRefine. Our novel partitioning scheme, Dynamic Low Variance, can handle very large relations with multiple attributes and can dynamically adapt to both concentrated and spread-out sets of attribute values, provably outperforming traditional partitioning schemes such as KD-Tree. We further optimize our system by replacing our off-the-shelf optimization software with customized ILP and LP solvers, called Dual Reducer and Parallel Dual Simplex respectively, that are highly accurate and orders of magnitude faster.
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Graded type systems, such as the one underlying the Granule programming language, allow various different properties of a program's behaviour to be tracked via annotating types with additional information, which we call grades. One example of such a property, often used as a case study in prior work on graded types, is information flow control, in which types are graded by a lattice of security levels allowing noninterference properties to be automatically verified and enforced. These typically focus on one particular aspect of security, however, known as confidentiality; public outputs are prohibited from depending on private inputs. Integrity, a property specifying that trusted outputs must not depend on untrusted inputs, has not been examined in this context. This short paper aims to remedy this omission. It is well-known that confidentiality and integrity are in some sense dual properties, but simply reversing the ordering of the security lattice turns out to be unsatisfactory for the purpose of combining both kinds of property in a single system, at least in our setting. We analogize the situation to recent work on embedding both linear and uniqueness types in a graded framework, and use this framing to demonstrate that we can enforce both integrity and confidentiality alongside one another. The main idea is to add an additional flavour of modality annotated for integrity, such that the existing graded comonad for tracking confidentiality now also acts as a relative monad over the new modality, with rules allowing information to flow from trusted to public to private.
We introduce two new classes of measures of information for statistical experiments which generalise and subsume $\phi$-divergences, integral probability metrics, $\mathfrak{N}$-distances (MMD), and $(f,\Gamma)$ divergences between two or more distributions. This enables us to derive a simple geometrical relationship between measures of information and the Bayes risk of a statistical decision problem, thus extending the variational $\phi$-divergence representation to multiple distributions in an entirely symmetric manner. The new families of divergence are closed under the action of Markov operators which yields an information processing equality which is a refinement and generalisation of the classical data processing inequality. This equality gives insight into the significance of the choice of the hypothesis class in classical risk minimization.
The choice of the objective function is crucial in emerging high-quality representations from self-supervised learning. This paper investigates how different formulations of the Barlow Twins (BT) objective impact downstream task performance for speech data. We propose Modified Barlow Twins (MBT) with normalized latents to enforce scale-invariance and evaluate on speaker identification, gender recognition and keyword spotting tasks. Our results show MBT improves representation generalization over original BT, especially when fine-tuning with limited target data. This highlights the importance of designing objectives that encourage invariant and transferable representations. Our analysis provides insights into how the BT learning objective can be tailored to produce speech representations that excel when adapted to new downstream tasks. This study is an important step towards developing reusable self-supervised speech representations.
We study the optimization problem of choosing strings of finite length to maximize string submodular functions on string matroids, which is a broader class of problems than maximizing set submodular functions on set matroids. We provide a lower bound for the performance of the greedy algorithm in our problem, and then prove that our bound is superior to the greedy curvature bound of Conforti and Cornuejols. Our bound has lower computational complexity than most previously proposed curvature bounds. Finally, we demonstrate the strength of our result on a sensor coverage problem.
We provide a method, based on automata theory, to mechanically prove the correctness of many numeration systems based on Fibonacci numbers. With it, long case-based and induction-based proofs of correctness can be replaced by simply constructing a regular expression (or finite automaton) specifying the rules for valid representations, followed by a short computation. Examples of the systems that can be handled using our technique include Brown's lazy representation (1965), the far-difference representation developed by Alpert (2009), and three representations proposed by Hajnal (2023). We also provide three additional systems and prove their validity.
Reinforcement learning (RL) with linear temporal logic (LTL) objectives can allow robots to carry out symbolic event plans in unknown environments. Most existing methods assume that the event detector can accurately map environmental states to symbolic events; however, uncertainty is inevitable for real-world event detectors. Such uncertainty in an event detector generates multiple branching possibilities on LTL instructions, confusing action decisions. Moreover, the queries to the uncertain event detector, necessary for the task's progress, may increase the uncertainty further. To cope with those issues, we propose an RL framework, Learning Action and Query over Belief LTL (LAQBL), to learn an agent that can consider the diversity of LTL instructions due to uncertain event detection while avoiding task failure due to the unnecessary event-detection query. Our framework simultaneously learns 1) an embedding of belief LTL, which is multiple branching possibilities on LTL instructions using a graph neural network, 2) an action policy, and 3) a query policy which decides whether or not to query for the event detector. Simulations in a 2D grid world and image-input robotic inspection environments show that our method successfully learns actions to follow LTL instructions even with uncertain event detectors.
This paper proposes a new multilinear projection method for dimension-reduction in modeling high-dimensional matrix-variate time series. It assumes that a $p_1\times p_2$ matrix-variate time series consists of a dynamically dependent, lower-dimensional matrix-variate factor process and a $p_1\times p_2$ matrix white noise series. Covariance matrix of the vectorized white noises assumes a Kronecker structure such that the row and column covariances of the noise all have diverging/spiked eigenvalues to accommodate the case of low signal-to-noise ratio often encountered in applications, such as in finance and economics. We use an iterative projection procedure to {reduce the dimensions and noise effects in estimating} front and back loading matrices and {to} obtain faster convergence rates than those of the traditional methods available in the literature. Furthermore, we introduce a two-way projected Principal Component Analysis to mitigate the diverging noise effects, and implement a high-dimensional white-noise testing procedure to estimate the dimension of the factor matrix. Asymptotic properties of the proposed method are established as the dimensions and sample size go to infinity. Simulated and real examples are used to assess the performance of the proposed method. We also compared the proposed method with some existing ones in the literature concerning the forecasting ability of the identified factors and found that the proposed approach fares well in out-of-sample forecasting.
Robotic manipulation tasks, such as object rearrangement, play a crucial role in enabling robots to interact with complex and arbitrary environments. Existing work focuses primarily on single-level rearrangement planning and, even if multiple levels exist, dependency relations among substructures are geometrically simpler, like tower stacking. We propose Structural Concept Learning (SCL), a deep learning approach that leverages graph attention networks to perform multi-level object rearrangement planning for scenes with structural dependency hierarchies. It is trained on a self-generated simulation data set with intuitive structures, works for unseen scenes with an arbitrary number of objects and higher complexity of structures, infers independent substructures to allow for task parallelization over multiple manipulators, and generalizes to the real world. We compare our method with a range of classical and model-based baselines to show that our method leverages its scene understanding to achieve better performance, flexibility, and efficiency. The dataset, supplementary details, videos, and code implementation are available at: //manavkulshrestha.github.io/scl
Video instance segmentation (VIS) is the task that requires simultaneously classifying, segmenting and tracking object instances of interest in video. Recent methods typically develop sophisticated pipelines to tackle this task. Here, we propose a new video instance segmentation framework built upon Transformers, termed VisTR, which views the VIS task as a direct end-to-end parallel sequence decoding/prediction problem. Given a video clip consisting of multiple image frames as input, VisTR outputs the sequence of masks for each instance in the video in order directly. At the core is a new, effective instance sequence matching and segmentation strategy, which supervises and segments instances at the sequence level as a whole. VisTR frames the instance segmentation and tracking in the same perspective of similarity learning, thus considerably simplifying the overall pipeline and is significantly different from existing approaches. Without bells and whistles, VisTR achieves the highest speed among all existing VIS models, and achieves the best result among methods using single model on the YouTube-VIS dataset. For the first time, we demonstrate a much simpler and faster video instance segmentation framework built upon Transformers, achieving competitive accuracy. We hope that VisTR can motivate future research for more video understanding tasks.
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use as a layer in neural networks trained by backpropagation. To address this issue, we propose to smooth the max operator in the dynamic programming recursion, using a strongly convex regularizer. This allows to relax both the optimal value and solution of the original combinatorial problem, and turns a broad class of DP algorithms into differentiable operators. Theoretically, we provide a new probabilistic perspective on backpropagating through these DP operators, and relate them to inference in graphical models. We derive two particular instantiations of our framework, a smoothed Viterbi algorithm for sequence prediction and a smoothed DTW algorithm for time-series alignment. We showcase these instantiations on two structured prediction tasks and on structured and sparse attention for neural machine translation.
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