OpenRaiser/Intern-Atlas huggingface dataset:
On Low-rank Trace Regression under General Sampling Distribution
Venue: arXiv cs.LG 2023
Year: 2023

In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy near-optimal error bounds under assumptions on the rank, coherence, and spikiness of B*. We start by introducing a general notion of spikiness for B* that provides a generic recipe to prove the restricted strong convexity of the sampling operator of the trace regression and obtain near-optimal and non-asymptotic error bounds for the estimation error. Similar to the existing literature, these results require the regularization parameter to be above a certain theory-inspired threshold that depends on observation noise that may be unknown in practice. Next, we extend the error bounds to cases where the regularization parameter is chosen via cross-validation. This result is significant in that existing theoretical results on cross-validated estimators (Kale et al., 2011; Kumar et al., 2013; Abou-Moustafa and Szepesvari, 2017) do not apply to our setting since the estimators we study are not known to satisfy their required notion of stability. Finally, using simulations on synthetic and real data, we show that the cross-validated estimator selects a near-optimal penalty parameter and outperforms the theory-inspired approach of selecting the parameter.
TS Cache: A Fast Cache with Timing-speculation Mechanism Under Low Supply Voltages
Venue: arXiv cs.AR 2023
Year: 2023

To mitigate the ever-worsening Power Wall problem, more and more applications need to expand their power supply to the wide-voltage range including the near-threshold region. However, the read delay distribution of the SRAM cells under the near-threshold voltage shows a more serious long-tail characteristic than that under the nominal voltage due to the process fluctuation. Such degradation of SRAM delay makes the SRAM-based cache a performance bottleneck of systems as well. To avoid the unreliable data reading, circuit-level studies use larger/more transistors in a bitcell by scarifying chip area and the static power of cache arrays. Architectural studies propose the auxiliary error correction or block disabling/remapping methods in fault-tolerant caches, which worsen both the hit latency and energy efficiency due to the complex accessing logic. This paper proposes the Timing-Speculation (TS) cache to boost the cache frequency and improve energy efficiency under low supply voltages. In the TS cache, the voltage differences of bitlines are continuously evaluated twice by a sense amplifier (SA), and the access timing error can be detected much earlier than that in prior methods. According to the measurement results from the fabricated chips, the TS L1 cache aggressively increases its frequency to 1.62X and 1.92X compared with the conventional scheme at 0.5V and 0.6V supply voltages, respectively.
Optimal Sparse Decision Trees
Venue: arXiv cs.LG 2023
Year: 2023

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of optimality, or lack of guarantees of closeness to optimality: decision tree algorithms are often greedy or myopic, and sometimes produce unquestionably suboptimal models. Hardness of decision tree optimization is both a theoretical and practical obstacle, and even careful mathematical programming approaches have not been able to solve these problems efficiently. This work introduces the first practical algorithm for optimal decision trees for binary variables. The algorithm is a co-design of analytical bounds that reduce the search space and modern systems techniques, including data structures and a custom bit-vector library. Our experiments highlight advantages in scalability, speed, and proof of optimality. The code is available at https://github.com/xiyanghu/OSDT.
On a Certain NP-Complete Problem
Venue: arXiv cs.CC 2023
Year: 2023

We intend to create new concepts aimed at finding necessary and sufficient conditions for Boolean satisfiability so that these conditions can be verified in polynomial time. Based on these conditions it will be possible to create an algorithm that determines in polynomial time whether a given Boolean formula represented in conjunctive normal form is satisfiable. The work will consist of three articles. This is the first of a planned series of these articles. In this article we introduce the concept of special decomposition of a set and the concept of special covering for a set under such a decomposition. We formulate the decision problem of existance of a special covering for a set under a special decompostition of this set. In order to determine the complexity class in which this problem is located, we study the relationship between the sat CNF problem and the problem of existence of a special covering for a set under a special decomposition of this set. The article proves that the decidability of the sat CNF problem is polynomially reduced to the problem of the existence of a special covering for a set. It is also proved that the problem of existence of a special covering for a set is polynomially reduced to the decidability of the sat CNF problem. Therefore, the mentioned problems are polynomially equivalent. And then, the problem of existence of a special covering for a set is an NP-complete problem. The conditions for the existence of special coverings for a set under special decompositions of this set will be study in the next articles.
Deep Image Feature Learning with Fuzzy Rules
Venue: arXiv cs.CV 2023
Year: 2023

The methods of extracting image features are the key to many image processing tasks. At present, the most popular method is the deep neural network which can automatically extract robust features through end-to-end training instead of hand-crafted feature extraction. However, the deep neural network currently faces many challenges: 1) its effectiveness is heavily dependent on large datasets, so the computational complexity is very high; 2) it is usually regarded as a black box model with poor interpretability. To meet the above challenges, a more interpretable and scalable feature learning method, i.e., deep image feature learning with fuzzy rules (DIFL-FR), is proposed in the paper, which combines the rule-based fuzzy modeling technique and the deep stacked learning strategy. The method progressively learns image features through a layer-by-layer manner based on fuzzy rules, so the feature learning process can be better explained by the generated rules. More importantly, the learning process of the method is only based on forward propagation without back propagation and iterative learning, which results in the high learning efficiency. In addition, the method is under the settings of unsupervised learning and can be easily extended to scenes of supervised and semi-supervised learning. Extensive experiments are conducted on image datasets of different scales. The results obviously show the effectiveness of the proposed method.
Fast and Robust Rank Aggregation against Model Misspecification
Venue: arXiv cs.LG 2023
Year: 2023

In rank aggregation (RA), a collection of preferences from different users are summarized into a total order under the assumption of homogeneity of users. Model misspecification in RA arises since the homogeneity assumption fails to be satisfied in the complex real-world situation. Existing robust RAs usually resort to an augmentation of the ranking model to account for additional noises, where the collected preferences can be treated as a noisy perturbation of idealized preferences. Since the majority of robust RAs rely on certain perturbation assumptions, they cannot generalize well to agnostic noise-corrupted preferences in the real world. In this paper, we propose CoarsenRank, which possesses robustness against model misspecification. Specifically, the properties of our CoarsenRank are summarized as follows: (1) CoarsenRank is designed for mild model misspecification, which assumes there exist the ideal preferences (consistent with model assumption) that locates in a neighborhood of the actual preferences. (2) CoarsenRank then performs regular RAs over a neighborhood of the preferences instead of the original dataset directly. Therefore, CoarsenRank enjoys robustness against model misspecification within a neighborhood. (3) The neighborhood of the dataset is defined via their empirical data distributions. Further, we put an exponential prior on the unknown size of the neighborhood, and derive a much-simplified posterior formula for CoarsenRank under particular divergence measures. (4) CoarsenRank is further instantiated to Coarsened Thurstone, Coarsened Bradly-Terry, and Coarsened Plackett-Luce with three popular probability ranking models. Meanwhile, tractable optimization strategies are introduced with regards to each instantiation respectively. In the end, we apply CoarsenRank on four real-world datasets.
Relaxing Concurrent Data-structure Semantics for Increasing Performance: A Multi-structure 2D Design Framework
Venue: arXiv cs.DS 2023
Year: 2023

There has been a significant amount of work in the literature proposing semantic relaxation of concurrent data structures for improving scalability and performance. By relaxing the semantics of a data structure, a bigger design space, that allows weaker synchronization and more useful parallelism, is unveiled. Investigating new data structure designs, capable of trading semantics for achieving better performance in a monotonic way, is a major challenge in the area. We algorithmically address this challenge in this paper.To address this challenge, we present an efficient lock-free, concurrent data structure design framework for out-of-order semantic relaxation. Our framework introduces a new two dimensional algorithmic design, that uses multiple instances of an implementation of the given data structure. The first dimension of our design is the number of data structure instances onto which operations are spread to, in order to achieve increased parallelism through disjoint memory accesses. The second dimension is the number of consecutive operations of a single thread that can stay at the same data structure instance in order to benefit from data locality. Our design can flexibly explore this two-dimensional space to achieve the property of monotonically increasing throughput performance via relaxing concurrent data structure semantics within a tight deterministic relaxation bound, as we prove in the paper. We show how our framework can instantiate lock-free out-of-order queues, stacks, counters and dequeues. The experimental evaluation shows that our two-dimensional data structures: i) significantly outperform the respected previous proposed ones with respect to scalability and throughput performance and ii) monotonically increase throughput as relaxation increases.
Randomized Exploration in Generalized Linear Bandits
Venue: arXiv cs.LG 2023
Year: 2023

We study two randomized algorithms for generalized linear bandits. The first, GLM-TSL, samples a generalized linear model (GLM) from the Laplace approximation to the posterior distribution. The second, GLM-FPL, fits a GLM to a randomly perturbed history of past rewards. We analyze both algorithms and derive $\tilde{O}(d \sqrt{n \log K})$ upper bounds on their $n$-round regret, where $d$ is the number of features and $K$ is the number of arms. The former improves on prior work while the latter is the first for Gaussian noise perturbations in non-linear models. We empirically evaluate both GLM-TSL and GLM-FPL in logistic bandits, and apply GLM-FPL to neural network bandits. Our work showcases the role of randomization, beyond posterior sampling, in exploration.
Neural Proximal/Trust Region Policy Optimization Attains Globally Optimal Policy
Venue: arXiv cs.LG 2023
Year: 2023

Proximal policy optimization and trust region policy optimization (PPO and TRPO) with actor and critic parametrized by neural networks achieve significant empirical success in deep reinforcement learning. However, due to nonconvexity, the global convergence of PPO and TRPO remains less understood, which separates theory from practice. In this paper, we prove that a variant of PPO and TRPO equipped with overparametrized neural networks converges to the globally optimal policy at a sublinear rate. The key to our analysis is the global convergence of infinite-dimensional mirror descent under a notion of one-point monotonicity, where the gradient and iterate are instantiated by neural networks. In particular, the desirable representation power and optimization geometry induced by the overparametrization of such neural networks allow them to accurately approximate the infinite-dimensional gradient and iterate.
Secure Summation via Subset Sums: A New Primitive for Privacy-Preserving Distributed Machine Learning
Venue: arXiv cs.CR 2023
Year: 2023

For population studies or for the training of complex machine learning models, it is often required to gather data from different actors. In these applications, summation is an important primitive: for computing means, counts or mini-batch gradients. In many cases, the data is privacy-sensitive and therefore cannot be collected on a central server. Hence the summation needs to be performed in a distributed and privacy-preserving way. Existing solutions for distributed summation with computational privacy guarantees make trust or connection assumptions - e.g., the existence of a trusted server or peer-to-peer connections between clients - that might not be fulfilled in real world settings. Motivated by these challenges, we propose Secure Summation via Subset Sums (S5), a method for distributed summation that works in the presence of a malicious server and only two honest clients, and without the need for peer-to-peer connections between clients. S5 adds zero-sum noise to clients' messages and shuffles them before sending them to the aggregating server. Our main contribution is a proof that this scheme yields a computational privacy guarantee based on the multidimensional subset sum problem. Our analysis of this problem may be of independent interest for other privacy and cryptography applications.
How to Staff When Customers Arrive in Batches
Venue: arXiv cs.PF 2023
Year: 2023

In many different settings, requests for service can arrive in near or true simultaneity with one another. This creates batches of arrivals to the underlying queueing system. In this paper, we study the staffing problem for the batch arrival queue. We show that batches place a dangerous and deceptive stress on services, requiring a high amount of resources and exhibiting a fundamentally larger tail in those demands. This uncovers a service regime in which a system with large batch arrivals may have low utilization but will still have non-trivial waiting. Methodologically, these staffing results follow from novel large batch and large batch-and-rate limits of the multi-server queueing model. In the large batch limit, we establish the first formal connection between general multi-server queues and storage processes, another family of stochastic models. By consequence, we show that the batch scaled queue length process is not asymptotically normal, and that, in fact, the fluid and diffusion-type limits coincide. Hence, the (safety) staffing of this system must be directly proportional to the batch size just to achieve a non-degenerate probability of wait. In exhibition of the existence and insights of this large batch regime, we apply our results to data on Covid-19 contact tracing in New York City. In doing so, we identify significant benefits produced by the tracing agency's decision to staff above national recommendations, and we also demonstrate that there may have been an opportunity to further improve the operation by optimizing the arrival pattern in the public health data pipeline.
Offensive Language and Hate Speech Detection for Danish
Venue: arXiv cs.CL 2023
Year: 2023

The presence of offensive language on social media platforms and the implications this poses is becoming a major concern in modern society. Given the enormous amount of content created every day, automatic methods are required to detect and deal with this type of content. Until now, most of the research has focused on solving the problem for the English language, while the problem is multilingual. We construct a Danish dataset containing user-generated comments from \textit{Reddit} and \textit{Facebook}. It contains user generated comments from various social media platforms, and to our knowledge, it is the first of its kind. Our dataset is annotated to capture various types and target of offensive language. We develop four automatic classification systems, each designed to work for both the English and the Danish language. In the detection of offensive language in English, the best performing system achieves a macro averaged F1-score of $0.74$, and the best performing system for Danish achieves a macro averaged F1-score of $0.70$. In the detection of whether or not an offensive post is targeted, the best performing system for English achieves a macro averaged F1-score of $0.62$, while the best performing system for Danish achieves a macro averaged F1-score of $0.73$. Finally, in the detection of the target type in a targeted offensive post, the best performing system for English achieves a macro averaged F1-score of $0.56$, and the best performing system for Danish achieves a macro averaged F1-score of $0.63$. Our work for both the English and the Danish language captures the type and targets of offensive language, and present automatic methods for detecting different kinds of offensive language such as hate speech and cyberbullying.
VST-A: A Foundationally Sound Annotation Verifier
Venue: arXiv cs.PL 2023
Year: 2023

Program verifiers for imperative languages such as C may be annotation-based, in which assertions and invariants are put into source files and then checked, or tactic-based, where proof scripts separate from programs are interactively developed in a proof assistant such as Coq. Annotation verifiers have been more automated and convenient, but some interactive verifiers have richer assertion languages and formal proofs of soundness. We present VST-A, an annotation verifier that uses the rich assertion language of VST, leverages the formal soundness proof of VST, but allows users to describe functional correctness proofs intuitively by inserting assertions. VST-A analyzes control flow graphs, decomposes every C function into control flow paths between assertions, and reduces program verification problems into corresponding straightline Hoare triples. Compared to existing foundational program verification tools like VST and Iris, in VST-A, such decompositions and reductions are allowed to be nonstructural, which makes VST-A more flexible to use. VST-A's decomposition and reduction is defined in Coq, proved sound in Coq, and computed in a call-by-value way in Coq. The soundness proof for reduction is totally logical, independent of the complicated semantic model (and soundness proof) of VST's Hoare triple. Because of the rich assertion language, not all reduced proof goals can be automatically checked, but the system allows users to prove residual proof goals using the full power of the Coq proof assistant.
MANAS: Multi-Agent Neural Architecture Search
Venue: arXiv cs.CV 2023
Year: 2023

The Neural Architecture Search (NAS) problem is typically formulated as a graph search problem where the goal is to learn the optimal operations over edges in order to maximise a graph-level global objective. Due to the large architecture parameter space, efficiency is a key bottleneck preventing NAS from its practical use. In this paper, we address the issue by framing NAS as a multi-agent problem where agents control a subset of the network and coordinate to reach optimal architectures. We provide two distinct lightweight implementations, with reduced memory requirements (1/8th of state-of-the-art), and performances above those of much more computationally expensive methods. Theoretically, we demonstrate vanishing regrets of the form O(sqrt(T)), with T being the total number of rounds. Finally, aware that random search is an, often ignored, effective baseline we perform additional experiments on 3 alternative datasets and 2 network configurations, and achieve favourable results in comparison.
Learning Graphs from Linear Measurements: Fundamental Trade-offs and Applications
Venue: arXiv cs.IT 2023
Year: 2023

We consider a specific graph learning task: reconstructing a symmetric matrix that represents an underlying graph using linear measurements. We present a sparsity characterization for distributions of random graphs (that are allowed to contain high-degree nodes), based on which we study fundamental trade-offs between the number of measurements, the complexity of the graph class, and the probability of error. We first derive a necessary condition on the number of measurements. Then, by considering a three-stage recovery scheme, we give a sufficient condition for recovery. Furthermore, assuming the measurements are Gaussian IID, we prove upper and lower bounds on the (worst-case) sample complexity for both noisy and noiseless recovery. In the special cases of the uniform distribution on trees with n nodes and the Erdos-Renyi (n,p) class, the fundamental trade-offs are tight up to multiplicative factors with noiseless measurements. In addition, for practical applications, we design and implement a polynomial-time (in n) algorithm based on the three-stage recovery scheme. Experiments show that the heuristic algorithm outperforms basis pursuit on star graphs. We apply the heuristic algorithm to learn admittance matrices in electric grids. Simulations for several canonical graph classes and IEEE power system test cases demonstrate the effectiveness and robustness of the proposed algorithm for parameter reconstruction.
Optimization Based Motion Planning for Multi-Limbed Vertical Climbing Robots
Venue: arXiv cs.RO 2023
Year: 2023

Motion planning trajectories for a multi-limbed robot to climb up walls requires a unique combination of constraints on torque, contact force, and posture. This paper focuses on motion planning for one particular setup wherein a six-legged robot braces itself between two vertical walls and climbs vertically with end effectors that only use friction. Instead of motion planning with a single nonlinear programming (NLP) solver, we decoupled the problem into two parts with distinct physical meaning: torso postures and contact forces. The first part can be formulated as either a mixed-integer convex programming (MICP) or NLP problem, while the second part is formulated as a series of standard convex optimization problems. Variants of the two wall climbing problem e.g., obstacle avoidance, uneven surfaces, and angled walls, help verify the proposed method in simulation and experimentation.