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In stochastic zeroth-order optimization, a problem of practical relevance is understanding how to fully exploit the local geometry of the underlying objective function. We consider a fundamental setting in which the objective function is quadratic, and provide the first tight characterization of the optimal Hessian-dependent sample complexity. Our contribution is twofold. First, from an information-theoretic point of view, we prove tight lower bounds on Hessian-dependent complexities by introducing a concept called energy allocation, which captures the interaction between the searching algorithm and the geometry of objective functions. A matching upper bound is obtained by solving the optimal energy spectrum. Then, algorithmically, we show the existence of a Hessian-independent algorithm that universally achieves the asymptotic optimal sample complexities for all Hessian instances. The optimal sample complexities achieved by our algorithm remain valid for heavy-tailed noise distributions, which are enabled by a truncation method.

Speakers tend to engage in adaptive behavior, known as entrainment, when they become similar to their interlocutor in various aspects of speaking. We present an unsupervised deep learning framework that derives meaningful representation from textual features for developing semantic entrainment. We investigate the model's performance by extracting features using different variations of the BERT model (DistilBERT and XLM-RoBERTa) and Google's universal sentence encoder (USE) embeddings on two human-human (HH) corpora (The Fisher Corpus English Part 1, Columbia games corpus) and one human-machine (HM) corpus (Voice Assistant Conversation Corpus (VACC)). In addition to semantic features we also trained DNN-based models utilizing two auditory embeddings (TRIpLet Loss network (TRILL) vectors, Low-level descriptors (LLD) features) and two units of analysis (Inter pausal unit and Turn). The results show that semantic entrainment can be assessed with our model, that models can distinguish between HH and HM interactions and that the two units of analysis for extracting acoustic features provide comparable findings.

The sliding cubes model is a well-established theoretical framework that supports the analysis of reconfiguration algorithms for modular robots consisting of face-connected cubes. The best algorithm currently known for the reconfiguration problem, by Abel and Kominers [arXiv, 2011], uses O(n3) moves to transform any n-cube configuration into any other n-cube configuration. As is common in the literature, this algorithm reconfigures the input into an intermediate canonical shape. In this paper we present an in-place algorithm that reconfigures any n-cube configuration into a compact canonical shape using a number of moves proportional to the sum of coordinates of the input cubes. This result is asymptotically optimal. Furthermore, our algorithm directly extends to dimensions higher than three.

Considering the challenges posed by the space and time complexities in handling extensive scientific volumetric data, various data representations have been developed for the analysis of large-scale scientific data. Multivariate functional approximation (MFA) is an innovative data model designed to tackle substantial challenges in scientific data analysis. It computes values and derivatives with high-order accuracy throughout the spatial domain, mitigating artifacts associated with zero- or first-order interpolation. However, the slow query time through MFA makes it less suitable for interactively visualizing a large MFA model. In this work, we develop the first scalable interactive volume visualization pipeline, MFA-DVV, for the MFA model encoded from large-scale datasets. Our method achieves low input latency through distributed architecture, and its performance can be further enhanced by utilizing a compressed MFA model while still maintaining a high-quality rendering result for scientific datasets. We conduct comprehensive experiments to show that MFA-DVV can decrease the input latency and achieve superior visualization results for big scientific data compared with existing approaches.

Lagrangian relaxation is a versatile mathematical technique employed to relax constraints in an optimization problem, enabling the generation of dual bounds to prove the optimality of feasible solutions and the design of efficient propagators in constraint programming (such as the weighted circuit constraint). However, the conventional process of deriving Lagrangian multipliers (e.g., using subgradient methods) is often computationally intensive, limiting its practicality for large-scale or time-sensitive problems. To address this challenge, we propose an innovative unsupervised learning approach that harnesses the capabilities of graph neural networks to exploit the problem structure, aiming to generate accurate Lagrangian multipliers efficiently. We apply this technique to the well-known Held-Karp Lagrangian relaxation for the travelling salesman problem. The core idea is to predict accurate Lagrangian multipliers and to employ them as a warm start for generating Held-Karp relaxation bounds. These bounds are subsequently utilized to enhance the filtering process carried out by branch-and-bound algorithms. In contrast to much of the existing literature, which primarily focuses on finding feasible solutions, our approach operates on the dual side, demonstrating that learning can also accelerate the proof of optimality. We conduct experiments across various distributions of the metric travelling salesman problem, considering instances with up to 200 cities. The results illustrate that our approach can improve the filtering level of the weighted circuit global constraint, reduce the optimality gap by a factor two for unsolved instances up to a timeout, and reduce the execution time for solved instances by 10%.

Meta-Bayesian optimisation (meta-BO) aims to improve the sample efficiency of Bayesian optimisation by leveraging data from related tasks. While previous methods successfully meta-learn either a surrogate model or an acquisition function independently, joint training of both components remains an open challenge. This paper proposes the first end-to-end differentiable meta-BO framework that generalises neural processes to learn acquisition functions via transformer architectures. We enable this end-to-end framework with reinforcement learning (RL) to tackle the lack of labelled acquisition data. Early on, we notice that training transformer-based neural processes from scratch with RL is challenging due to insufficient supervision, especially when rewards are sparse. We formalise this claim with a combinatorial analysis showing that the widely used notion of regret as a reward signal exhibits a logarithmic sparsity pattern in trajectory lengths. To tackle this problem, we augment the RL objective with an auxiliary task that guides part of the architecture to learn a valid probabilistic model as an inductive bias. We demonstrate that our method achieves state-of-the-art regret results against various baselines in experiments on standard hyperparameter optimisation tasks and also outperforms others in the real-world problems of mixed-integer programming tuning, antibody design, and logic synthesis for electronic design automation.

In knowledge discovery applications, the pattern set generated from data can be tremendously large and hard to explore by analysts. In the Formal Concept Analysis (FCA) framework, there have been studies to identify important formal concepts through the stability index and other quality measures. In this paper, we introduce the Base-Equivalent Conceptual Relevance (BECR) score, a novel conceptual relevance interestingness measure for improving the identification of actionable concepts. From a conceptual perspective, the base and equivalent attributes are considered meaningful information and are highly essential to maintain the conceptual structure of concepts. Thus, the basic idea of BECR is that the more base and equivalent attributes and minimal generators a concept intent has, the more relevant it is. As such, BECR quantifies these attributes and minimal generators per concept intent. Our preliminary experiments on synthetic and real-world datasets show the efficiency of BECR compared to the well-known stability index.

Generative models can serve as surrogates for some real data sources by creating synthetic training datasets, but in doing so they may transfer biases to downstream tasks. We focus on protecting quality and diversity when generating synthetic training datasets. We propose quality-diversity generative sampling (QDGS), a framework for sampling data uniformly across a user-defined measure space, despite the data coming from a biased generator. QDGS is a model-agnostic framework that uses prompt guidance to optimize a quality objective across measures of diversity for synthetically generated data, without fine-tuning the generative model. Using balanced synthetic datasets generated by QDGS, we first debias classifiers trained on color-biased shape datasets as a proof-of-concept. By applying QDGS to facial data synthesis, we prompt for desired semantic concepts, such as skin tone and age, to create an intersectional dataset with a combined blend of visual features. Leveraging this balanced data for training classifiers improves fairness while maintaining accuracy on facial recognition benchmarks. Code available at: //github.com/Cylumn/qd-generative-sampling

We study the problem of contextual feature selection, where the goal is to learn a predictive function while identifying subsets of informative features conditioned on specific contexts. Towards this goal, we generalize the recently proposed stochastic gates (STG) Yamada et al. [2020] by modeling the probabilistic gates as conditional Bernoulli variables whose parameters are predicted based on the contextual variables. Our new scheme, termed conditional-STG (c-STG), comprises two networks: a hypernetwork that establishes the mapping between contextual variables and probabilistic feature selection parameters and a prediction network that maps the selected feature to the response variable. Training the two networks simultaneously ensures the comprehensive incorporation of context and feature selection within a unified model. We provide a theoretical analysis to examine several properties of the proposed framework. Importantly, our model leads to improved flexibility and adaptability of feature selection and, therefore, can better capture the nuances and variations in the data. We apply c-STG to simulated and real-world datasets, including healthcare, housing, and neuroscience, and demonstrate that it effectively selects contextually meaningful features, thereby enhancing predictive performance and interpretability.

Cold-start problems are long-standing challenges for practical recommendations. Most existing recommendation algorithms rely on extensive observed data and are brittle to recommendation scenarios with few interactions. This paper addresses such problems using few-shot learning and meta learning. Our approach is based on the insight that having a good generalization from a few examples relies on both a generic model initialization and an effective strategy for adapting this model to newly arising tasks. To accomplish this, we combine the scenario-specific learning with a model-agnostic sequential meta-learning and unify them into an integrated end-to-end framework, namely Scenario-specific Sequential Meta learner (or s^2 meta). By doing so, our meta-learner produces a generic initial model through aggregating contextual information from a variety of prediction tasks while effectively adapting to specific tasks by leveraging learning-to-learn knowledge. Extensive experiments on various real-world datasets demonstrate that our proposed model can achieve significant gains over the state-of-the-arts for cold-start problems in online recommendation. Deployment is at the Guess You Like session, the front page of the Mobile Taobao.