Reasoning, the ability to logically draw conclusions from existing knowledge, is a hallmark of human. Together with perception, they constitute the two major themes of artificial intelligence. While deep learning has pushed the limit of perception beyond human-level performance, the progress in reasoning domains is way behind. One fundamental reason is that reasoning problems usually have flexible structures for both knowledge and queries, and many existing models only perform well on structures seen during training. Here we aim to push the boundary of reasoning models by devising algorithms that generalize across knowledge and query structures, as well as systems that accelerate development on structured data. This thesis consists of three parts. In Part I, we study models that can inductively generalize to unseen knowledge graphs with new entity and relation vocabularies. For new entities, we propose a framework that learns neural operators in a dynamic programming algorithm computing path representations. For relations, we construct a relation graph to capture the interactions between relations, thereby converting new relations into new entities. In Part II, we propose two solutions for generalizing across multi-step queries on knowledge graphs and text respectively. For knowledge graphs, we show that multi-step queries can be solved by multiple calls of graph neural networks and fuzzy logic operations. For text, we devise an algorithm to learn explicit knowledge as textual rules to improve large language models on multi-step queries. In Part III, we propose two systems to facilitate machine learning development on structured data. Our library treats structured data as first-class citizens and removes the barrier for developing algorithms on structured data. Our node embedding system solves the GPU memory bottleneck of embedding matrices and scales to graphs with billion nodes.

Current vision-language models (VLMs) still exhibit inferior performance on knowledge-intensive tasks, primarily due to the challenge of accurately encoding all the associations between visual objects and scenes to their corresponding entities and background knowledge. While retrieval augmentation methods offer an efficient way to integrate external knowledge, extending them to vision-language domain presents unique challenges in (1) precisely retrieving relevant information from external sources due to the inherent discrepancy within the multimodal queries, and (2) being resilient to the irrelevant, extraneous and noisy information contained in the retrieved multimodal knowledge snippets. In this work, we introduce RORA-VLM, a novel and robust retrieval augmentation framework specifically tailored for VLMs, with two key innovations: (1) a 2-stage retrieval process with image-anchored textual-query expansion to synergistically combine the visual and textual information in the query and retrieve the most relevant multimodal knowledge snippets; and (2) a robust retrieval augmentation method that strengthens the resilience of VLMs against irrelevant information in the retrieved multimodal knowledge by injecting adversarial noises into the retrieval-augmented training process, and filters out extraneous visual information, such as unrelated entities presented in images, via a query-oriented visual token refinement strategy. We conduct extensive experiments to validate the effectiveness and robustness of our proposed methods on three widely adopted benchmark datasets. Our results demonstrate that with a minimal amount of training instance, RORA-VLM enables the base model to achieve significant performance improvement and constantly outperform state-of-the-art retrieval-augmented VLMs on all benchmarks while also exhibiting a novel zero-shot domain transfer capability.

We study the \emph{secure} stochastic convex optimization problem: a learner aims to learn the optimal point of a convex function through sequentially querying a (stochastic) gradient oracle, in the meantime, there exists an adversary who aims to free-ride and infer the learning outcome of the learner from observing the learner's queries. The adversary observes only the points of the queries but not the feedback from the oracle. The goal of the learner is to optimize the accuracy, i.e., obtaining an accurate estimate of the optimal point, while securing her privacy, i.e., making it difficult for the adversary to infer the optimal point. We formally quantify this tradeoff between learner's accuracy and privacy and characterize the lower and upper bounds on the learner's query complexity as a function of desired levels of accuracy and privacy. For the analysis of lower bounds, we provide a general template based on information theoretical analysis and then tailor the template to several families of problems, including stochastic convex optimization and (noisy) binary search.

Suppose, we are given a set of n elements to be clustered into k (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, do two elements u and v belong to the same cluster?''. The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we provide a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and give strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix, which is used by an automated process to cluster similar points together. To improve accuracy of clustering, a fruitful approach in recent years has been to ask a domain expert or crowd to obtain labeled data interactively.

We study the query complexity of Bayesian Private Learning: a learner wishes to locate a random target within an interval by submitting queries, in the presence of an adversary who observes all of her queries but not the responses. How many queries are necessary and sufficient in order for the learner to accurately estimate the target, while simultaneously concealing the target from the adversary? Our main result is a query complexity lower bound that is tight up to the first order. We show that if the learner wants to estimate the target within an error of \epsilon, while ensuring that no adversary estimator can achieve a constant additive error with probability greater than 1/L, then the query complexity is on the order of L\log(1/\epsilon) as \epsilon \to 0 . Our result demonstrates that increased privacy, as captured by L, comes at the expense of a \emph{multiplicative} increase in query complexity.

Background. In the last decades, several life science resources have structured data using the same framework and made these accessible using the same query language to facilitate interoperability. Knowledge graphs have seen increased adoption in bioinformatics due to their advantages for representing data in a generic graph format. For example, yummydata.org catalogs more than 60 knowledge graphs accessible through SPARQL, a technical query language. Although SPARQL allows powerful, expressive queries, even across physically distributed knowledge graphs, formulating such queries is a challenge for most users. Therefore, to guide users in retrieving the relevant data, many of these resources provide representative examples. These examples can also be an important source of information for machine learning, if a sufficiently large number of examples are provided and published in a common, machine-readable and standardized format across different resources. Findings. We introduce a large collection of human-written natural language questions and their corresponding SPARQL queries over federated bioinformatics knowledge graphs (KGs) collected for several years across different research groups at the SIB Swiss Institute of Bioinformatics. The collection comprises more than 1000 example questions and queries, including 65 federated queries. We propose a methodology to uniformly represent the examples with minimal metadata, based on existing standards. Furthermore, we introduce an extensive set of open-source applications, including query graph visualizations and smart query editors, easily reusable by KG maintainers who adopt the proposed methodology. Conclusions. We encourage the community to adopt and extend the proposed methodology, towards richer KG metadata and improved Semantic Web services.

The authors obtain a tight fundamental limit of the query complexity using Fano's inequality, which is a standard tool for the lower bound analysis. The fundamental limit matches the query complexity of an upper bound algorithm (Replicated Bisection strategy) in the asymptotic order which is originally proposed in [11, 15]. The query complexity analysis shows a privacy-efficiency trade-off. The proof seems sound, and the paper is easy to follow.

We study the query complexity of Bayesian Private Learning: a learner wishes to locate a random target within an interval by submitting queries, in the presence of an adversary who observes all of her queries but not the responses. How many queries are necessary and sufficient in order for the learner to accurately estimate the target, while simultaneously concealing the target from the adversary? Our main result is a query complexity lower bound that is tight up to the first order. We show that if the learner wants to estimate the target within an error of, while ensuring that no adversary estimator can achieve a constant additive error with probability greater than 1/L, then the query complexity is on the order of L log(1/) as!

NOTE: I am reviewing two papers that appear to be by the same authors and on the same general topic. The other one is on noisy queries without any side information. This paper gives upper and lower bounds on the query complexity of clustering based on noiseless pairwise comparisons, along with random side-information associated with every pair. While I am familiar with some of the related literature, my knowledge of it is far from complete, so it's a little hard to fully judge the value of the contributions. The paper is also so dense that I couldn't spend as much time as ideal checking the correctness -- especially in the long upper bound proof.

Suppose, we are given a set of n elements to be clustered into k (unknown) clusters, and an oracle/expert labeler that can interactively answer pair-wise queries of the form, "do two elements u and v belong to the same cluster?". The goal is to recover the optimum clustering by asking the minimum number of queries. In this paper, we provide a rigorous theoretical study of this basic problem of query complexity of interactive clustering, and give strong information theoretic lower bounds, as well as nearly matching upper bounds. Most clustering problems come with a similarity matrix, which is used by an automated process to cluster similar points together. However, obtaining an ideal similarity function is extremely challenging due to ambiguity in data representation, poor data quality etc., and this is one of the primary reasons that makes clustering hard.