In anytime-valid sequential inference, it is known that any admissible procedure must be based on e-processes, which are composite generalizations of test martingales that quantify the accumulated evidence against a composite null hypothesis at any arbitrary stopping time. This paper studies methods for combining e-processes constructed using different information sets (filtrations) for the same null. Although e-processes constructed in the same filtration can be combined effortlessly (e.g., by averaging), e-processes constructed in different filtrations cannot, because their validity in a coarser filtration does not translate to validity in a finer filtration. This issue arises in exchangeability tests, independence tests, and tests for comparing forecasts with lags. We first establish that a class of functions called adjusters allows us to lift e-processes from a coarser filtration into any finer filtration. We then introduce a characterization theorem for adjusters, formalizing a sense in which using adjusters is necessary. There are two major implications. First, if we have a powerful e-process in a coarsened filtration, then we readily have a powerful e-process in the original filtration. Second, when we coarsen the filtration to construct an e-process, there is an asymptotically logarithmic cost of recovering anytime-validity in the original filtration.
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We consider the private set union (PSU) problem, where two parties each hold a private set of elements, and they want one of the parties (the receiver) to learn the union of the two sets and nothing else. Our protocols are targeted for the unbalanced case where the receiver's set size is larger than the sender's set size, with the goal of minimizing the costs for the sender both in terms of communication volume and local computation time. This setting is motivated by applications where the receiver has significantly more data (input set size) and computational resources than the sender which might be realized on a small, low-power device. Asymptotically, we achieve communication cost linear in the sender's (smaller) set size, and computation costs for sender and receiver which are nearly-linear in their respective set sizes. To our knowledge, ours is the first algorithm to achieve nearly-linear communication and computation for PSU in this unbalanced setting. Our protocols utilize fully homomorphic encryption (FHE) and, optionally, linearly homomorphic encryption (LHE) to perform the necessary computations while preserving privacy. The underlying computations are based on univariate polynomial arithmetic realized within homomorphic encryption, namely fast multiplication, modular reduction, and multi-point evaluation. These asymptotically fast HE polynomial arithmetic algorithms may be of independent interest.
In the noisy intermediate-scale quantum era, scientists are trying to improve the entanglement swapping success rate by researching anti-noise technology on the physical level, thereby obtaining a higher generation rate of long-distance entanglement. However, we may improve the generation rate from another perspective, which is studying an efficient entanglement swapping strategy. This paper analyzes the challenges faced by existing entanglement swapping strategies, including the node allocation principle, time synchronization, and processing of entanglement swapping failure. We present Parallel Segment Entanglement Swapping (PSES) to solve these problems. The core idea of PSES is to segment the path and perform parallel entanglement swapping between segments to improve the generation rate of long-distance entanglement. We construct a tree-like model as the carrier of PSES and propose heuristic algorithms called Layer Greedy and Segment Greedy to transform the path into a tree-like model. Moreover, we realize the time synchronization and design the on-demand retransmission mechanism to process entanglement swapping failure. The experiments show that PSES performs superiorly to other entanglement swapping strategies, and the on-demand retransmission mechanism can reduce the average entanglement swapping time by 80% and the average entanglement consumption by 80%.
Conditional computing processes an input using only part of the neural network's computational units. Learning to execute parts of a deep convolutional network by routing individual samples has several advantages: Reducing the computational burden is an obvious advantage. Furthermore, if similar classes are routed to the same path, that part of the network learns to discriminate between finer differences and better classification accuracies can be attained with fewer parameters. Recently, several papers have exploited this idea to take a particular child of a node in a tree-shaped network or to skip parts of a network. In this work, we follow a Trellis-based approach for generating specific execution paths in a deep convolutional neural network. We have designed routing mechanisms that use differentiable information gain-based cost functions to determine which subset of features in a convolutional layer will be executed. We call our method Conditional Information Gain Trellis (CIGT). We show that our conditional execution mechanism achieves comparable or better model performance compared to unconditional baselines, using only a fraction of the computational resources.
We introduce a new notion of stability--which we call stable list decoding--and demonstrate its applicability in designing differentially private density estimators. This definition is weaker than global stability [ABLMM22] and is related to the notions of replicability [ILPS22] and list replicability [CMY23]. We show that if a class of distributions is stable list decodable, then it can be learned privately in the agnostic setting. As the main application of our framework, we prove the first upper bound on the sample complexity of private density estimation for Gaussian Mixture Models in the agnostic setting, extending the realizable result of Afzali et al. [AAL24].
Protecting personal data about individuals, such as event traces in process mining, is an inherently difficult task: an event trace leaks information about the path in a process model that an individual has triggered. Yet, prior anonymization methods of event traces like k-anonymity or event log sanitization struggled to protect against such leakage, in particular against adversaries with sufficient background knowledge. In this work, we provide a method that tackles the challenge of summarizing sensitive event traces by learning the underlying process tree in a privacy-preserving manner. We prove via the so-called Differential Privacy (DP) property that from the resulting summaries no useful inference can be drawn about any personal data in an event trace. On the technical side, we introduce a differentially private approximation (DPIM) of the Inductive Miner. Experimentally, we compare our DPIM with the Inductive Miner on 8 real-world event traces by evaluating well-known metrics: fitness, precision, simplicity, and generalization. The experiments show that our DPIM not only protects personal data but also generates faithful process trees that exhibit little utility loss above the Inductive Miner.
Modern cyber-physical systems are becoming increasingly complex to model, thus motivating data-driven techniques such as reinforcement learning (RL) to find appropriate control agents. However, most systems are subject to hard constraints such as safety or operational bounds. Typically, to learn to satisfy these constraints, the agent must violate them systematically, which is computationally prohibitive in most systems. Recent efforts aim to utilize feasibility models that assess whether a proposed action is feasible to avoid applying the agent's infeasible action proposals to the system. However, these efforts focus on guaranteeing constraint satisfaction rather than the agent's learning efficiency. To improve the learning process, we introduce action mapping, a novel approach that divides the learning process into two steps: first learn feasibility and subsequently, the objective by mapping actions into the sets of feasible actions. This paper focuses on the feasibility part by learning to generate all feasible actions through self-supervised querying of the feasibility model. We train the agent by formulating the problem as a distribution matching problem and deriving gradient estimators for different divergences. Through an illustrative example, a robotic path planning scenario, and a robotic grasping simulation, we demonstrate the agent's proficiency in generating actions across disconnected feasible action sets. By addressing the feasibility step, this paper makes it possible to focus future work on the objective part of action mapping, paving the way for an RL framework that is both safe and efficient.
Most curriculum learning methods require an approach to sort the data samples by difficulty, which is often cumbersome to perform. In this work, we propose a novel curriculum learning approach termed Learning Rate Curriculum (LeRaC), which leverages the use of a different learning rate for each layer of a neural network to create a data-agnostic curriculum during the initial training epochs. More specifically, LeRaC assigns higher learning rates to neural layers closer to the input, gradually decreasing the learning rates as the layers are placed farther away from the input. The learning rates increase at various paces during the first training iterations, until they all reach the same value. From this point on, the neural model is trained as usual. This creates a model-level curriculum learning strategy that does not require sorting the examples by difficulty and is compatible with any neural network, generating higher performance levels regardless of the architecture. We conduct comprehensive experiments on 12 data sets from the computer vision (CIFAR-10, CIFAR-100, Tiny ImageNet, ImageNet-200, Food-101, UTKFace, PASCAL VOC), language (BoolQ, QNLI, RTE) and audio (ESC-50, CREMA-D) domains, considering various convolutional (ResNet-18, Wide-ResNet-50, DenseNet-121, YOLOv5), recurrent (LSTM) and transformer (CvT, BERT, SepTr) architectures. We compare our approach with the conventional training regime, as well as with Curriculum by Smoothing (CBS), a state-of-the-art data-agnostic curriculum learning approach. Unlike CBS, our performance improvements over the standard training regime are consistent across all data sets and models. Furthermore, we significantly surpass CBS in terms of training time (there is no additional cost over the standard training regime for LeRaC). Our code is freely available at: //github.com/CroitoruAlin/LeRaC.
Recently, a considerable literature has grown up around the theme of Graph Convolutional Network (GCN). How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly propagating and updating the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the Knowledge Embedding based Graph Convolutional Network (KE-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge embedding (a.k.a. knowledge graph embedding) methods, and goes beyond. Our theoretical analysis shows that KE-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of KE-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.
We introduce an approach for deep reinforcement learning (RL) that improves upon the efficiency, generalization capacity, and interpretability of conventional approaches through structured perception and relational reasoning. It uses self-attention to iteratively reason about the relations between entities in a scene and to guide a model-free policy. Our results show that in a novel navigation and planning task called Box-World, our agent finds interpretable solutions that improve upon baselines in terms of sample complexity, ability to generalize to more complex scenes than experienced during training, and overall performance. In the StarCraft II Learning Environment, our agent achieves state-of-the-art performance on six mini-games -- surpassing human grandmaster performance on four. By considering architectural inductive biases, our work opens new directions for overcoming important, but stubborn, challenges in deep RL.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
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