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Rule learning approaches for knowledge graph completion are efficient, interpretable and competitive to purely neural models. The rule aggregation problem is concerned with finding one plausibility score for a candidate fact which was simultaneously predicted by multiple rules. Although the problem is ubiquitous, as data-driven rule learning can result in noisy and large rulesets, it is underrepresented in the literature and its theoretical foundations have not been studied before in this context. In this work, we demonstrate that existing aggregation approaches can be expressed as marginal inference operations over the predicting rules. In particular, we show that the common Max-aggregation strategy, which scores candidates based on the rule with the highest confidence, has a probabilistic interpretation. Finally, we propose an efficient and overlooked baseline which combines the previous strategies and is competitive to computationally more expensive approaches.

Defect detection aims to detect and localize regions out of the normal distribution.Previous approaches model normality and compare it with the input to identify defective regions, potentially limiting their generalizability.This paper proposes a one-stage framework that detects defective patterns directly without the modeling process.This ability is adopted through the joint efforts of three parties: a generative adversarial network (GAN), a newly proposed scaled pattern loss, and a dynamic masked cycle-consistent auxiliary network. Explicit information that could indicate the position of defects is intentionally excluded to avoid learning any direct mapping.Experimental results on the texture class of the challenging MVTec AD dataset show that the proposed method is 2.9% higher than the SOTA methods in F1-Score, while substantially outperforming SOTA methods in generalizability.

In previous literature, backward error analysis was used to find ordinary differential equations (ODEs) approximating the gradient descent trajectory. It was found that finite step sizes implicitly regularize solutions because terms appearing in the ODEs penalize the two-norm of the loss gradients. We prove that the existence of similar implicit regularization in RMSProp and Adam depends on their hyperparameters and the training stage, but with a different "norm" involved: the corresponding ODE terms either penalize the (perturbed) one-norm of the loss gradients or, on the contrary, hinder its decrease (the latter case being typical). We also conduct numerical experiments and discuss how the proven facts can influence generalization.

Efficient methods for the representation and simulation of quantum states and quantum operations are crucial for the optimization of quantum circuits. Decision diagrams (DDs), a well-studied data structure originally used to represent Boolean functions, have proven capable of capturing relevant aspects of quantum systems, but their limits are not well understood. In this work, we investigate and bridge the gap between existing DD-based structures and the stabilizer formalism, an important tool for simulating quantum circuits in the tractable regime. We first show that although DDs were suggested to succinctly represent important quantum states, they actually require exponential space for certain stabilizer states. To remedy this, we introduce a more powerful decision diagram variant, called Local Invertible Map-DD (LIMDD). We prove that the set of quantum states represented by poly-sized LIMDDs strictly contains the union of stabilizer states and other decision diagram variants. Finally, there exist circuits which LIMDDs can efficiently simulate, while their output states cannot be succinctly represented by two state-of-the-art simulation paradigms: the stabilizer decomposition techniques for Clifford + $T$ circuits and Matrix-Product States. By uniting two successful approaches, LIMDDs thus pave the way for fundamentally more powerful solutions for simulation and analysis of quantum computing.

In energy-efficient schemes, finding the optimal size of deep learning models is very important and has a broad impact. Meanwhile, recent studies have reported an unexpected phenomenon, the sparse double descent: as the model's sparsity increases, the performance first worsens, then improves, and finally deteriorates. Such a non-monotonic behavior raises serious questions about the optimal model's size to maintain high performance: the model needs to be sufficiently over-parametrized, but having too many parameters wastes training resources. In this paper, we aim to find the best trade-off efficiently. More precisely, we tackle the occurrence of the sparse double descent and present some solutions to avoid it. Firstly, we show that a simple $\ell_2$ regularization method can help to mitigate this phenomenon but sacrifices the performance/sparsity compromise. To overcome this problem, we then introduce a learning scheme in which distilling knowledge regularizes the student model. Supported by experimental results achieved using typical image classification setups, we show that this approach leads to the avoidance of such a phenomenon.

Open-World Object Detection (OWOD) extends object detection problem to a realistic and dynamic scenario, where a detection model is required to be capable of detecting both known and unknown objects and incrementally learning newly introduced knowledge. Current OWOD models, such as ORE and OW-DETR, focus on pseudo-labeling regions with high objectness scores as unknowns, whose performance relies heavily on the supervision of known objects. While they can detect the unknowns that exhibit similar features to the known objects, they suffer from a severe label bias problem that they tend to detect all regions (including unknown object regions) that are dissimilar to the known objects as part of the background. To eliminate the label bias, this paper proposes a novel approach that learns an unsupervised discriminative model to recognize true unknown objects from raw pseudo labels generated by unsupervised region proposal methods. The resulting model can be further refined by a classification-free self-training method which iteratively extends pseudo unknown objects to the unlabeled regions. Experimental results show that our method 1) significantly outperforms the prior SOTA in detecting unknown objects while maintaining competitive performance of detecting known object classes on the MS COCO dataset, and 2) achieves better generalization ability on the LVIS and Objects365 datasets.

We consider a statistical problem to estimate variables (effects) that are associated with the edges of a complete bipartite graph $K_{v_1, v_2}=(V_1, V_2 \, ; E)$. Each data is obtained as a sum of selected effects, a subset of $E$. In order to estimate efficiently, we propose a design called Spanning Bipartite Block Design (SBBD). For SBBDs such that the effects are estimable, we proved that the estimators have the same variance (variance balanced). If each block (a subgraph of $K_{v_1, v_2}$) of SBBD is a semi-regular or a regular bipartite graph, we show that the design is A-optimum. We also show a construction of SBBD using an ($r,\lambda$)-design and an ordered design. A BIBD with prime power blocks gives an A-optimum semi-regular or regular SBBD. At last, we mention that this SBBD is able to use for deep learning.

We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with iterative refinement with a factorization in half precision. We analyze the method as an inexact Newton method. This analysis shows that, except for very poorly conditioned Jacobians, the number of nonlinear iterations needed is the same that one would get if one stored and factored the Jacobian in double precision. In many ill-conditioned cases one can use the low precision factorization as a preconditioner for a GMRES iteration. That approach can recover fast convergence of the nonlinear iteration. We present an example to illustrate the results.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.

Knowledge graph completion aims to predict missing relations between entities in a knowledge graph. While many different methods have been proposed, there is a lack of a unifying framework that would lead to state-of-the-art results. Here we develop PathCon, a knowledge graph completion method that harnesses four novel insights to outperform existing methods. PathCon predicts relations between a pair of entities by: (1) Considering the Relational Context of each entity by capturing the relation types adjacent to the entity and modeled through a novel edge-based message passing scheme; (2) Considering the Relational Paths capturing all paths between the two entities; And, (3) adaptively integrating the Relational Context and Relational Path through a learnable attention mechanism. Importantly, (4) in contrast to conventional node-based representations, PathCon represents context and path only using the relation types, which makes it applicable in an inductive setting. Experimental results on knowledge graph benchmarks as well as our newly proposed dataset show that PathCon outperforms state-of-the-art knowledge graph completion methods by a large margin. Finally, PathCon is able to provide interpretable explanations by identifying relations that provide the context and paths that are important for a given predicted relation.