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Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from fuzzy or real-valued logic that are parameter-free thus diminishing their capacity to fit the data, other approaches are only loosely based on logic making it difficult to interpret the learned ``rules&quot;. In this paper, we propose learning rules with the recently proposed logical neural networks (LNN). Compared to others, LNNs offer a strong connection to classical Boolean logic thus allowing for precise interpretation of learned rules while harboring parameters that can be trained with gradient-based optimization to effectively fit the data. We extend LNNs to induce rules in first-order logic. Our experiments on standard benchmarking tasks confirm that LNN rules are highly interpretable and can achieve comparable or higher accuracy due to their flexible parameterization.

AAAI 2022

Neuro-Symbolic Inductive Logic Programming with Logical Neural Networks

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ACL-IJCNLP 2021

The great event is jointly organized by the Association for Computational Linguistics (ACL) and Asian Federation of Natural Language Processing (AFNLP).

Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from fuzzy or real-valued logic that are parameter-free thus diminishing their capacity to fit the data, other approaches are only loosely based on logic making it difficult to interpret the learned ``rules". In this paper, we propose learning rules with the recently proposed logical neural networks (LNN). Compared to others, LNNs offer a strong connection to classical Boolean logic thus allowing for precise interpretation of learned rules while harboring parameters that can be trained with gradient-based optimization to effectively fit the data. We extend LNNs to induce rules in first-order logic. Our experiments on standard benchmarking tasks confirm that LNN rules are highly interpretable and can achieve comparable or higher accuracy due to their flexible parameterization.

technical paper

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

The Cumulative constraint greatly contributes to the success of constraint programming at solving scheduling problems. The SoftCumulative, a version of the Cumulative where overloading the resource incurs a penalty is, however, less studied. We introduce a checker and a filtering algorithm for the SoftCumulative, which are inspired by the powerful energetic reasoning rule for the Cumulative. Both algorithms can be used with classic linear penalty function, but also with a quadratic penalty function, where the penalty of overloading the resource increases quadratically with the amount of the overload. We show that these algorithms are more general than existing algorithms and vastly outperform a decomposition of the SoftCumulative in practice.

The SoftCumulative Constraint with Quadratic Penalty

We study single-item single-unit Bayesian posted price auctions, where buyers arrive sequentially and their valuations for the item being sold depend on a random, unknown state of nature. The seller has complete knowledge of the actual state and can send signals to the buyers so as to disclose information about it. For instance, the state of nature may reflect the condition and/or some particular features of the item, which are known to the seller only. The problem faced by the seller is about how to partially disclose information about the state so as to maximize revenue. Unlike classical signaling problems, in this setting, the seller must also correlate the signals being sent to the buyers with some price proposals for them. This introduces additional challenges compared to standard settings. We consider two cases: the one where the seller can only send signals publicly visible to all buyers, and the case in which the seller can privately send a different signal to each buyer. As a first step, we prove that, in both settings, the problem of maximizing the seller's revenue does not admit an FPTAS unless P=NP, even for basic instances with a single buyer. As a result, in the rest of the paper, we focus on designing PTASs. In order to do so, we first introduce a unifying framework encompassing both public and private signaling, whose core result is a decomposition lemma that allows focusing on a finite set of possible buyers' posteriors. This forms the basis on which our PTASs are developed. In particular, in the public signaling setting, our PTAS employs some ad hoc techniques based on linear programming, while our PTAS for the private setting relies on the ellipsoid method to solve an exponentially-sized LP in polynomial time. In the latter case, we need a custom approximate separation oracle, which we implement with a dynamic programming approach.

Signaling in Posted Price Auctions

Dynamic Vision Sensor (DVS) can asynchronously output the events reflecting apparent motion of objects with microsecond resolution, and shows great application potential in monitoring and other fields. However, the output event stream of existing DVS inevitably contains background activity noise (BA noise) due to dark current and junction leakage current, which will affect the temporal correlation of objects, resulting in deteriorated motion estimation performance. Particularly, the existing filter-based denoising methods cannot be directly applied to suppress the noise in event stream, since there is no spatial correlation. To address this issue, this paper presents a novel progressive framework, in which a Motion Estimation (ME) module and an Event Denoising (ED) module are jointly optimized in a mutually reinforced manner. Specifically, based on the maximum sharpness criterion, ME module divides the input event into several segments by adaptive clustering in a motion compensating warp field, and captures the temporal correlation of event stream according to the clustered motion parameters. Taking temporal correlation as guidance, ED module calculates the confidence that each event belongs to real activity events, and transmits it to ME module to update energy function of motion segmentation for noise suppression. The two steps are iteratively updated until stable motion segmentation results are obtained. Extensive experimental results on both synthetic and real datasets demonstrate the superiority of our proposed approaches against the State-Of-The-Art (SOTA) methods.

ProgressiveMotionSeg: Mutually Reinforced Framework for Event-Based Motion Segmentation

We study a multi-leader single-follower congestion game where multiple users (leaders) choose one resource out of a set of resources and, after observing the realized loads, an adversary (single-follower) attacks the resources with maximum loads causing additional costs for the leaders. For the resulting strategic game among the leaders, we show that pure Nash equilibria fail to exist and therefore, we consider approximate equilibria instead.
 
 As our first main result, we show that the existence of a K-approximate equilibrium can always be guaranteed, where K (approximately equal to 1.1974) is the unique solution of a cubic polynomial equation. To this end, we give a polynomial time combinatorial algorithm which computes a K-approximate equilibrium. The factor K is tight, meaning that there is an instance that does not admit an A-approximate equilibrium for any A < K. Thus A = K is the smallest possible value of A such that the existence of an A-approximate equilibrium can be guaranteed for any instance of the considered game. 
 
 Secondly, we focus on approximate equilibria of a given fixed instance. We show how to compute efficiently a best approximate equilibrium, that is, with smallest possible A among all A-approximate equilibria of the given instance.

Multi-Leader Congestion Games with an Adversary

In point cloud compression, sufficient contexts are significant for modeling the point cloud distribution. However, the contexts gathered by the previous voxel-based methods decrease when handling sparse point clouds. To address this problem, we propose a multiple-contexts deep learning framework called OctAttention employing the octree structure, a memory-efficient representation for point clouds. Our approach encodes octree symbol sequences in a lossless way by gathering the information of sibling and ancestor nodes. Expressly, we first represent point clouds with octree to reduce spatial redundancy, which is robust for point clouds with different resolutions. We then design a conditional entropy model with a large receptive field that models the sibling and ancestor contexts to exploit the strong dependency among the neighboring nodes and employ an attention mechanism to emphasize the correlated nodes in the context. Furthermore, we introduce a mask operation during training and testing to make a trade-off between encoding time and performance. Compared to the previous state-of-the-art works, our approach obtains a 10%-35% BD-Rate gain on the LiDAR benchmark (e.g. SemanticKITTI) and object point cloud dataset (e.g. MPEG 8i, MVUB), and saves 95% coding time compared to the voxel-based baseline. The code is available at https://github.com/zb12138/OctAttention.

OctAttention: Octree-Based Large-Scale Contexts Model for Point Cloud Compression

Oversubscription planning (OSP) is the problem of finding plans that maximize the utility value of their end state while staying within a specified cost bound. Recently, it has been shown that OSP problems can be reformulated as classical planning problems with multiple cost functions but no utilities. Here we take advantage of this reformulation to show that OSP problems can be solved optimally using the A* search algorithm, in contrast to previous approaches that have used variations on branch-and-bound search. This allows many powerful techniques developed for classical planning to be applied to OSP problems. We also introduce novel bound-sensitive heuristics, which are able to reason about the primary cost of a solution while taking into account secondary cost functions and bounds, to provide superior guidance compared to heuristics that do not take these bounds into account. We propose two such bound-sensitive variants of existing classical planning heuristics, and show experimentally that the resulting search is significantly more informed than with comparable heuristics that do not consider bounds.

A* Search and Bound-Sensitive Heuristics for Oversubscription Planning

Variational Autoencoders (VAEs) suffer from degenerated performance, when learning several successive tasks. This is caused by catastrophic forgetting. In order to address the knowledge loss, VAEs are using either Generative Replay (GR) mechanisms or Expanding Network Architectures (ENA). In this paper we study the forgetting behaviour of VAEs using a joint GR and ENA methodology, by deriving an upper bound on the negative marginal log-likelihood. This theoretical analysis provides new insights into how VAEs forget the previously learnt knowledge during lifelong learning. The analysis indicates the best performance achieved when considering model mixtures, under the ENA framework, where there are no restrictions on the number of components. However, an ENA-based approach may require an excessive number of parameters. This motivates us to propose a novel Dynamic Expansion Graph Model (DEGM). DEGM expands its architecture, according to the novelty associated with each new database, when compared to the information already learnt by the network from previous tasks. DEGM training optimizes knowledge structuring, characterizing the joint probabilistic representations corresponding to the past and more recently learned tasks. We demonstrate that DEGM guarantees optimal performance for each task while also minimizing the required number of parameters.

Lifelong Generative Modelling Using Dynamic Expansion Graph Model

Parameter-free stochastic gradient descent (PFSGD) algorithms do not require setting learning rates while achieving optimal theoretical performance. In practical applications, however, there remains an empirical gap between tuned stochastic gradient descent (SGD) and PFSGD. In this paper, we close the empirical gap with a new parameter-free algorithm based on continuous-time Coin-Betting on truncated models. The new update is derived through the solution of an Ordinary Differential Equation (ODE) and solved in a closed form. We show empirically that this new parameter-free algorithm outperforms algorithms with the ``best default'' learning rates and almost matches the performance of finely tuned baselines without anything to tune.

Better Parameter-Free Stochastic Optimization with ODE Updates for Coin-Betting

A promising trend in deep learning replaces traditional feedforward networks with implicit networks. Unlike traditional networks, implicit networks solve a fixed point equation to compute inferences. Solving for the fixed point varies in complexity, depending on provided data and an error tolerance. Importantly, implicit networks may be trained with fixed memory costs in stark contrast to feedforward networks, whose memory requirements scale linearly with depth. However, there is no free
 lunch --- backpropagation through implicit networks often requires solving a costly Jacobian-based equation arising from the implicit function theorem. We propose Jacobian-Free Backpropagation (JFB), a fixed-memory approach that circumvents the need to solve Jacobian-based equations. JFB makes implicit networks faster to train and significantly easier to implement, without sacrificing test accuracy. Our experiments show implicit networks trained with JFB are competitive with feedforward networks and prior implicit networks given the same number of parameters.

JFB: Jacobian-Free Backpropagation for Implicit Networks

Accelerated gradient methods are the cornerstones of large-scale, data-driven optimization problems that arise naturally in machine learning and other fields concerning data analysis. We introduce a gradient-based optimization framework for achieving acceleration, based on the recently introduced notion of fixed-time stability of dynamical systems. The method presents itself as a generalization of simple gradient-based methods suitably scaled to achieve convergence to the optimizer in a fixed-time, independent of the initialization. We achieve this by first leveraging a continuous-time framework for designing fixed-time stable dynamical systems, and later providing a consistent discretization strategy, such that the equivalent discrete-time algorithm tracks the optimizer in a practically fixed number of iterations. We also provide a theoretical analysis of the convergence behavior of the proposed gradient flows, and their robustness to additive disturbances for a range of functions obeying strong convexity, strict convexity, and possibly nonconvexity but satisfying the Polyak-Åojasiewicz inequality. We also show that the regret bound on the convergence rate is constant by virtue of the fixed-time convergence. The hyperparameters have intuitive interpretations and can be tuned to fit the requirements on the desired convergence rates. We validate the accelerated convergence properties of the proposed schemes on a range of numerical examples against the state-of-the-art optimization algorithms. Our work provides insights on developing novel optimization algorithms via discretization of continuous-time flows.

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