Some of the most successful knowledge graph embedding (KGE) models for link prediction -- CP, RESCAL, TuckER, ComplEx -- can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits -- constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design. Furthermore, our models scale more gracefully than the original KGEs on graphs with millions of entities.
Continual learning (CL) is one of the most promising trends in recent machine learning research. Its goal is to go beyond classical assumptions in machine learning and develop models and learning strategies that present high robustness in dynamic environments. The landscape of CL research is fragmented into several learning evaluation protocols, comprising different learning tasks, datasets, and evaluation metrics. Additionally, the benchmarks adopted so far are still distant from the complexity of real-world scenarios, and are usually tailored to highlight capabilities specific to certain strategies. In such a landscape, it is hard to objectively assess strategies. In this work, we fill this gap for CL on image data by introducing two novel CL benchmarks that involve multiple heterogeneous tasks from six image datasets, with varying levels of complexity and quality. Our aim is to fairly evaluate current state-of-the-art CL strategies on a common ground that is closer to complex real-world scenarios. We additionally structure our benchmarks so that tasks are presented in increasing and decreasing order of complexity -- according to a curriculum -- in order to evaluate if current CL models are able to exploit structure across tasks. We devote particular emphasis to providing the CL community with a rigorous and reproducible evaluation protocol for measuring the ability of a model to generalize and not to forget while learning. Furthermore, we provide an extensive experimental evaluation showing that popular CL strategies, when challenged with our benchmarks, yield sub-par performance, high levels of forgetting, and present a limited ability to effectively leverage curriculum task ordering. We believe that these results highlight the need for rigorous comparisons in future CL works as well as pave the way to design new CL strategies that are able to deal with more complex scenarios.
While showing impressive performance on various kinds of learning tasks, it is yet unclear whether deep learning models have the ability to robustly tackle reasoning tasks. than by learning the underlying reasoning process that is actually required to solve the tasks. Measuring the robustness of reasoning in machine learning models is challenging as one needs to provide a task that cannot be easily shortcut by exploiting spurious statistical correlations in the data, while operating on complex objects and constraints. reasoning task. To address this issue, we propose ChemAlgebra, a benchmark for measuring the reasoning capabilities of deep learning models through the prediction of stoichiometrically-balanced chemical reactions. ChemAlgebra requires manipulating sets of complex discrete objects -- molecules represented as formulas or graphs -- under algebraic constraints such as the mass preservation principle. We believe that ChemAlgebra can serve as a useful test bed for the next generation of machine reasoning models and as a promoter of their development.
We design a predictive layer for structured-output prediction (SOP) that can be plugged into any neural network guaranteeing its predictions are consistent with a set of predefined symbolic constraints. Our Semantic Probabilistic Layer (SPL) can model intricate correlations, and hard constraints, over a structured output space all while being amenable to end-to-end learning via maximum likelihood. SPLs combine exact probabilistic inference with logical reasoning in a clean and modular way, learning complex distributions and restricting their support to solutions of the constraint. As such, they can faithfully, and efficiently, model complex SOP tasks beyond the reach of alternative neuro-symbolic approaches. We empirically demonstrate that SPLs outperform these competitors in terms of accuracy on challenging SOP tasks including hierarchical multi-label classification, pathfinding and preference learning, while retaining perfect constraint satisfaction.
In this position paper, we study interactive learning for structured output spaces, with a focus on active learning, in which labels are unknown and must be acquired, and on skeptical learning, in which the labels are noisy and may need relabeling. These scenarios require expressive models that guarantee reliable and efficient computation of probabilistic quantities to measure uncertainty. We identify conditions under which a class of probabilistic models -- which we denote CRISPs -- meet all of these conditions, thus delivering tractable computation of the above quantities while preserving expressiveness. Building on prior work on tractable probabilistic circuits, we illustrate how CRISPs enable robust and efficient active and skeptical learning in large structured output spaces.
Computing the expectation of some kernel function is ubiquitous in machine learning, from the classical theory of support vector machines, to exploiting kernel embeddings of distributions in applications ranging from probabilistic modeling, statistical inference, casual discovery, and deep learning. In all these scenarios, we tend to resort to Monte Carlo estimates as expectations of kernels are intractable in general. In this work, we characterize the conditions under which we can compute expected kernels exactly and efficiently, by leveraging recent advances in probabilistic circuit representations. We first construct a circuit representation for kernels and propose an approach to such tractable computation. We then demonstrate possible advancements for kernel embedding frameworks by exploiting tractable expected kernels to derive new algorithms for two challenging scenarios: 1) reasoning under missing data with kernel support vector regressors; 2) devising a collapsed black-box importance sampling scheme. Finally, we empirically evaluate both algorithms and show that they outperform standard baselines on a variety of datasets.
Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine learning -- from computing the expectations of decision tree ensembles to information-theoretic divergences of deep mixture models -- can be represented in terms of tractable modular operations over circuits. Specifically, we characterize the tractability of a vocabulary of simple transformations -- sums, products, quotients, powers, logarithms, and exponentials -- in terms of sufficient structural constraints of the circuits they operate on, and present novel hardness results for the cases in which these properties are not satisfied. Building on these operations, we derive a unified framework for reasoning about tractable models that generalizes several results in the literature and opens up novel tractable inference scenarios.
Guessing games are a prototypical instance of the "learning by interacting" paradigm. This work investigates how well an artificial agent can benefit from playing guessing games when later asked to perform on novel NLP downstream tasks such as Visual Question Answering (VQA). We propose two ways to exploit playing guessing games: 1) a supervised learning scenario in which the agent learns to mimic successful guessing games and 2) a novel way for an agent to play by itself, called Self-play via Iterated Experience Learning (SPIEL). We evaluate the ability of both procedures to generalize: an in-domain evaluation shows an increased accuracy (+7.79) compared with competitors on the evaluation suite CompGuessWhat?!; a transfer evaluation shows improved performance for VQA on the TDIUC dataset in terms of harmonic average accuracy (+5.31) thanks to more fine-grained object representations learned via SPIEL.
In visual guessing games, a Guesser has to identify a target object in a scene by asking questions to an Oracle. An effective strategy for the players is to learn conceptual representations of objects that are both discriminative and expressive enough to ask questions and guess correctly. However, as shown by Suglia et al. (2020), existing models fail to learn truly multi-modal representations, relying instead on gold category labels for objects in the scene both at training and inference time. This provides an unnatural performance advantage when categories at inference time match those at training time, and it causes models to fail in more realistic "zero-shot" scenarios where out-of-domain object categories are involved. To overcome this issue, we introduce a novel "imagination" module based on Regularized Auto-Encoders, that learns context-aware and category-aware latent embeddings without relying on category labels at inference time. Our imagination module outperforms state-of-the-art competitors by 8.26% gameplay accuracy in the CompGuessWhat?! zero-shot scenario (Suglia et al., 2020), and it improves the Oracle and Guesser accuracy by 2.08% and 12.86% in the GuessWhat?! benchmark, when no gold categories are available at inference time. The imagination module also boosts reasoning about object properties and attributes.
Probabilistic circuits (PCs) represent a probability distribution as a computational graph. Enforcing structural properties on these graphs guarantees that several inference scenarios become tractable. Among these properties, structured decomposability is a particularly appealing one: it enables the efficient and exact computations of the probability of complex logical formulas, and can be used to reason about the expected output of certain predictive models under missing data. This paper proposes Strudel, a simple, fast and accurate learning algorithm for structured-decomposable PCs. Compared to prior work for learning structured-decomposable PCs, Strudel delivers more accurate single PC models in fewer iterations, and dramatically scales learning when building ensembles of PCs. It achieves this scalability by exploiting another structural property of PCs, called determinism, and by sharing the same computational graph across mixture components. We show these advantages on standard density estimation benchmarks and challenging inference scenarios.