Differentiable Reasoning

Compared with static knowledge graphs, temporal knowledge graphs (tKG), which can capture the evolution and change of information over time, are more realistic and general. However, due to the complexity that the notion of time introduces to the learning of the rules, an accurate graph reasoning, e.g., predicting new links between entities, is still a difficult problem. In this paper, we propose TILP, a differentiable framework for temporal logical rules learning. By designing a constrained random walk mechanism and the introduction of temporal operators, we ensure the efficiency of our model. We present temporal features modeling in tKG, e.g., recurrence, temporal order, interval between pair of relations, and duration, and incorporate it into our learning process. We compare TILP with state-of-the-art methods on two benchmark datasets. We show that our proposed framework can improve upon the performance of baseline methods while providing interpretable results. In particular, we consider various scenarios in which training samples are limited, data is biased, and the time range between training and inference are different. In all these cases, TILP works much better than the state-of-the-art methods.

Chain-of-thought prompting has demonstrated remarkable performance on various natural language reasoning tasks. However, it tends to perform poorly on tasks which requires solving problems harder than the exemplars shown in the prompts. To overcome this challenge of easy-to-hard generalization, we propose a novel prompting strategy, least-to-most prompting. The key idea in this strategy is to break down a complex problem into a series of simpler subproblems and then solve them in sequence. Solving each subproblem is facilitated by the answers to previously solved subproblems. Our experimental results on tasks related to symbolic manipulation, compositional generalization, and math reasoning reveal that least-to-most prompting is capable of generalizing to more difficult problems than those seen in the prompts. A notable finding is that when the GPT-3 code-davinci-002 model is used with least-to-most prompting, it can solve the compositional generalization benchmark SCAN in any split (including length split) with an accuracy of at least 99\% using just 14 exemplars, compared to only 16\% accuracy with chain-of-thought prompting. This is particularly noteworthy because neural-symbolic models in the literature that specialize in solving SCAN are trained on the entire training set containing over 15,000 examples. We have included prompts for all the tasks in the Appendix.

Differentiable neural architecture search methods are increasingly popular due to their computational efficiency. However, these methods have unsatisfactory generalizability and stability. Their searched architectures are often degenerate with a dominant number of skip connections and perform unsatisfactorily on test data. Existing methods for solving this problem have a variety of limitations, such as cannot prevent the happening of architecture degeneration, being excessively restrictive in setting the number of skip connections, etc. To address these limitations, we propose a new approach for improving the generalizability and stability of differentiable NAS, by developing a transferability-encouraging tri-level optimization framework which improves the architecture of a main model by encouraging good transferability to an auxiliary model. Our framework involves three stages performed end-to-end: 1) train network weights of a main model; 2) transfer knowledge from the main model to an auxiliary model; 3) optimize the architecture of the main model by maximizing its transferability to the auxiliary model. We propose a new knowledge transfer approach based on matching quadruple relative similarities. Experiments on several datasets demonstrate the effectiveness of our method.

Probabilistic logical rule learning has shown great strength in logical rule mining and knowledge graph completion. It learns logical rules to predict missing edges by reasoning on existing edges in the knowledge graph. However, previous efforts have largely been limited to only modeling chain-like Horn clauses such as R1(x; z) ^ R2(z; y) ) H(x; y). This formulation overlooks additional contextual information from neighboring sub-graphs of entity variables x, y and z. Intuitively, there is a large gap here, as local sub-graphs have been found to provide important information for knowledge graph completion. Inspired by these observations, we propose Logical Entity RePresentation (LERP) to encode contextual information of entities in the knowledge graph. A LERP is designed as a vector of probabilistic logical functions on the entity’s neighboring sub-graph. It is an interpretable representation while allowing for differentiable optimization. We can then incorporate LERP into probabilistic logical rule learning to learn more expressive rules. Empirical results demonstrate that with LERP, our model outperforms other rule learning methods in knowledge graph completion and is comparable or even superior to state-of-the-art black-box methods. Moreover, we find that our model can discover a more expressive family of logical rules. LERP can also be further combined with embedding learning methods like TransE to make it more interpretable.

Natural language inference (NLI) aims to determine the logical relationship between two sentences, such as Entailment, Contradiction, and Neutral. In recent years, deep learning models have become a prevailing approach to NLI, but they lack interpretability and explainability. In this work, we address the explainability of NLI by weakly supervised logical reasoning, and propose an Explainable Phrasal Reasoning (EPR) approach. Our model first detects phrases as the semantic unit and aligns corresponding phrases in the two sentences. Then, the model predicts the NLI label for the aligned phrases, and induces the sentence label by fuzzy logic formulas. Our EPR is almost everywhere differentiable and thus the system can be trained end to end. In this way, we are able to provide explicit explanations of phrasal logical relationships in a weakly supervised manner. We further show that such reasoning results help textual explanation generation.

Despite the success of neural network models in a range of domains, it remains an open question whether they can learn to represent abstract logical operators such as negation and disjunction. We test the hypothesis that neural networks without inherent inductive biases for logical reasoning can acquire an implicit representation of negation and disjunction. Here, implicit refers to limited, domain-specific forms of these operators, and work in psychology suggests these operators may be a precursor (developmentally and evolutionarily) to the type of abstract, domain-general logic that is characteristic of adult humans. To test neural networks, we adapt a test designed to diagnose the presence of negation and disjunction in animals and pre-verbal children, which requires inferring the location of a hidden object using constraints of the physical environment as well as implicit logic: if a ball is hidden in A or B, and shown not to be in A, can the subject infer that it is in B? Our results show that, despite the neural networks learning to track objects behind occlusion, they are unable to generalize to a task that requires implicit logic. We further show that models are unable to generalize to the test task even when they are trained directly on a logically identical (though visually dissimilar) task. However, experiments using transfer learning reveal that the models do recognize structural similarity between tasks which invoke the same logical reasoning pattern, suggesting that some desirable abstractions are learned, even if they are not yet sufficient to pass established tests of logical reasoning.

Differentiable rendering allows the application of computer graphics on vision tasks, e.g. object pose and shape fitting, via analysis-by-synthesis, where gradients at occluded regions are important when inverting the rendering process.To obtain those gradients, state-of-the-art (SoTA) differentiable renderers use rasterization to collect a set of nearest components for each pixel and aggregate them based on the viewing distance. In this paper, we propose VoGE, which uses ray tracing to capture nearest components with their volume density distributions on the rays and aggregates via integral of the volume densities based on Gaussian ellipsoids, which brings more efficient and stable gradients. To efficiently render via VoGE, we propose an approximate close-form solution for the volume density aggregation and a coarse-to-fine rendering strategy. Finally, we provide a CUDA implementation of VoGE, which gives a competitive rendering speed in comparison to PyTorch3D. Quantitative and qualitative experiment results show VoGE outperforms SoTA counterparts when applied to various vision tasks, e.g., object pose estimation, shape/texture fitting, and occlusion reasoning. The VoGE code is available at: https://github.com/Angtian/VoGE.

Partitioning a set of elements into subsets of a priori unknown sizes is essential in many applications. These subset sizes are rarely explicitly learned - be it the cluster sizes in clustering applications or the number of shared versus independent generative latent factors in weakly-supervised learning. Probability distributions over correct combinations of subset sizes are non-differentiable due to hard constraints, which prohibit gradient-based optimization. In this work, we propose the differentiable hypergeometric distribution. The hypergeometric distribution models the probability of different group sizes based on their relative importance. We introduce reparameterizable gradients to learn the importance between groups and highlight the advantage of explicitly learning the size of subsets in two typical applications: weakly-supervised learning and clustering. In both applications, we outperform previous approaches, which rely on suboptimal heuristics to model the unknown size of groups.

Offline reinforcement learning, which aims at optimizing sequential decision-making strategies with historical data, has been extensively applied in real-life applications. State-Of-The-Art algorithms usually leverage powerful function approximators (e.g. neural networks) to alleviate the sample complexity hurdle for better empirical performances. Despite the successes, a more systematic under- standing of the statistical complexity for function approximation remains lacking. Towards bridging the gap, we take a step by considering offline reinforcement learning with differentiable function class approximation (DFA). This function class naturally incorporates a wide range of models with nonlinear/nonconvex structures. We show offline RL with differentiable function approximation is provably efficient by analyzing the pessimistic fitted Q-learning (PFQL) algorithm, and our results provide the theoretical basis for understanding a variety of practical heuristics that rely on Fitted Q-Iteration style design. In addition, we further im- prove our guarantee with a tighter instance-dependent characterization. We hope our work could draw interest in studying reinforcement learning with differentiable function approximation beyond the scope of current research.

Comprehensive studies of synthetic optical flow datasets have attempted to reveal what properties lead to accuracy improvement in learning-based optical flow estimation. However, manually identifying and verifying the properties that contribute to accurate optical flow estimation require large-scale trial-and-error experiments with iteratively generating whole synthetic datasets and training on them, \ie, impractical. To address this challenge, we propose a differentiable optical flow data generation pipeline and a loss function to drive the pipeline, called DFlow. DFlow efficiently synthesizes a dataset effective for a target domain without the need for cumbersome try-and-errors. This favorable property is achieved by proposing an efficient dataset comparison method that uses neural networks to approximately encode each dataset and compares the proxy networks instead of explicitly comparing datasets in a pairwise way. Our experiments show the competitive performance of our DFlow against the prior arts in pre-training. Furthermore, compared to competing datasets, DFlow achieves the best fine-tuning performance on the Sintel public benchmark with RAFT.