Differentiable Reasoning

We study the problem of learning comparisons between numbers with neural networks. Despite comparisons being a seemingly simple problem, we find that both general-purpose models such as multilayer perceptrons (MLPs) as well as arithmetic architectures such as the Neural Arithmetic Logic Unit (NALU) struggle with learning comparisons. Neither architecture can extrapolate to much larger numbers than those seen in the training set. We propose a novel differentiable architecture, the Neural Status Register (NSR) to solve this problem. We experimentally validate the NSR in various settings. We can combine the NSR with other neural models to solve interesting problems such as piecewise-defined arithmetic, comparison of digit images, recurrent problems, or finding shortest paths in graphs. The NSR outperforms all baseline architectures, especially when it comes to extrapolating to larger numbers.

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

We study a synthetic corpus based approach for language models (LMs) to acquire logical deductive reasoning ability. The previous studies generated deduction examples using specific sets of deduction rules. However, these rules were limited or otherwise arbitrary. This can limit the generalizability of acquired deductive reasoning ability. We rethink this and adopt a well-grounded set of deduction rules based on formal logic theory, which can derive any other deduction rules when combined in a multistep way. We empirically verify that LMs trained on the proposed corpora, which we name $\textbf{FLD}$ ($\textbf{F}$ormal $\textbf{L}$ogic $\textbf{D}$eduction), acquire more generalizable deductive reasoning ability. Furthermore, we identify the aspects of deductive reasoning ability on which deduction corpora can enhance LMs and those on which they cannot. Finally, on the basis of these results, we discuss the future directions for applying deduction corpora or other approaches for each aspect. We release the code, data, and models.

In the context of structure-to-structure transformation tasks, learning sequences of discrete symbolic operations poses significant challenges due to their non-differentiability. To facilitate the learning of these symbolic sequences, we introduce a differentiable tree interpreter that compiles high-level symbolic tree operations into subsymbolic matrix operations on tensors. We present a novel Differentiable Tree Machine (DTM) architecture that integrates our interpreter with an external memory and an agent that learns to sequentially select tree operations to execute the target transformation in an end-to-end manner. With respect to out-of-distribution compositional generalization on synthetic semantic parsing and language generation tasks, DTM achieves 100% while existing baselines such as Transformer, Tree Transformer, LSTM, and Tree2Tree LSTM achieve less than 30%. DTM remains highly interpretable in addition to its perfect performance.

Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts. However, state-of-the-art concept-based models rely on high-dimensional concept embedding representations which lack a clear semantic meaning, thus questioning the interpretability of their decision process. To overcome this limitation, we propose the Deep Concept Reasoner (DCR), the first interpretable concept-based model that builds upon concept embeddings. In DCR, neural networks do not make task predictions directly, but they build syntactic rule structures using concept embeddings. DCR then executes these rules on meaningful concept truth degrees to provide a final interpretable and semantically-consistent prediction in a differentiable manner. Our experiments show that DCR: (i) improves up to +25% w.r.t. state-of-the-art interpretable concept-based models on challenging benchmarks (ii) discovers meaningful logic rules matching known ground truths even in the absence of concept supervision during training, and (iii), facilitates the generation of counterfactual examples providing the learnt rules as guidance.