Achieving precise semantic control over the latent spaces of Variational AutoEncoders (VAEs) holds significant value for downstream tasks in NLP as the underlying generative mechanisms could be better localised, explained and improved upon. Recent research, however, has struggled to achieve consistent results, primarily due to the inevitable loss of semantic information in the variational bottleneck and limited control over the decoding mechanism. To overcome these challenges, we investigate discrete latent spaces in Vector Quantized Variational AutoEncoders (VQVAEs) to improve semantic control and generation in Transformer-based VAEs. In particular, We propose T5VQVAE, a novel model that leverages the controllability of VQVAEs to guide the self-attention mechanism in T5 at the token-level, exploiting its full generalization capabilities. Experimental results indicate that T5VQVAE outperforms existing state-of-the-art VAE models, including Optimus, in terms of controllability and preservation of semantic information across different tasks such as auto-encoding of sentences and mathematical expressions, text transfer, and inference. Moreover, T5VQVAE exhibits improved inference capabilities, suggesting potential applications for downstream natural language and symbolic reasoning tasks.

Deep generative neural networks, such as Variational AutoEncoders (VAEs), offer an opportunity to better understand and control language models from the perspective of sentence-level latent spaces. To combine the controllability of VAE latent spaces with the state-of-the-art performance of recent large language models (LLMs), we present in this work LlaMaVAE, which combines expressive encoder and decoder models (sentenceT5 and LlaMA) with a VAE architecture, aiming to provide better text generation control to LLMs. In addition, to conditionally guide the VAE generation, we investigate a new approach based on flow-based invertible neural networks (INNs) named Invertible CVAE. Experimental results reveal that LlaMaVAE can outperform the previous state-of-the-art VAE language model, Optimus, across various tasks, including language modelling, semantic textual similarity and definition modelling. Qualitative analysis on interpolation and traversal experiments also indicates an increased degree of semantic clustering and geometric consistency, which enables better generation control.

The injection of syntactic information in Variational AutoEncoders (VAEs) has been shown to result in an overall improvement of performances and generalisation. An effective strategy to achieve such a goal is to separate the encoding of distributional semantic features and syntactic structures into heterogeneous latent spaces via multi-task learning or dual encoder architectures. However, existing works employing such techniques are limited to LSTM-based VAEs. In this paper, we investigate latent space separation methods for structural syntactic injection in Transformer-based VAE architectures (i.e., Optimus). Specifically, we explore how syntactic structures can be leveraged in the encoding stage through the integration of graph-based and sequential models, and how multiple, specialised latent representations can be injected into the decoder's attention mechanism via low-rank operators. Our empirical evaluation, carried out on natural language sentences and mathematical expressions, reveals that the proposed end-to-end VAE architecture can result in a better overall organisation of the latent space, alleviating the information loss occurring in standard VAE setups, resulting in enhanced performances on language modelling and downstream generation tasks.

Explainable natural language inference aims to provide a mechanism to produce explanatory (abductive) inference chains which ground claims to their supporting premises. A recent corpus called EntailmentBank strives to advance this task by explaining the answer to a question using an entailment tree \cite{dalvi2021explaining}. They employ the T5 model to directly generate the tree, which can explain how the answer is inferred. However, it lacks the ability to explain and control the generation of intermediate steps, which is crucial for the multi-hop inference process. % One recent corpus, EntailmentBank, aims to push this task forward by explaining an answer to a question according to an entailment tree \cite{dalvi2021explaining}. They employ T5 to generate the tree directly, which can explain how the answer is inferred but cannot explain how the intermediate is generated, which is essential to the multi-hop inference process. In this work, we focus on proposing a controlled natural language inference architecture for multi-premise explanatory inference. To improve control and enable explanatory analysis over the generation, we define lexical inference types based on Abstract Meaning Representation (AMR) graph and modify the architecture of T5 to learn a latent sentence representation (T5 bottleneck) conditioned on said type information. We also deliver a dataset of approximately 5000 annotated explanatory inference steps, with well-grounded lexical-symbolic operations. Experimental results indicate that the inference typing induced at the T5 bottleneck can help T5 to generate a conclusion under explicit control.

Disentangling sentence representations over continuous spaces can be a critical process in improving interpretability and semantic control by localising explicit generative factors. Such process confers to neural-based language models some of the advantages that are characteristic of symbolic models, while keeping their flexibility. This work presents a methodology for disentangling the hidden space of a BERT-GPT2 autoencoder by transforming it into a more separable semantic space with the support of a flow-based invertible neural network (INN). Experimental results indicate that the INN can transform the distributed hidden space into a better semantically disentangled latent space, resulting in better interpretability and controllability, when compared to recent state-of-the-art models.

State-of-the-art deep-learning-based approaches to Natural Language Processing (NLP) are credited with various capabilities that involve reasoning with natural language texts. In this paper we carry out a large-scale empirical study investigating the detection of formally valid inferences in controlled fragments of natural language for which the satisfiability problem becomes increasingly complex. We find that, while transformer-based language models perform surprisingly well in these scenarios, a deeper analysis re-veals that they appear to overfit to superficial patterns in the data rather than acquiring the logical principles governing the reasoning in these fragments.

Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive interpretations such as "It is true at no fewer than 15 accessible worlds that...", or "It is true at no more than 2 accessible worlds that...". We investigate the complexity of satisfiability for this language over some familiar classes of frames. This problem is more challenging than its ordinary modal logic counterpart--especially in the case of transitive frames, where graded modal logic lacks the tree-model property. We obtain tight complexity bounds for the problem of determining the satisfiability of a given graded modal logic formula over the classes of frames characterized by any combination of reflexivity, seriality, symmetry, transitivity and the Euclidean property.

The Aristotelian syllogistic cannot account for the validity of many inferences involving relational facts. In this paper, we investigate the prospects for providing a relational syllogistic. We identify several fragments based on (a) whether negation is permitted on all nouns, including those in the subject of a sentence; and (b) whether the subject noun phrase may contain a relative clause. The logics we present are extensions of the classical syllogistic, and we pay special attention to the question of whether reductio ad absurdum is needed. Thus our main goal is to derive results on the existence (or non-existence) of syllogistic proof systems for relational fragments. We also determine the computational complexity of all our fragments.

The data-complexity of both satisfiability and finite satisfiability for the two-variable fragment with counting is NP-complete; the data-complexity of both query-answering and finite query-answering for the two-variable guarded fragment with counting is co-NP-complete.

In this paper, we determine the complexity of the satisfiability problem for various logics obtained by adding numerical quantifiers, and other constructions, to the traditional syllogistic. In addition, we demonstrate the incompleteness of some recently proposed proof-systems for these logics.