The relational representations relied upon by such methods, however, are abstract. We aim to deconstruct this abstraction by expressing them as interpretable graphs over image views. We begin by theoretically showing that abstract relational representations are nothing but a way of recovering transitive relationships among local views. Based on this, we design Transitivity Recovering Decompositions (TRD), a graph-space search algorithm that identifies interpretable equivalents of abstract emergent relationships at both instance and class levels, and with no post-hoc computations. We additionally show that TRD is provably robust to noisy views, with empirical evidence also supporting this finding. The latter allows TRD to perform at par or even better than the state-of-the-art, while being fully interpretable. Implementation is available at https://github.com/abhrac/trd.

The relational representations relied upon by such methods, however, are abstract.

The relational representations relied upon by such methods, however, are abstract. We aim to deconstruct this abstraction by expressing them as interpretable graphs over image views. We begin by theoretically showing that abstract relational representations are nothing but a way of recovering transitive relationships among local views. Based on this, we design Transitivity Recovering Decompositions (TRD), a graph-space search algorithm that identifies interpretable equivalents of abstract emergent relationships at both instance and class levels, and with no post-hoc computations. We additionally show that TRD is provably robust to noisy views, with empirical evidence also supporting this finding.

Modern transformer-based encoder-decoder architectures struggle with reasoning tasks due to their inability to effectively extract relational information between input objects (data/tokens). Recent work introduced the Abstractor module, embedded between transformer layers, to address this gap. However, the Abstractor layer while excelling at capturing relational information (pure relational reasoning), faces challenges in tasks that require both object and relational-level reasoning (partial relational reasoning). To address this, we propose RESOLVE, a neuro-vector symbolic architecture that combines object-level features with relational representations in high-dimensional spaces, using fast and efficient operations such as bundling (summation) and binding (Hadamard product) allowing both object-level features and relational representations to coexist within the same structure without interfering with one another. RESOLVE is driven by a novel attention mechanism that operates in a bipolar high dimensional space, allowing fast attention score computation compared to the state-of-the-art. By leveraging this design, the model achieves both low compute latency and memory efficiency. RESOLVE also offers better generalizability while achieving higher accuracy in purely relational reasoning tasks such as sorting as well as partial relational reasoning tasks such as math problem-solving compared to state-of-the-art methods.

We introduce a novel approach to program synthesis that decomposes complex functional tasks into simpler relational synthesis sub-tasks. We demonstrate the effectiveness of our approach using an off-the-shelf inductive logic programming (ILP) system on three challenging datasets. Our results show that (i) a relational representation can outperform a functional one, and (ii) an off-the-shelf ILP system with a relational encoding can outperform domain-specific approaches.

Relational concepts are indeed foundational to the structure of knowledge representation, as they facilitate the association between various entity concepts, allowing us to express and comprehend complex world knowledge. By expressing relational concepts in natural language prompts, people can effortlessly interact with large language models (LLMs) and recall desired factual knowledge. However, the process of knowledge recall lacks interpretability, and representations of relational concepts within LLMs remain unknown to us. In this paper, we identify hidden states that can express entity and relational concepts through causal mediation analysis in fact recall processes. Our finding reveals that at the last token position of the input prompt, there are hidden states that solely express the causal effects of relational concepts. Based on this finding, we assume that these hidden states can be treated as relational representations and we can successfully extract them from LLMs. The experimental results demonstrate high credibility of the relational representations: they can be flexibly transplanted into other fact recall processes, and can also be used as robust entity connectors. Moreover, we also show that the relational representations exhibit significant potential for controllable fact recall through relation rewriting.

Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both paradigms. In parallel, recent studies have proposed the use of a "relational bottleneck" that separates object-level features from abstract rules, allowing learning from limited amounts of data . While powerful, it is vulnerable to the curse of compositionality meaning that object representations with similar features tend to interfere with each other. In this paper, we leverage hyperdimensional computing, which is inherently robust to such interference to build a compositional architecture. We adapt the "relational bottleneck" strategy to a high-dimensional space, incorporating explicit vector binding operations between symbols and relational representations. Additionally, we design a novel high-dimensional attention mechanism that leverages this relational representation. Our system benefits from the low overhead of operations in hyperdimensional space, making it significantly more efficient than the state of the art when evaluated on a variety of test datasets, while maintaining higher or equal accuracy.

Although database systems perform well in data access and manipulation, their relational model hinders data scientists from formulating machine learning algorithms in SQL. Nevertheless, we argue that modern database systems perform well for machine learning algorithms expressed in relational algebra. To overcome the barrier of the relational model, this paper shows how to transform data into a relational representation for training neural networks in SQL: We first describe building blocks for data transformation, model training and inference in SQL-92 and their counterparts using an extended array data type. Then, we compare the implementation for model training and inference using array data types to the one using a relational representation in SQL-92 only. The evaluation in terms of runtime and memory consumption proves the suitability of modern database systems for matrix algebra, although specialised array data types perform better than matrices in relational representation.

Recent advances in fine-grained representation learning leverage local-to-global (emergent) relationships for achieving state-of-the-art results. The relational representations relied upon by such methods, however, are abstract. We aim to deconstruct this abstraction by expressing them as interpretable graphs over image views. We begin by theoretically showing that abstract relational representations are nothing but a way of recovering transitive relationships among local views. Based on this, we design Transitivity Recovering Decompositions (TRD), a graph-space search algorithm that identifies interpretable equivalents of abstract emergent relationships at both instance and class levels, and with no post-hoc computations. We additionally show that TRD is provably robust to noisy views, with empirical evidence also supporting this finding. The latter allows TRD to perform at par or even better than the state-of-the-art, while being fully interpretable. Implementation is available at https://github.com/abhrac/trd.