In this work, we investigate whether analogical reasoning can enable in-context composition over composable elements of visual stimuli.

Neural Information Processing Systems http://nips.cc/

In this work, we investigate whether analogical reasoning can enable in-context composition over composable elements of visual stimuli.

We propose a new way of constructing invertible neural networks by combining simple building blocks with a novel set of composition rules. This leads to a rich set of invertible architectures, including those similar to ResNets. Inversion is achieved with a locally convergent iterative procedure that is parallelizable and very fast in practice.

Spatial reasoning is a crucial component of both biological and artificial intelligence. In this work, we present a comprehensive study of the capability of current state-of-the-art large language models (LLMs) on spatial reasoning. To support our study, we created and contribute a novel Spatial Reasoning Characterization (SpaRC) framework and Spatial Reasoning Paths (SpaRP) datasets, to enable an in-depth understanding of the spatial relations and compositions as well as the usefulness of spatial reasoning chains. We found that all the state-of-the-art LLMs do not perform well on the datasets -- their performances are consistently low across different setups. The spatial reasoning capability improves substantially as model sizes scale up. Finetuning both large language models (e.g., Llama-2-70B) and smaller ones (e.g., Llama-2-13B) can significantly improve their F1-scores by 7--32 absolute points. We also found that the top proprietary LLMs still significantly outperform their open-source counterparts in topological spatial understanding and reasoning.

Images are ambiguous at each of many levels of a contextual hi(cid:173) erarchy. Nevertheless, the high-level interpretation of most scenes is unambiguous, as evidenced by the superior performance of hu(cid:173) mans. This observation argues for global vision models, such as de(cid:173) formable templates. Unfortunately, such models are computation(cid:173) ally intractable for unconstrained problems. We propose a composi(cid:173) tional model in which primitives are recursively composed, subject to syntactic restrictions, to form tree-structured objects and object groupings.

Region based knowledge graph embeddings represent relations as geometric regions. This has the advantage that the rules which are captured by the model are made explicit, making it straightforward to incorporate prior knowledge and to inspect learned models. Unfortunately, existing approaches are severely restricted in their ability to model relational composition, and hence also their ability to model rules, thus failing to deliver on the main promise of region based models. With the aim of addressing these limitations, we investigate regions which are composed of axis-aligned octagons. Such octagons are particularly easy to work with, as intersections and compositions can be straightforwardly computed, while they are still sufficiently expressive to model arbitrary knowledge graphs. Among others, we also show that our octagon embeddings can properly capture a non-trivial class of rule bases. Finally, we show that our model achieves competitive experimental results.

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional data representations. However, how many training examples are required to learn such representations remains unknown. To quantitatively study this question, we introduce the Random Hierarchy Model: a family of synthetic tasks inspired by the hierarchical structure of language and images. The model is a classification task where each class corresponds to a group of high-level features, chosen among several equivalent groups associated with the same class. In turn, each feature corresponds to a group of sub-features chosen among several equivalent ones and so on, following a hierarchy of composition rules. We find that deep networks learn the task by developing internal representations invariant to exchanging equivalent groups. Moreover, the number of data required corresponds to the point where correlations between low-level features and classes become detectable. Overall, our results indicate how deep networks overcome the curse of dimensionality by building invariant representations, and provide an estimate of the number of data required to learn a hierarchical task.