Kuinan Hou

Kuinan Hou, Marco Zorzi, Alberto Testolin

Reliably counting and generating sequences of items remain a significant challenge for neural networks, including Large Language Models (LLMs). Indeed, although this capability is readily handled by rule-based symbolic systems based on serial computation, learning to systematically deploy counting procedures is difficult for neural models, which should acquire these skills through learning. Previous research has demonstrated that recurrent architectures can only approximately track and enumerate sequences of events, and it remains unclear whether modern deep learning systems, including LLMs, can deploy systematic counting procedures over sequences of discrete symbols. This paper aims to fill this gap by investigating the sequential enumeration abilities of five state-of-the-art LLMs, including proprietary, open-source, and reasoning models. We probe LLMs in sequential naming and production tasks involving lists of letters and words, adopting a variety of prompting instructions to explore the role of chain-of-thought in the spontaneous emerging of counting strategies. We also evaluate open-source models with the same architecture but increasing size to see whether the mastering of counting principles follows scaling laws, and we analyze the embedding dynamics during sequential enumeration to investigate the emergent encoding of numerosity. We find that some LLMs are indeed capable of deploying counting procedures when explicitly prompted to do so, but none of them spontaneously engage in counting when simply asked to enumerate the number of items in a sequence. Our results suggest that, despite their impressive emergent abilities, LLMs cannot yet robustly and systematically deploy counting procedures, highlighting a persistent gap between neural and symbolic approaches to compositional generalization.

Kuinan Hou, Marco Zorzi, Alberto Testolin

Humans share with many animal species the ability to perceive and approximately represent the number of objects in visual scenes. This ability improves throughout childhood, suggesting that learning and development play a key role in shaping our number sense. This hypothesis is further supported by computational investigations based on deep learning, which have shown that numerosity perception can spontaneously emerge in neural networks that learn the statistical structure of images with a varying number of items. However, neural network models are usually trained using synthetic datasets that might not faithfully reflect the statistical structure of natural environments, and there is also growing interest in using more ecological visual stimuli to investigate numerosity perception in humans. In this work, we exploit recent advances in computer vision algorithms to design and implement an original pipeline that can be used to estimate the distribution of numerosity and non-numerical magnitudes in large-scale datasets containing thousands of real images depicting objects in daily life situations. We show that in natural visual scenes the frequency of appearance of different numerosities follows a power law distribution. Moreover, we show that the correlational structure for numerosity and continuous magnitudes is stable across datasets and scene types (homogeneous vs. heterogeneous object sets). We suggest that considering such "ecological" pattern of covariance is important to understand the influence of non-numerical visual cues on numerosity judgements.

Kuinan Hou, Jing Mi, Marco Zorzi et al.

Counting the number of items in a visual scene remains a fundamental yet challenging task in computer vision. Traditional approaches to solving this problem rely on domain-specific counting architectures, which are trained using datasets annotated with a predefined set of object categories. However, recent progress in creating large-scale multimodal vision-language models (VLMs) suggests that these domain-general architectures may offer a flexible alternative for open-set object counting. In this study, we therefore systematically compare the performance of state-of-the-art specialized counting architectures against VLMs on two popular counting datasets, as well as on a novel benchmark specifically created to have a finer-grained control over the visual properties of test images. Our findings show that most VLMs can approximately enumerate the number of items in a visual scene, matching or even surpassing the performance of specialized computer vision architectures. Notably, enumeration accuracy significantly improves when VLMs are prompted to generate intermediate representations (i.e., locations and verbal labels) of each object to be counted. Nevertheless, none of the models can reliably count the number of objects in complex visual scenes, showing that further research is still needed to create AI systems that can reliably deploy counting procedures in realistic environments.

Alberto Testolin, Kuinan Hou, Marco Zorzi

Many animal species can approximately judge the number of objects in a visual scene at a single glance, and humans can further determine the exact cardinality of a set by deploying systematic counting procedures. In contrast, it has been observed that even state-of-the-art AI systems have very limited enumeration skills. In this work, we propose two benchmark tasks inspired by cognitive science that allow to precisely evaluate the visual enumeration capabilities of multimodal foundation models, thereby providing an objective measure of their number sense and counting level. We consider popular visual question answering models (BLIP, LLaVA and ViLT) as well as advanced image-to-text (Gemini, GPT and Qwen) and text-to-image (DALL-E, FLUX and Stable Diffusion) AI systems. Our analyses show that even the most advanced models cannot reliably name the number of objects in simple visual stimuli or generate images containing a target number of items, as indexed by their low accuracy in both types of tasks. Especially for numbers outside the subitizing range, their responses are often far from the target numerosity, and, in stark contrast with human behavior, in many cases the distribution of errors depends on the object category. We also observe some striking mistakes with small numbers. Our findings demonstrate that developing an intuitive visual understanding of number remains challenging for AI models and that merely increasing model size might not be a viable strategy to promote the emergence of systematic counting skills. We release the full code of our benchmark to facilitate the evaluation of enumeration skills in future AI systems.