Sadegh Mohammadian

Hosein Hasani, Mohammadali Banayeeanzade, Ali Nafisi et al.

Large language models (LLMs), despite strong performance on complex mathematical problems, exhibit systematic limitations in counting tasks. This issue arises from the architectural limits of transformers, where counting is performed across layers, leading to degraded precision for larger counting problems due to depth constraints. To address this limitation, we propose a simple test-time strategy inspired by System-2 cognitive processes that decomposes large counting tasks into smaller, independent sub-problems that the model can reliably solve. We evaluate this approach using observational and causal mediation analyses to understand the underlying mechanism of this System-2-like strategy. Our mechanistic analysis identifies key components: latent counts are computed and stored in the final item representations of each part, transferred to intermediate steps via dedicated attention heads, and aggregated in the final stage to produce the total count. Experimental results demonstrate that this strategy enables LLMs to surpass architectural limitations and achieve higher accuracy on large-scale counting tasks. This work provides mechanistic insight into System-2 counting in LLMs and presents a generalizable approach for improving and understanding their reasoning behavior.

Hosein Hasani, Amirmohammad Izadi, Fatemeh Askari et al.

This paper examines how large language models (LLMs) and large vision-language models (LVLMs) represent and compute numerical information in counting tasks. We use controlled experiments with repeated textual and visual items and analyze model behavior through causal mediation and activation patching. To this end, we design a specialized tool, CountScope, for mechanistic interpretability of numerical content. Results show that individual tokens or visual features encode latent positional count information that can be extracted and transferred across contexts. Layerwise analyses reveal a progressive emergence of numerical representations, with lower layers encoding small counts and higher layers representing larger ones. We identify an internal counter mechanism that updates with each item, stored mainly in the final token or region and transferable between contexts. In LVLMs, numerical information also appears in visual embeddings, shifting between background and foreground regions depending on spatial composition. Models rely on structural cues such as separators in text, which act as shortcuts for tracking item counts and influence the accuracy of numerical predictions. Overall, counting emerges as a structured, layerwise process in LLMs and follows the same general pattern in LVLMs, shaped by the properties of the vision encoder.

Hosein Hasani, Amirmohammad Izadi, Fatemeh Askari et al.

Large vision-language models (LVLMs) show strong performance across multimodal benchmarks but remain limited in structured reasoning and precise grounding. Recent work has demonstrated that adding simple visual structures, such as partitions and annotations, improves accuracy, yet the internal mechanisms underlying these gains remain unclear. We investigate this phenomenon and propose the concept of Grounding IDs, latent identifiers induced by external cues that bind objects to their designated partitions across modalities. Through representation analysis, we find that these identifiers emerge as robust within-partition alignment in embedding space and reduce the modality gap between image and text. Causal interventions further confirm that these identifiers mediate binding between objects and symbolic cues. We show that Grounding IDs strengthen attention between related components, which in turn improves cross-modal grounding and reduces hallucinations. Taken together, our results identify Grounding IDs as a key symbolic mechanism explaining how external cues enhance multimodal binding, offering both interpretability and practical improvements in robustness.