Differentiable Fuzzy Inference Layer: A Monotone, Compositional Ordinal Reasoning Head for Large Language Models

Zhen Zhang; Amr Alanwar

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arXiv · 2609.26113

Differentiable Fuzzy Inference Layer: A Monotone, Compositional Ordinal Reasoning Head for Large Language Models

Zhen Zhang·Amr Alanwar

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Abstract

A state-of-the-art language model asked to interpret "most of most students passed" typically answers "most," though composing two instances of "most" yields a proportion closer to "some." We trace this failure to an architectural choice rather than a data deficit: standard classifier heads treat ordinal categories as independent labels, with no mechanism to respect their natural ordering or compose them algebraically. We introduce the Differentiable Fuzzy Inference Layer (DFIL), a dual-path prediction head pairing a standard classifier with a scalar-bottlenecked branch grounded in a bank of ordered membership functions. DFIL supplies two structural primitives that a label-only head cannot inherit: monotonicity in the underlying quantity, and compositional reasoning via t-norm operations without any compositional training data. The scalar branch additionally provides an interpretable interface for analyzing residual errors. We instantiate DFIL on ordinal natural-language tasks across diverse LLM families.

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BibTeX RIS

Zhen Zhang, Amr Alanwar. 2026-08-17. Differentiable Fuzzy Inference Layer: A Monotone, Compositional Ordinal Reasoning Head for Large Language Models. https://arxiv.org/abs/2609.26113

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