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ARXIV:2603.16123 · NEURAL ARCHITECTURE · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE
ARXIV:2603.16123NEURAL ARCHITECTURESUBMITTED 02 APR · 02:30 UTCFRESHNESS STALEarXiv
A novel approach to enhance compositional generalization in neural networks through functorial architectures.
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Pain A novel approach to enhance compositional generalization in neural networks through functorial architectures.
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A novel approach to enhance compositional generalization in neural networks through functorial architectures. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and this perspective yields both…
Neural networks systematically fail at compositional generalization -- producing correct outputs for novel combinations of known parts. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and…
ScienceToStartup currently rates this 4.0/10 on the public viability pass. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and this perspective yields both guarantees and impossibility…
Neural Architecture moved forward this cycle; last verified April 2026. Public score 4.0/10.
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A novel approach to enhance compositional generalization in neural networks through functorial architectures.
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10.48550/arXiv.2603.16123A novel approach to enhance compositional generalization in neural networks through functorial architectures.
Abstract
Neural networks systematically fail at compositional generalization -- producing correct outputs for novel combinations of known parts. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and this perspective yields both guarantees and impossibility results. We compile Higher Inductive Type (HIT) specifications into neural architectures via a monoidal functor from the path groupoid of a target space to a category of parametric maps: path constructors become generator networks, composition becomes structural concatenation, and 2-cells witnessing group relations become learned natural transformations. We prove that decoders assembled by structural concatenation of independently generated segments are strict monoidal functors (compositional by construction), while softmax self-attention is not functorial for any non-trivial compositional task. Both results are formalized in Cubical Agda. Experiments on three spaces validate the full hierarchy: on the torus ($\mathbb{Z}^2$), functorial decoders outperform non-functorial ones by 2-2.7x; on $S^1 \vee S^1$ ($F_2$), the type-A/B gap widens to 5.5-10x; on the Klein bottle ($\mathbb{Z} \rtimes \mathbb{Z}$), a learned 2-cell closes a 46% error gap on words exercising the group relation.
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A novel approach to enhance compositional generalization in neural networks through functorial architectures. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and this perspective yields both guarantees and i...
METHOD
Neural networks systematically fail at compositional generalization -- producing correct outputs for novel combinations of known parts. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and this perspective yi...
RESULT
ScienceToStartup currently rates this 4.0/10 on the public viability pass. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and this perspective yields both guarantees and impossibility results.
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Neural Architecture moved forward this cycle; last verified April 2026. Public score 4.0/10.
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A novel approach to enhance compositional generalization in neural networks through functorial architectures. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and this perspective yields both guarantees and impossibility results.
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Neural networks systematically fail at compositional generalization -- producing correct outputs for novel combinations of known parts. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and this perspective yields both guarantees and impossibility results.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 4.0/10 on the public viability pass. We show that this failure is architectural: compositional generalization is equivalent to functoriality of the decoder, and this perspective yields both guarantees and impossibility results.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Neural Architecture moved forward this cycle; last verified April 2026. Public score 4.0/10.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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A novel approach to enhance compositional generalization in neural networks through functorial architectures.
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