An AI Monkey Gets Grapes for Sure -- Sphere Neural Networks for Reliable Decision-Making
Tiansi Dong, Henry He, Pietro Li\`o, Mateja Jamnik

TL;DR
This paper introduces Sphere Neural Networks that embed concepts on a sphere to enable reliable logical reasoning, outperforming traditional neural methods in syllogistic tasks and avoiding catastrophic forgetting.
Contribution
It proposes Sphere Neural Networks with concept embeddings on a sphere, improving logical reasoning reliability and handling negation effectively, surpassing existing neural reasoning approaches.
Findings
Sphere Neural Networks master 16 syllogistic reasoning tasks.
They effectively represent negation via complement circles.
They outperform LLMs and supervised learning in reliability.
Abstract
This paper compares three methodological categories of neural reasoning: LLM reasoning, supervised learning-based reasoning, and explicit model-based reasoning. LLMs remain unreliable and struggle with simple decision-making that animals can master without extensive corpora training. Through disjunctive syllogistic reasoning testing, we show that reasoning via supervised learning is less appealing than reasoning via explicit model construction. Concretely, we show that an Euler Net trained to achieve 100.00% in classic syllogistic reasoning can be trained to reach 100.00% accuracy in disjunctive syllogistic reasoning. However, the retrained Euler Net suffers severely from catastrophic forgetting (its performance drops to 6.25% on already-learned classic syllogistic reasoning), and its reasoning competence is limited to the pattern level. We propose a new version of Sphere Neural…
Peer Reviews
Decision·Submitted to ICLR 2026
* The problem of if/how neural networks can account for classical logical reasoning is long standing and thus novel insights and architectures that speak to this are interesting * The focus on this particular geometry of an embedding space is, from my understanding, fairly novel
My primary concern with the paper is that I found it hard to follow. I am not an expert in this particular type of architecture, but do consider myself to be reasonable well versed in logic and the application of NNs to classical logic and semantics problems (at least as much as the average ICLR attendee if not moreso). Therefore, if the paper was not "clicking" for me, I take it as a signal that it needs to be reworked in order to have impact. It seems that there is a real contribution here, bu
1. Clear, structured mapping from logical relations to geometric constraints and a catalogue of 16 syllogistic types. 2. Direct comparative experiments with Euler Net and GPT-5. 3. Excellent and detailed drawing and presentation.
1. Novelty concern: The paper does not clearly and rigorously state what technical advances are new vs prior work (Dong et al. 2024/2025). The paper devotes considerable space to the story's background and the monkey example, but fails to sufficiently highlight its own innovative points, leaving its unique aspects under-emphasized. 2. Evaluation limitation. All evaluations are conducted through textual descriptions. Presenting the improvements achieved by the method in tabular form would be more
1. The paper focuses on an important problem, i.e., how to let a model conduct logical reasoning in a deterministic and reliable way. 2. The proposed improvement over the original SphNN is novel and the illustrations in figures are clear.
1. The model is restricted to highly structured input, e.g., syllogistic reasoning tasks. It is unclear how the proposed method would scale to more complex, real-world reasoning that involves ambiguity, common sense, or relational logic (e.g., "A is taller than B, B is to the left of C"). Moreover, the paper assumes that logical statements are already perfectly translated into formal representations. In reality, reasoning problems may come in the form of ambiguous natural language. 2. The time
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Taxonomy
TopicsNeural Networks and Reservoir Computing · Multimodal Machine Learning Applications · Topic Modeling
