LLM hallucination paper(using math) accepted to ICML workshop[R]

Hello guys. I want to introduce my recent research presented at ICML workshop.

github link : genji970/SRM-LoRA: official implementation of "SRM-LoRA: Sub-Riemannian-Metric Updates for Mitigating LLM Hallucination in Low-Rank Adaptation" ICML2026 Workshop FoGen

Shot summarization of Paper.

"""

SRM-LoRA is a sub-Riemannian-inspired LoRA method designed to reduce LLM hallucination.
It builds a sensitivity-based Riemannian metric that reshapes backward gradients in the LoRA parameter space.
This metric suppresses high-cost update directions while leaving the forward computation and inference cost unchanged.
Trained only on HaluEval-QA, SRM-LoRA improves factual reliability on both related and out-of-distribution benchmarks.

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Experiment

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https://preview.redd.it/3uyvbtoa76dh1.png?width=740&format=png&auto=webp&s=4431233186dffae885db8e989f009bf37710fe22

"""

In my view, the reason mathematics is not effectively used in the context of improving the performance of the latest AI systems, such as LLMs, is that progress in discussions about what should serve as the elements of mathematical theories has been slow.

For example, suppose that we use a Riemannian metric. In the parameter space of an LLM, the update vector produced by backpropagation arises from a loss objective that contains the training data. However, if we introduce learnable parameters in order to construct the Riemannian metric and train those learnable parameters by passing through them the same signal as the main training signal, then this may simply amount to a more complicated form of training and may only increase the possibility of overfitting to the training data.

Then, how can we obtain the benefits of mathematical theory while moving in a direction that can generalize? In this paper, the Riemannian metric is constructed based on the rate of change of the LLM model parameters with respect to the loss signal. The reason for defining it in this way is as follows.

No matter how good the data or the distribution that can be learned may be, in practice there is still a high possibility of overfitting that results in hallucinations. Therefore, the cost used to construct the Riemannian metric, where a higher cost indicates a worse path, is defined using this sensitivity, which can be understood simply as gradient(loss)/gradient(parameter). In other words, rather than merely introducing a more complicated metric, the Riemannian metric acts as a brake on the updates generated from the training data, which is the main signal.

I believe that mathematics can be incorporated more deeply into AI if, when using theory A and theory B, the elements of theory A and the elements of theory B are each designed appropriately for the specific situation.