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Eren Mehmet Kıral

Publications and source records attributed to Eren Mehmet Kıral.

5 recordsLinked to original sources
arXiv2026

Guided Data Generation for Understanding Model Behavior

We propose a method for generating distributions over the input space as an inspection tool for understanding trained models. Our framework poses questions of the form ``which inputs would make a trained model exhibit a specified behavior?'' and encodes each question through a guidance function. The generated data provide insights into how the models behave. To showcase our framework, we pose queries such as generating distributions of data where a specified label would be predicted by the model, where two distinct models would disagree, where the output is sensitive to parameter perturbations, and where predictions would be risky. Our method can be applied with a variety of classification and regression tasks and on a range of model types.

cs.LG↗
arXiv2025

Log-Normal Multiplicative Dynamics for Stable Low-Precision Training of Large Networks

Studies in neuroscience have shown that biological synapses follow a log-normal distribution whose transitioning can be explained by noisy multiplicative dynamics. Biological networks can function stably even under dynamically fluctuating conditions arising due to unreliable synaptic transmissions. Here we ask: Is it possible to design similar multiplicative training in artificial neural networks? To answer this question, we derive a Bayesian learning rule that assumes log-normal posterior distributions over weights which gives rise to a new Log-Normal Multiplicative Dynamics (LMD) algorithm. The algorithm uses multiplicative updates with both noise and regularization applied multiplicatively. The method is as easy to implement as Adam and only requires one additional vector to store. Our results show that LMD achieves stable and accurate training-from-scratch under low-precision forward operations for Vision Transformer and GPT-2. These results suggest that multiplicative dynamics, a biological feature, may enable stable low-precision inference and learning on future energy-efficient hardware.

cs.LG↗
arXiv2023

The Lie-Group Bayesian Learning Rule

The Bayesian Learning Rule provides a framework for generic algorithm design but can be difficult to use for three reasons. First, it requires a specific parameterization of exponential family. Second, it uses gradients which can be difficult to compute. Third, its update may not always stay on the manifold. We address these difficulties by proposing an extension based on Lie-groups where posteriors are parametrized through transformations of an arbitrary base distribution and updated via the group's exponential map. This simplifies all three difficulties for many cases, providing flexible parametrizations through group's action, simple gradient computation through reparameterization, and updates that always stay on the manifold. We use the new learning rule to derive a new algorithm for deep learning with desirable biologically-plausible attributes to learn sparse features. Our work opens a new frontier for the design of new algorithms by exploiting Lie-group structures.

cs.LG↗
arXiv2020

Parametrization of Kloosterman sets and $\mathrm{SL}_3$-Kloosterman sums

We stratify the $\mathrm{SL}_3$ big cell Kloosterman sets using the reduced word decomposition of the Weyl group element, inspired by the Bott-Samelson factorization. Thus the $\mathrm{SL}_3$ long word Kloosterman sum is decomposed into finer parts, and we write it as a finite sum of a product of two classical Kloosterman sums. The fine Kloosterman sums end up being the correct pieces to consider in the Bruggeman-Kuznetsov trace formula on the congruence subgroup $Γ_0(N)\subseteq \mathrm{SL}_3(\mathbb{Z})$. Another application is a new explicit formula, expressing the triple divisor sum function in terms of a double Dirichlet series of exponential sums, generalizing Ramanujan's formula.

math.NT↗