Yeachan Park

Hyoje Lee, Yeachan Park, Hyun Seo et al.

To boost the performance, deep neural networks require deeper or wider network structures that involve massive computational and memory costs. To alleviate this issue, the self-knowledge distillation method regularizes the model by distilling the internal knowledge of the model itself. Conventional self-knowledge distillation methods require additional trainable parameters or are dependent on the data. In this paper, we propose a simple and effective self-knowledge distillation method using a dropout (SD-Dropout). SD-Dropout distills the posterior distributions of multiple models through a dropout sampling. Our method does not require any additional trainable modules, does not rely on data, and requires only simple operations. Furthermore, this simple method can be easily combined with various self-knowledge distillation approaches. We provide a theoretical and experimental analysis of the effect of forward and reverse KL-divergences in our work. Extensive experiments on various vision tasks, i.e., image classification, object detection, and distribution shift, demonstrate that the proposed method can effectively improve the generalization of a single network. Further experiments show that the proposed method also improves calibration performance, adversarial robustness, and out-of-distribution detection ability.

Yeachan Park, Geonho Hwang, Wonyeol Lee et al.

Most existing expressivity theories for neural networks assume exact real arithmetic, whereas practical neural networks are executed under finite-precision floating-point arithmetic with implementation-dependent execution semantics. Recent works have begun studying the expressive power of floating-point neural networks, but existing results are limited to highly restricted activation functions and idealized assumptions such as fixed left-to-right reduction orders and correctly rounded activation implementations. In this work, we study the expressive power of floating-point neural networks under generalized floating-point execution semantics, including arbitrary reduction orders and inexact activation implementations with bounded ulp errors. We investigate when floating-point neural networks can represent arbitrary functions between floating-point domains exactly. To this end, we introduce a general distinguishability framework and show that the ability to distinguish every pair of distinct inputs in the first layer is necessary for universal representability. This characterization yields broad classes of activation implementations that are not universal representators, extending previous isolated counterexamples such as the correctly rounded cosine activation. We further prove that a suitable form of distinguishability is also sufficient for universal representability under mild conditions on the activation implementation. Using this framework, we establish universal representability results for a broad class of practical activation functions, including implementations of $\mathrm{Sigmoid}$, $\tanh$, $\mathrm{ReLU}$, $\mathrm{ELU}$, $\mathrm{SeLU}$, $\mathrm{GeLU}$, $\mathrm{Swish}$, $\mathrm{Mish}$, and $\sin$, under significantly more realistic floating-point execution models than previously known.

Seewoo Lee, Byung-Hak Hwang, Hyojae Lim et al.

We present Lean-GAP (Lean-Graduate Agebra Problems), 430 formalized graduate-level algebra problems from the textbook Abstract Algebra by Dummit and Foote. We develop a scalable pipeline consisting of PDF-to-LaTeX preprocessing, autoformalization into Lean 4, and verification of informal-formal correspondence. While the preprocessing and autoformalization stages can be largely automated, we find that verification remains the most subtle and labor-intensive component, requiring careful human oversight. Our contributions include (i) the construction of a structured dataset of formalized exercises, (ii) a systematic methodology for formalizing textbook mathematics, and (iii) an analysis of recurring challenges in the formalization process. We also compare the performance of different autoformalization models and highlight key bottlenecks in translating informal statements into formal language.

Hyeonbin Hwang, Yeachan Park

Grokking, the sudden transition from memorization to generalization, is characterized by the emergence of low-dimensional representations, yet the mechanism underlying this organization remains elusive. We propose that intrinsic task symmetries primarily drive grokking and shape the geometry of the model's representation space. We identify a consistent three-stage training dynamic underlying grokking: (i) memorization, (ii) symmetry acquisition, and (iii) geometric organization. We show that generalization emerges during the symmetry acquisition phase, after which representations reorganize into a structured, task-aligned geometry. We validate this symmetry-driven account across diverse algorithmic domains, including algebraic, structural, and relational reasoning tasks. Building on these findings, we introduce a symmetry-based diagnostic that anticipates the onset of generalization and propose strategies to accelerate it. Together, our results establish intrinsic symmetry as the key factor enabling neural networks to move beyond memorization and achieve robust algorithmic reasoning.

Guijin Son, Seungone Kim, Catherine Arnett et al.

Following the recent achievement of gold-medal performance on the IMO by frontier LLMs, the community is searching for the next meaningful and challenging target for measuring LLM reasoning. Whereas olympiad-style problems measure step-by-step reasoning alone, research-level problems use such reasoning to advance the frontier of mathematical knowledge itself, emerging as a compelling alternative. Yet research-level math benchmarks remain scarce because such problems are difficult to source (e.g., Riemann Bench and FrontierMath-Tier 4 contain 25 and 50 problems, respectively). To support reliable evaluation of next-generation frontier models, we introduce Soohak, a 439-problem benchmark newly authored from scratch by 64 mathematicians. Soohak comprises two subsets. On the Challenge subset, frontier models including Gemini-3-Pro, GPT-5, and Claude-Opus-4.5 reach 30.4%, 26.4%, and 10.4% respectively, leaving substantial headroom, while leading open-weight models such as Qwen3-235B, GPT-OSS-120B, and Kimi-2.5 remain below 15%. Notably, beyond standard problem solving, Soohak introduces a refusal subset that probes a capability intrinsic to research mathematics: recognizing ill-posed problems and pausing rather than producing confident but unjustified answers. On this subset, no model exceeds 50%, identifying refusal as a new optimization target that current models do not directly address. To prevent contamination, the dataset will be publicly released in late 2026, with model evaluations available upon request in the interim.

Yeachan Park, Sejun Park, Geonho Hwang

Existing works on the expressive power of neural networks typically assume real parameters and exact operations. In this work, we study the expressive power of quantized networks under discrete fixed-point parameters and inexact fixed-point operations with round-off errors. We first provide a necessary condition and a sufficient condition on fixed-point arithmetic and activation functions for quantized networks to represent all fixed-point functions from fixed-point vectors to fixed-point numbers. Then, we show that various popular activation functions satisfy our sufficient condition, e.g., Sigmoid, ReLU, ELU, SoftPlus, SiLU, Mish, and GELU. In other words, networks using those activation functions are capable of representing all fixed-point functions. We further show that our necessary condition and sufficient condition coincide under a mild condition on activation functions: e.g., for an activation function $σ$, there exists a fixed-point number $x$ such that $σ(x)=0$. Namely, we find a necessary and sufficient condition for a large class of activation functions. We lastly show that even quantized networks using binary weights in $\{-1,1\}$ can also represent all fixed-point functions for practical activation functions.

Sejun Park, Yeachan Park, Geonho Hwang

The study on the expressive power of transformers shows that transformers are permutation equivariant, and they can approximate all permutation-equivariant continuous functions on a compact domain. However, these results are derived under real parameters and exact operations, while real implementations on computers can only use a finite set of numbers and inexact machine operations with round-off errors. In this work, we investigate the representability of floating-point transformers that use floating-point parameters and floating-point operations. Unlike existing results under exact operations, we first show that floating-point transformers can represent a class of non-permutation-equivariant functions even without positional encoding. Furthermore, we prove that floating-point transformers can represent all permutation-equivariant functions when the sequence length is bounded, but they cannot when the sequence length is large. We also found the minimal equivariance structure in floating-point transformers, and show that all non-trivial additive positional encoding can harm the representability of floating-point transformers.

Sejun Park, Yeachan Park, Geonho Hwang

Theoretical studies show that for any differentiable function on a compact domain, there exists a neural network that approximates both the function values and gradients. However, such a result cannot be used in practice since it assumes real parameters and exact internal operations. In contrast, real implementations only use a finite subset of reals and machine operations with round-off errors. In this work, we investigate whether a similar result holds for neural networks under floating-point arithmetic, when the gradient with respect to the input is computed by the automatic differentiation algorithm $D^\mathtt{AD}$. We first show that given a floating-point function $ϕ$ (e.g., a loss function), arbitrary function values and gradients can be represented by a floating-point network $f$ and $D^\mathtt{AD}(ϕ\circ f)$, respectively. We further extend this result: given $ϕ_1,\dots,ϕ_n$, $D^\mathtt{AD}(ϕ_i\circ f)$ can simultaneously represent arbitrary gradients while $f$ represents the target values, under mild conditions. Our results hold for practical activation functions, e.g., $\mathrm{ReLU}$, $\mathrm{ELU}$, $\mathrm{GeLU}$, $\mathrm{Swish}$, $\mathrm{Sigmoid}$, and $\mathrm{tanh}$.

Yeachan Park

In the field of machine learning, comprehending the intricate training dynamics of neural networks poses a significant challenge. This paper explores the training dynamics of neural networks, particularly whether these dynamics can be expressed in a general closed-form solution. We demonstrate that the dynamics of the gradient flow in two-layer narrow networks is not an integrable system. Integrable systems are characterized by trajectories confined to submanifolds defined by level sets of first integrals (invariants), facilitating predictable and reducible dynamics. In contrast, non-integrable systems exhibit complex behaviors that are difficult to predict. To establish the non-integrability, we employ differential Galois theory, which focuses on the solvability of linear differential equations. We demonstrate that under mild conditions, the identity component of the differential Galois group of the variational equations of the gradient flow is non-solvable. This result confirms the system's non-integrability and implies that the training dynamics cannot be represented by Liouvillian functions, precluding a closed-form solution for describing these dynamics. Our findings highlight the necessity of employing numerical methods to tackle optimization problems within neural networks. The results contribute to a deeper understanding of neural network training dynamics and their implications for machine learning optimization strategies.

Yoonsoo Nam, Seok Hyeong Lee, Clementine C J Domine et al.

In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural network dynamics. These models follow the dynamical feedback principle, which describes how layers mutually govern and amplify each other's evolution. This principle extends beyond the simplified models, successfully explaining a wide range of dynamical phenomena in deep neural networks, including neural collapse, emergence, lazy and rich regimes, and grokking. In this position paper, we call for the use of layerwise linear models retaining the core principles of neural dynamical phenomena to accelerate the science of deep learning.

Geonho Hwang, Wonyeol Lee, Yeachan Park et al.

The classical universal approximation (UA) theorem for neural networks establishes mild conditions under which a feedforward neural network can approximate a continuous function $f$ with arbitrary accuracy. A recent result shows that neural networks also enjoy a more general interval universal approximation (IUA) theorem, in the sense that the abstract interpretation semantics of the network using the interval domain can approximate the direct image map of $f$ (i.e., the result of applying $f$ to a set of inputs) with arbitrary accuracy. These theorems, however, rest on the unrealistic assumption that the neural network computes over infinitely precise real numbers, whereas their software implementations in practice compute over finite-precision floating-point numbers. An open question is whether the IUA theorem still holds in the floating-point setting. This paper introduces the first IUA theorem for floating-point neural networks that proves their remarkable ability to perfectly capture the direct image map of any rounded target function $f$, showing no limits exist on their expressiveness. Our IUA theorem in the floating-point setting exhibits material differences from the real-valued setting, which reflects the fundamental distinctions between these two computational models. This theorem also implies surprising corollaries, which include (i) the existence of provably robust floating-point neural networks; and (ii) the computational completeness of the class of straight-line programs that use only floating-point additions and multiplications for the class of all floating-point programs that halt.

Yeachan Park, Geonho Hwang, Wonyeol Lee et al.

The study of the expressive power of neural networks has investigated the fundamental limits of neural networks. Most existing results assume real-valued inputs and parameters as well as exact operations during the evaluation of neural networks. However, neural networks are typically executed on computers that can only represent a tiny subset of the reals and apply inexact operations, i.e., most existing results do not apply to neural networks used in practice. In this work, we analyze the expressive power of neural networks under a more realistic setup: when we use floating-point numbers and operations as in practice. Our first set of results assumes floating-point operations where the significand of a float is represented by finite bits but its exponent can take any integer value. Under this setup, we show that neural networks using a binary threshold unit or ReLU can memorize any finite input/output pairs and can approximate any continuous function within an arbitrary error. In particular, the number of parameters in our constructions for universal approximation and memorization coincides with that in classical results assuming exact mathematical operations. We also show similar results on memorization and universal approximation when floating-point operations use finite bits for both significand and exponent; these results are applicable to many popular floating-point formats such as those defined in the IEEE 754 standard (e.g., 32-bit single-precision format) and bfloat16.

Yeachan Park, Myeongho Jeon, Junho Lee et al.

A recent line of convolutional neural network-based works has succeeded in capturing rain streaks. However, difficulties in detailed recovery still remain. In this paper, we present a multi-level connection and wide regional non-local block network (MCW-Net) to properly restore the original background textures in rainy images. Unlike existing encoder-decoder-based image deraining models that improve performance with additional branches, MCW-Net improves performance by maximizing information utilization without additional branches through the following two proposed methods. The first method is a multi-level connection that repeatedly connects multi-level features of the encoder network to the decoder network. Multi-level connection encourages the decoding process to use the feature information of all levels. In multi-level connection, channel-wise attention is considered to learn which level of features is important in the decoding process of the current level. The second method is a wide regional non-local block. As rain streaks primarily exhibit a vertical distribution, we divide the grid of the image into horizontally-wide patches and apply a non-local operation to each region to explore the rich rain-free background information. Experimental results on both synthetic and real-world rainy datasets demonstrate that the proposed model significantly outperforms existing state-of-the-art models. Furthermore, the results of the joint deraining and segmentation experiment prove that our model contributes effectively to other vision tasks.

Yeachan Park, Myungjoo Kang

Machine learning models can leak information regarding the dataset they have trained. In this paper, we present the first membership inference attack against black-boxed object detection models that determines whether the given data records are used in the training. To attack the object detection model, we devise a novel method named as called a canvas method, in which predicted bounding boxes are drawn on an empty image for the attack model input. Based on the experiments, we successfully reveal the membership status of privately sensitive data trained using one-stage and two-stage detection models. We then propose defense strategies and also conduct a transfer attack between the models and datasets. Our results show that object detection models are also vulnerable to inference attacks like other models.