Sungyoon Kim

Euna Jung, Jungwon Park, Jaekeol Choi et al.

The recent advancement in language representation modeling has broadly affected the design of dense retrieval models. In particular, many of the high-performing dense retrieval models evaluate representations of query and document using BERT, and subsequently apply a cosine-similarity based scoring to determine the relevance. BERT representations, however, are known to follow an anisotropic distribution of a narrow cone shape and such an anisotropic distribution can be undesirable for the cosine-similarity based scoring. In this work, we first show that BERT-based DR also follows an anisotropic distribution. To cope with the problem, we introduce unsupervised post-processing methods of Normalizing Flow and whitening, and develop token-wise method in addition to the sequence-wise method for applying the post-processing methods to the representations of dense retrieval models. We show that the proposed methods can effectively enhance the representations to be isotropic, then we perform experiments with ColBERT and RepBERT to show that the performance (NDCG at 10) of document re-ranking can be improved by 5.17\%$\sim$8.09\% for ColBERT and 6.88\%$\sim$22.81\% for RepBERT. To examine the potential of isotropic representation for improving the robustness of DR models, we investigate out-of-distribution tasks where the test dataset differs from the training dataset. The results show that isotropic representation can achieve a generally improved performance. For instance, when training dataset is MS-MARCO and test dataset is Robust04, isotropy post-processing can improve the baseline performance by up to 24.98\%. Furthermore, we show that an isotropic model trained with an out-of-distribution dataset can even outperform a baseline model trained with the in-distribution dataset.

Calvin Ang, Sungyoon Kim, Mert Pilanci

We study entrywise scalar quantization of two matrices prior to multiplication. Given $A\in R^{m\times k}$ and $B\in R^{k\times n}$, we quantize entries of $A$ and $B$ independently using scalar quantizers with $K_X$ and $K_Y$ levels per entry, and form $\widehat C=\widehat A\,\widehat B$. The objective is to minimize the matrix multiplication mean-squared error (MSE) $E[\|{AB-\widehat A\widehat B}\|_F^2]$ under a pair-i.i.d.\ inner-product model. In the high-resolution regime $K_X,K_Y\to\infty$, we derive a sharp $K^{-2}$ asymptotic expansion for $\mathcal{E}$, identify the exact optimal leading constants, and characterize asymptotically optimal quantization center densities in terms of conditional second moments. We then specialize to correlated Gaussian multiplicative pairs, obtaining a closed-form optimal point density \[ λ^\star(u)\ \propto\ \exp\!\left(-\frac{u^2}{6}\right)\bigl((1-ρ^2)+ρ^2u^2\bigr)^{1/3}, \qquad u=\frac{x}{σ_X}, \] with the same form for $y/σ_Y$, and prove a correlation-driven phase transition: the density is unimodal at the origin for $|ρ|\leq 1/\sqrt{3}$ and becomes bimodal for $|ρ|>1/\sqrt{3}$ with peaks at $u_{\mathrm{peak}}=\pm\sqrt{3-1/ρ^2}$. We show our method's applicability in synthetic experiments such as matrix multiplication quantization and least squares optimization, as well as quantization of large language model key and query activations.

Fangzhao Zhang, Sungyoon Kim, Erica Zhang et al.

Mode connectivity has been widely studied, yet the role of the optimizer remains underexplored. We revisit it through optimizer-induced implicit regularization, asking how connectivity behaves when restricted to solutions constrained by a given optimizer. For two-layer ReLU networks, we show that solutions from a single optimizer -- AdamW, Muon, or others in the Lion-$\mathcal{K}$ family -- form a connected set at sufficiently large width, a result not implied by prior work. We then characterize how optimizer-induced regions interact: at large width two different regions can be disjoint or overlap depending on regularization, while in our small-width example AdamW and Muon converge to disconnected zero-loss components separated by a provable loss barrier. Empirically, in GPT-2 pretraining, we observe same-optimizer paths preserve each model's spectrum while cross-optimizer paths traverse a smooth transition. Our results reveal optimizer-dependent structure beyond classical mode connectivity literature.

Sungyoon Kim, Youngjun Kim, Kihyo Moon et al.

The advent of large language models has revolutionized natural language processing, but their increasing complexity has led to substantial training costs, resource demands, and environmental impacts. In response, sparse Mixture-of-Experts (MoE) models have emerged as a promising alternative to dense models. Since training MoE models from scratch can be prohibitively expensive, recent studies have explored leveraging knowledge from pre-trained non-MoE models. However, existing approaches have limitations, such as requiring significant hardware resources and data. We propose a novel algorithm, LaDiMo, which efficiently converts a Transformer-based non-MoE model into a MoE model with minimal additional training cost. LaDiMo consists of two stages: layer-wise expert construction and routing policy decision. By harnessing the concept of Knowledge Distillation, we compress the model and rapidly recover its performance. Furthermore, we develop an adaptive router that optimizes inference efficiency by profiling the distribution of routing weights and determining a layer-wise policy that balances accuracy and latency. We demonstrate the effectiveness of our method by converting the LLaMA2-7B model to a MoE model using only 100K tokens, reducing activated parameters by over 20% while keeping accuracy. Our approach offers a flexible and efficient solution for building and deploying MoE models.

Sungyoon Kim, Yunseon Choi, Daiki E. Matsunaga et al.

Offline Goal-Conditioned Reinforcement Learning (Offline GCRL) is an important problem in RL that focuses on acquiring diverse goal-oriented skills solely from pre-collected behavior datasets. In this setting, the reward feedback is typically absent except when the goal is achieved, which makes it difficult to learn policies especially from a finite dataset of suboptimal behaviors. In addition, realistic scenarios involve long-horizon planning, which necessitates the extraction of useful skills within sub-trajectories. Recently, the conditional diffusion model has been shown to be a promising approach to generate high-quality long-horizon plans for RL. However, their practicality for the goal-conditioned setting is still limited due to a number of technical assumptions made by the methods. In this paper, we propose SSD (Sub-trajectory Stitching with Diffusion), a model-based offline GCRL method that leverages the conditional diffusion model to address these limitations. In summary, we use the diffusion model that generates future plans conditioned on the target goal and value, with the target value estimated from the goal-relabeled offline dataset. We report state-of-the-art performance in the standard benchmark set of GCRL tasks, and demonstrate the capability to successfully stitch the segments of suboptimal trajectories in the offline data to generate high-quality plans.

Sungyoon Kim, Mert Pilanci

In this paper, we study the optimality gap between two-layer ReLU networks regularized with weight decay and their convex relaxations. We show that when the training data is random, the relative optimality gap between the original problem and its relaxation can be bounded by a factor of O(log n^0.5), where n is the number of training samples. A simple application leads to a tractable polynomial-time algorithm that is guaranteed to solve the original non-convex problem up to a logarithmic factor. Moreover, under mild assumptions, we show that local gradient methods converge to a point with low training loss with high probability. Our result is an exponential improvement compared to existing results and sheds new light on understanding why local gradient methods work well.

Sungyoon Kim, Aaron Mishkin, Mert Pilanci · stanford

We discuss several aspects of the loss landscape of regularized neural networks: the structure of stationary points, connectivity of optimal solutions, path with nonincreasing loss to arbitrary global optimum, and the nonuniqueness of optimal solutions, by casting the problem into an equivalent convex problem and considering its dual. Starting from two-layer neural networks with scalar output, we first characterize the solution set of the convex problem using its dual and further characterize all stationary points. With the characterization, we show that the topology of the global optima goes through a phase transition as the width of the network changes, and construct counterexamples where the problem may have a continuum of optimal solutions. Finally, we show that the solution set characterization and connectivity results can be extended to different architectures, including two-layer vector-valued neural networks and parallel three-layer neural networks.

Sungyoon Kim, Rajat Vadiraj Dwaraknath, Longling geng et al.

Iterative methods for computing matrix functions have been extensively studied and their convergence speed can be significantly improved with the right tuning of parameters and by mixing different iteration types. Handtuning the design options for optimal performance can be cumbersome, especially in modern computing environments: numerous different classical iterations and their variants exist, each with non-trivial per-step cost and tuning parameters. To this end, we propose MatRL -- a reinforcement learning based framework that automatically discovers iterative algorithms for computing matrix functions. The key idea is to treat algorithm design as a sequential decision-making process. Monte-Carlo tree search is then used to plan a hybrid sequence of matrix iterations and step sizes, tailored to a specific input matrix distribution and computing environment. Moreover, we also show that the learned algorithms provably generalize to sufficiently large matrices drawn from the same distribution. Finally, we corroborate our theoretical results with numerical experiments demonstrating that MatRL produces algorithms that outperform various baselines in the literature.

Yifei Wang, Sungyoon Kim, Paul Chu et al.

We introduce randomized algorithms to Clifford's Geometric Algebra, generalizing randomized linear algebra to hypercomplex vector spaces. This novel approach has many implications in machine learning, including training neural networks to global optimality via convex optimization. Additionally, we consider fine-tuning large language model (LLM) embeddings as a key application area, exploring the intersection of geometric algebra and modern AI techniques. In particular, we conduct a comparative analysis of the robustness of transfer learning via embeddings, such as OpenAI GPT models and BERT, using traditional methods versus our novel approach based on convex optimization. We test our convex optimization transfer learning method across a variety of case studies, employing different embeddings (GPT-4 and BERT embeddings) and different text classification datasets (IMDb, Amazon Polarity Dataset, and GLUE) with a range of hyperparameter settings. Our results demonstrate that convex optimization and geometric algebra not only enhances the performance of LLMs but also offers a more stable and reliable method of transfer learning via embeddings.