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Yongyi Yang

Publications and source records attributed to Yongyi Yang.

At least 19 recordsLinked to original sources
arXiv2026

Revisiting RaBitQ and TurboQuant: A Symmetric Comparison of Methods, Theory, and Experiments

This technical note revisits the relationship between RaBitQ and TurboQuant under a unified comparison framework. We compare the two methods in terms of methodology, theoretical guarantees, and empirical performance, using a reproducible, transparent, and symmetric setup. Our results show that, despite the claimed advantage of TurboQuant, TurboQuant performs worse than RaBitQ in most tested settings of inner-product estimation, nearest-neighbor search and KV cache quantization. We further find that several reported runtime and recall results in the TurboQuant paper could not be reproduced from the released implementation under the stated configuration. Overall, this note clarifies the shared structure and genuine differences between the two lines of work, while documenting reproducibility issues in the experimental results reported by the TurboQuant paper.

cs.LG↗
arXiv2026

SNIP: An Adaptive Mixed Precision Framework for Subbyte Large Language Model Training

Training large language models (LLMs) efficiently while preserving model quality poses significant challenges, particularly with subbyte precision supported by state-of-the-art GPUs. Current mixed-precision training approaches either apply uniform precision to all GEMM operations or rely on heuristic-based methods that fail to generalize during training, leading to suboptimal convergence and instability. To address these challenges, this paper introduces SNIP, a fine-grained adaptive mixed-precision training framework for LLM pretraining that supports subbyte precision. SNIP periodically collects statistics on activations, gradients, and optimizer states to assess the precision loss impact on model quality. We define two key metrics: loss divergence in the forward pass, caused by quantization-induced increases in training loss, and weight divergence in the backward pass, which measures error propagation through gradients affecting model updates. These metrics guide an Integer Linear Programming (ILP) problem that systematically optimizes layerwise precision to minimize overall quality loss while meeting efficiency targets. Experiments on 1B, 3B, 7B and 70B Llama-like models demonstrate that SNIP consistently outperforms existing baselines, reducing FLOPs by up to 80% while preserving model quality across different model sizes and training phases with minimal computational overhead.

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arXiv2026

mHC-lite: You Don't Need 20 Sinkhorn-Knopp Iterations

Hyper-Connections (HC) generalizes residual connections by introducing dynamic residual matrices that mix information across multiple residual streams, accelerating convergence in deep neural networks. However, unconstrained residual matrices can compromise training stability. To address this, DeepSeek's Manifold-Constrained Hyper-Connections (mHC) approximately projects these matrices onto the Birkhoff polytope via iterative Sinkhorn--Knopp (SK) normalization. We identify two limitations of this approach: (i) finite SK iterations do not guarantee exact doubly stochasticity, leaving an approximation gap that can accumulate through network depth and undermine stability; (ii) efficient SK implementation requires highly specialized CUDA kernels, raising engineering barriers and reducing portability. Motivated by the Birkhoff--von Neumann theorem, we propose mHC-lite, a simple reparameterization that explicitly constructs doubly stochastic matrices as convex combinations of permutation matrices. This approach guarantees exact doubly stochasticity by construction and can be implemented using only native matrix operations. Extensive experiments demonstrate that mHC-lite matches or exceeds mHC in performance while achieving higher training throughput with a naive implementation and eliminating the residual instabilities observed in both HC and mHC. The code is publicly available at https://github.com/FFTYYY/mhc-lite.

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arXiv2025

An Equivariance Toolbox for Learning Dynamics

Many theoretical results in deep learning can be traced to symmetry or equivariance of neural networks under parameter transformations. However, existing analyses are typically problem-specific and focus on first-order consequences such as conservation laws, while the implications for second-order structure remain less understood. We develop a general equivariance toolbox that yields coupled first- and second-order constraints on learning dynamics. The framework extends classical Noether-type analyses in three directions: from gradient constraints to Hessian constraints, from symmetry to general equivariance, and from continuous to discrete transformations. At the first order, our framework unifies conservation laws and implicit-bias relations as special cases of a single identity. At the second order, it provides structural predictions about curvature: which directions are flat or sharp, how the gradient aligns with Hessian eigenspaces, and how the loss landscape geometry reflects the underlying transformation structure. We illustrate the framework through several applications, recovering known results while also deriving new characterizations that connect transformation structure to modern empirical observations about optimization geometry.

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arXiv2025

Topological Invariance and Breakdown in Learning

We prove that for a broad class of permutation-equivariant learning rules (including SGD, Adam, and others), the training process induces a bi-Lipschitz mapping between neurons and strongly constrains the topology of the neuron distribution during training. This result reveals a qualitative difference between small and large learning rates $\eta$. With a learning rate below a topological critical point $\eta^*$, the training is constrained to preserve all topological structure of the neurons. In contrast, above $\eta^*$, the learning process allows for topological simplification, making the neuron manifold progressively coarser and thereby reducing the model's expressivity. Viewed in combination with the recent discovery of the edge of stability phenomenon, the learning dynamics of neuron networks under gradient descent can be divided into two phases: first they undergo smooth optimization under topological constraints, and then enter a second phase where they learn through drastic topological simplifications. A key feature of our theory is that it is independent of specific architectures or loss functions, enabling the universal application of topological methods to the study of deep learning.

cs.LG↗
arXiv2025

Provable Low-Frequency Bias of In-Context Learning of Representations

In-context learning (ICL) enables large language models (LLMs) to acquire new behaviors from the input sequence alone without any parameter updates. Recent studies have shown that ICL can surpass the original meaning learned in pretraining stage through internalizing the structure the data-generating process (DGP) of the prompt into the hidden representations. However, the mechanisms by which LLMs achieve this ability is left open. In this paper, we present the first rigorous explanation of such phenomena by introducing a unified framework of double convergence, where hidden representations converge both over context and across layers. This double convergence process leads to an implicit bias towards smooth (low-frequency) representations, which we prove analytically and verify empirically. Our theory explains several open empirical observations, including why learned representations exhibit globally structured but locally distorted geometry, and why their total energy decays without vanishing. Moreover, our theory predicts that ICL has an intrinsic robustness towards high-frequency noise, which we empirically confirm. These results provide new insights into the underlying mechanisms of ICL, and a theoretical foundation to study it that hopefully extends to more general data distributions and settings.

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arXiv2025

New Evidence of the Two-Phase Learning Dynamics of Neural Networks

Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this transition is still incomplete. In this paper, we introduce an interval-wise perspective that compares network states across a time window, revealing two new phenomena that illuminate the two-phase nature of deep learning. i) \textbf{The Chaos Effect.} By injecting an imperceptibly small parameter perturbation at various stages, we show that the response of the network to the perturbation exhibits a transition from chaotic to stable, suggesting there is an early critical period where the network is highly sensitive to initial conditions; ii) \textbf{The Cone Effect.} Tracking the evolution of the empirical Neural Tangent Kernel (eNTK), we find that after this transition point the model's functional trajectory is confined to a narrow cone-shaped subset: while the kernel continues to change, it gets trapped into a tight angular region. Together, these effects provide a structural, dynamical view of how deep networks transition from sensitive exploration to stable refinement during training.

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arXiv2025

RaanA: A Fast, Flexible, and Data-Efficient Post-Training Quantization Algorithm

Post-training Quantization (PTQ) has become a widely used technique for improving inference efficiency of large language models (LLMs). However, existing PTQ methods generally suffer from crucial limitations such as heavy calibration data requirements and inflexible choice of target number of bits. In this paper, we propose RaanA, a unified PTQ framework that overcomes these challenges by introducing two novel components: 1) RaBitQ-H, a variant of a randomized vector quantization method RaBitQ, designed for fast, accurate, and highly efficient quantization; and 2) AllocateBits, an algorithm that optimally allocates bit-widths across layers based on their quantization sensitivity. RaanA achieves competitive performance with state-of-the-art quantization methods while being extremely fast, requiring minimal calibration data, and enabling flexible bit allocation. Extensive experiments demonstrate RaanA's efficacy in balancing efficiency and accuracy. The code is publicly available at https://github.com/FFTYYY/RaanA .

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arXiv2025

On the Cone Effect in the Learning Dynamics

Understanding the learning dynamics of neural networks is a central topic in the deep learning community. In this paper, we take an empirical perspective to study the learning dynamics of neural networks in real-world settings. Specifically, we investigate the evolution process of the empirical Neural Tangent Kernel (eNTK) during training. Our key findings reveal a two-phase learning process: i) in Phase I, the eNTK evolves significantly, signaling the rich regime, and ii) in Phase II, the eNTK keeps evolving but is constrained in a narrow space, a phenomenon we term the cone effect. This two-phase framework builds on the hypothesis proposed by Fort et al. (2020), but we uniquely identify the cone effect in Phase II, demonstrating its significant performance advantages over fully linearized training.

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arXiv2024

ICLR: In-Context Learning of Representations

Recent work has demonstrated that semantics specified by pretraining data influence how representations of different concepts are organized in a large language model (LLM). However, given the open-ended nature of LLMs, e.g., their ability to in-context learn, we can ask whether models alter these pretraining semantics to adopt alternative, context-specified ones. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, do models reorganize their representations in accordance with these novel semantics? To answer this question, we take inspiration from the theory of conceptual role semantics and define a toy "graph tracing" task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.) and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization from pretrained semantic representations to in-context representations aligned with the graph structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, providing evidence towards an implicit optimization process to infer context-specified semantics. Overall, our findings indicate scaling context-size can flexibly re-organize model representations, possibly unlocking novel capabilities.

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arXiv2024

Swing-by Dynamics in Concept Learning and Compositional Generalization

Prior work has shown that text-conditioned diffusion models can learn to identify and manipulate primitive concepts underlying a compositional data-generating process, enabling generalization to entirely novel, out-of-distribution compositions. Beyond performance evaluations, these studies develop a rich empirical phenomenology of learning dynamics, showing that models generalize sequentially, respecting the compositional hierarchy of the data-generating process. Moreover, concept-centric structures within the data significantly influence a model's speed of learning the ability to manipulate a concept. In this paper, we aim to better characterize these empirical results from a theoretical standpoint. Specifically, we propose an abstraction of prior work's compositional generalization problem by introducing a structured identity mapping (SIM) task, where a model is trained to learn the identity mapping on a Gaussian mixture with structurally organized centroids. We mathematically analyze the learning dynamics of neural networks trained on this SIM task and show that, despite its simplicity, SIM's learning dynamics capture and help explain key empirical observations on compositional generalization with diffusion models identified in prior work. Our theory also offers several new insights -- e.g., we find a novel mechanism for non-monotonic learning dynamics of test loss in early phases of training. We validate our new predictions by training a text-conditioned diffusion model, bridging our simplified framework and complex generative models. Overall, this work establishes the SIM task as a meaningful theoretical abstraction of concept learning dynamics in modern generative models.

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arXiv2024

Practical and Asymptotically Optimal Quantization of High-Dimensional Vectors in Euclidean Space for Approximate Nearest Neighbor Search

Approximate nearest neighbor (ANN) query in high-dimensional Euclidean space is a key operator in database systems. For this query, quantization is a popular family of methods developed for compressing vectors and reducing memory consumption. Recently, a method called RaBitQ achieves the state-of-the-art performance among these methods. It produces better empirical performance in both accuracy and efficiency when using the same compression rate and provides rigorous theoretical guarantees. However, the method is only designed for compressing vectors at high compression rates (32x) and lacks support for achieving higher accuracy by using more space. In this paper, we introduce a new quantization method to address this limitation by extending RaBitQ. The new method inherits the theoretical guarantees of RaBitQ and achieves the asymptotic optimality in terms of the trade-off between space and error bounds as to be proven in this study. Additionally, we present efficient implementations of the method, enabling its application to ANN queries to reduce both space and time consumption. Extensive experiments on real-world datasets confirm that our method consistently outperforms the state-of-the-art baselines in both accuracy and efficiency when using the same amount of memory.

cs.DB↗
arXiv2024

HERTA: A High-Efficiency and Rigorous Training Algorithm for Unfolded Graph Neural Networks

As a variant of Graph Neural Networks (GNNs), Unfolded GNNs offer enhanced interpretability and flexibility over traditional designs. Nevertheless, they still suffer from scalability challenges when it comes to the training cost. Although many methods have been proposed to address the scalability issues, they mostly focus on per-iteration efficiency, without worst-case convergence guarantees. Moreover, those methods typically add components to or modify the original model, thus possibly breaking the interpretability of Unfolded GNNs. In this paper, we propose HERTA: a High-Efficiency and Rigorous Training Algorithm for Unfolded GNNs that accelerates the whole training process, achieving a nearly-linear time worst-case training guarantee. Crucially, HERTA converges to the optimum of the original model, thus preserving the interpretability of Unfolded GNNs. Additionally, as a byproduct of HERTA, we propose a new spectral sparsification method applicable to normalized and regularized graph Laplacians that ensures tighter bounds for our algorithm than existing spectral sparsifiers do. Experiments on real-world datasets verify the superiority of HERTA as well as its adaptability to various loss functions and optimizers.

cs.LG↗
arXiv2023

Going Beyond Linear Mode Connectivity: The Layerwise Linear Feature Connectivity

Recent work has revealed many intriguing empirical phenomena in neural network training, despite the poorly understood and highly complex loss landscapes and training dynamics. One of these phenomena, Linear Mode Connectivity (LMC), has gained considerable attention due to the intriguing observation that different solutions can be connected by a linear path in the parameter space while maintaining near-constant training and test losses. In this work, we introduce a stronger notion of linear connectivity, Layerwise Linear Feature Connectivity (LLFC), which says that the feature maps of every layer in different trained networks are also linearly connected. We provide comprehensive empirical evidence for LLFC across a wide range of settings, demonstrating that whenever two trained networks satisfy LMC (via either spawning or permutation methods), they also satisfy LLFC in nearly all the layers. Furthermore, we delve deeper into the underlying factors contributing to LLFC, which reveal new insights into the spawning and permutation approaches. The study of LLFC transcends and advances our understanding of LMC by adopting a feature-learning perspective.

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arXiv2023

Are Neurons Actually Collapsed? On the Fine-Grained Structure in Neural Representations

Recent work has observed an intriguing ''Neural Collapse'' phenomenon in well-trained neural networks, where the last-layer representations of training samples with the same label collapse into each other. This appears to suggest that the last-layer representations are completely determined by the labels, and do not depend on the intrinsic structure of input distribution. We provide evidence that this is not a complete description, and that the apparent collapse hides important fine-grained structure in the representations. Specifically, even when representations apparently collapse, the small amount of remaining variation can still faithfully and accurately captures the intrinsic structure of input distribution. As an example, if we train on CIFAR-10 using only 5 coarse-grained labels (by combining two classes into one super-class) until convergence, we can reconstruct the original 10-class labels from the learned representations via unsupervised clustering. The reconstructed labels achieve $93\%$ accuracy on the CIFAR-10 test set, nearly matching the normal CIFAR-10 accuracy for the same architecture. We also provide an initial theoretical result showing the fine-grained representation structure in a simplified synthetic setting. Our results show concretely how the structure of input data can play a significant role in determining the fine-grained structure of neural representations, going beyond what Neural Collapse predicts.

cs.LG↗
arXiv2023

Transformers from an Optimization Perspective

Deep learning models such as the Transformer are often constructed by heuristics and experience. To provide a complementary foundation, in this work we study the following problem: Is it possible to find an energy function underlying the Transformer model, such that descent steps along this energy correspond with the Transformer forward pass? By finding such a function, we can view Transformers as the unfolding of an interpretable optimization process across iterations. This unfolding perspective has been frequently adopted in the past to elucidate more straightforward deep models such as MLPs and CNNs; however, it has thus far remained elusive obtaining a similar equivalence for more complex models with self-attention mechanisms like the Transformer. To this end, we first outline several major obstacles before providing companion techniques to at least partially address them, demonstrating for the first time a close association between energy function minimization and deep layers with self-attention. This interpretation contributes to our intuition and understanding of Transformers, while potentially laying the ground-work for new model designs.

cs.LG↗
arXiv2022

Descent Steps of a Relation-Aware Energy Produce Heterogeneous Graph Neural Networks

Heterogeneous graph neural networks (GNNs) achieve strong performance on node classification tasks in a semi-supervised learning setting. However, as in the simpler homogeneous GNN case, message-passing-based heterogeneous GNNs may struggle to balance between resisting the oversmoothing that may occur in deep models, and capturing long-range dependencies of graph structured data. Moreover, the complexity of this trade-off is compounded in the heterogeneous graph case due to the disparate heterophily relationships between nodes of different types. To address these issues, we propose a novel heterogeneous GNN architecture in which layers are derived from optimization steps that descend a novel relation-aware energy function. The corresponding minimizer is fully differentiable with respect to the energy function parameters, such that bilevel optimization can be applied to effectively learn a functional form whose minimum provides optimal node representations for subsequent classification tasks. In particular, this methodology allows us to model diverse heterophily relationships between different node types while avoiding oversmoothing effects. Experimental results on 8 heterogeneous graph benchmarks demonstrates that our proposed method can achieve competitive node classification accuracy

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arXiv2021

Graph Neural Networks Inspired by Classical Iterative Algorithms

Despite the recent success of graph neural networks (GNN), common architectures often exhibit significant limitations, including sensitivity to oversmoothing, long-range dependencies, and spurious edges, e.g., as can occur as a result of graph heterophily or adversarial attacks. To at least partially address these issues within a simple transparent framework, we consider a new family of GNN layers designed to mimic and integrate the update rules of two classical iterative algorithms, namely, proximal gradient descent and iterative reweighted least squares (IRLS). The former defines an extensible base GNN architecture that is immune to oversmoothing while nonetheless capturing long-range dependencies by allowing arbitrary propagation steps. In contrast, the latter produces a novel attention mechanism that is explicitly anchored to an underlying end-to-end energy function, contributing stability with respect to edge uncertainty. When combined we obtain an extremely simple yet robust model that we evaluate across disparate scenarios including standardized benchmarks, adversarially-perturbated graphs, graphs with heterophily, and graphs involving long-range dependencies. In doing so, we compare against SOTA GNN approaches that have been explicitly designed for the respective task, achieving competitive or superior node classification accuracy. Our code is available at https://github.com/FFTYYY/TWIRLS.

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