arXiv subjects

Daning Cheng

Publications and source records attributed to Daning Cheng.

At least 19 recordsLinked to original sources

arXiv2026

Quantifying Depth Sufficiency in Residual Neural Networks: A First-Order Criterion

How can we determine whether a trained neural network is already deep enough? We study this under a fixed function-preserving residual-growth protocol specifying insertion locations, residual families, zero-output initializations, and zero-state first-order updates. We define first-order residual depth saturation as the absence of a strict local decrease from every admissible insertion. We prove residual non-degeneracy is necessary and sufficient: additional depth has first-order value exactly when conditional activation gradients have a nonzero projection onto at least one admissible residual tangent space. This boundary is shared by descent-compatible zero-state updates and invariant under regular local reparameterizations preserving that tangent space. Under residual-signal realizability, raw activation-gradient vanishing exactly certifies saturation. Across ResNets, GPT-2-style models, and continued-pretrained Pythia checkpoints, the maximum activation-gradient norm decreases toward a low-signal regime with depth. Function-preserving growth also achieves converged performance competitive with training from scratch. These results support activation-gradient magnitude as a conservative diagnostic of the remaining empirical first-order value of residual depth.

cs.LG↗

arXiv2026

Mechanisms of Width Scaling in Normalized Residual Networks: The Effective Alignment Dimension

Existing theories of neural-network width characterize asymptotic limits, but provide limited guidance on whether an expansion direction identified from finite training data remains beneficial on unseen data. We study this problem for function-preserving residual expansion and introduce the effective alignment dimension, a measurable quantity describing the signal-noise geometry of activation gradients. By deriving the exact mean and variance of the inner product between independently estimated training and test gradients, we obtain a finite-sample upper bound on misalignment probability. The bound depends only on the effective alignment dimension and an effective sample size, requiring finite second moments and a nonzero population gradient, without covariance spectral assumptions or prescribed width-growth rates. We integrate this certificate into the train-test residual-expansion framework, yielding a high-probability condition for test-risk improvement. Experiments across width-controlled LLaMA-style Transformers, Pythia, and ResNet-20 show that wider models exhibit larger effective alignment dimensions and lower empirical misalignment. Direct residual interventions confirm that the alignment statistic predicts the sign and magnitude of held-out loss changes.

cs.LG↗

arXiv2026

ReMP: Low-Downtime Runtime Model-Parallelism Reconfiguration for LLM Serving

Current large language model (LLM) inference systems universally deploy ultra-large-scale models using a combination of Tensor Parallelism (TP) and Pipeline Parallelism (PP). However, existing systems treat the model parallelism topology as a static configuration that cannot be flexibly adjusted at runtime. This rigid design creates a fundamental contradiction with the dynamically changing inference workloads in real-world scenarios. State-of-the-art systems lack online reconfiguration capabilities and can only switch configurations by restarting the service, resulting in several minutes of service interruption, KV cache loss, and prohibitive recomputation overhead. To address this problem, this paper presents ReMP, a runtime model parallelism reconfiguration framework that supports low downtime. ReMP achieves dynamic adjustment through three key techniques: (1) decoupling the model parallelism topology from runtime state to avoid full service reconstruction; (2) designing a two-dimensional KV cache migration mechanism to preserve reusable cache states after TP/PP changes; and (3) implementing end-to-end online reconfiguration. Experiments demonstrate that ReMP can complete most topology switches within 1-7 seconds on models ranging from 7B to 70B parameters, achieving speedups of tens to over a hundred times compared to the restart approach. Moreover, ReMP significantly outperforms fixed configurations under dynamic workloads, delivering superior performance in terms of TTFT, TPOT, and output throughput.

cs.DC↗

arXiv2026

DynaTrain: Fast Online Parallelism Switching for Elastic LLM Training

Modern large language model (LLM) training is inherently dynamic: resource fluctuations, RLHF phase shifts, and cluster elasticity continually reshape the optimal parallelism layout, posing a significant challenge to existing training frameworks built around a static execution model. We present DynaTrain, a distributed training system for sub-second, online reconfiguration across arbitrary multi-dimensional parallelism. At its core, we propose a Virtual Parameter Space (VPS) abstraction that unifies all distributed training states under one logical coordinate space, turning any parallelism configuration into a deterministic mapping and collapsing complex transition into manageable geometric intersections. On top of VPS, a state routing-and-transition layer executes rank-local transfers under a memory-aware, deadlock-free schedule, and an Elastic Device Manager overlaps new-world construction with ongoing training to mask topology-change cost. On dense and MoE models up to 235B parameters, DynaTrain reconfigures a 70B dense model in under 2s and a 235B MoE model in 4.36s, outperforming state-of-the-art checkpoint-based and elastic systems by up to three orders of magnitude while preserving correctness.

cs.LG↗

arXiv2026

A Qualitative Test-Risk Mechanism for Scaling Behavior in Normalized Residual Networks

The scaling behavior, in which test performance often improves as model size and data increase, is a central empirical phenomenon in modern deep learning, yet its theoretical basis remains incomplete. In this paper, we study depth expansion in normalized residual networks: starting from a trained model in an old hypothesis class, we insert a new residual block at an intermediate layer and ask when such an expansion can yield a provable improvement in test risk. We develop a unified framework that decomposes this question into representational gain, optimization gain, and generalization transfer. First, under a first-order descent condition near zero initialization, we prove that the expanded hypothesis class contains an auxiliary jumpboard model with strictly smaller population risk than the original model. Second, under norm control tailored to post-normalized residual architectures, we establish a norm-based Rademacher complexity bound for the expanded model class. These ingredients lead to two complementary test-risk guarantees: one route passes through population risk and is tighter when a positive population margin is available, while the other works directly at the train/test level, avoids Hoeffding transfer, and is more robust in degenerate regimes. Together, these results provide a theorem-driven mechanism under which residual depth expansion can improve test performance in normalized residual networks. More broadly, they suggest that scaling is inherently joint: depth creates new improving directions, width enhances the finite-sample observability of weak signals, and data determines whether the statistical cost of expansion can be controlled.

cs.LG↗

arXiv2026

HeRo-Q: A General Framework for Stable Low Bit Quantization via Hessian Conditioning

Post Training Quantization (PTQ), a mainstream model compression technique, often leads to the paradoxical 'low error, high loss' phenomenon because it focuses solely on minimizing quantization error. The root cause lies in the Hessian matrix of the LLM loss landscape: a few high curvature directions are extremely sensitive to perturbations. To address this, we propose the Hessian Robust Quantization (HeRo Q) algorithm, which applies a lightweight, learnable rotation-compression matrix to the weight space prior to quantization. This joint framework reshapes the loss landscape by reducing the largest Hessian eigenvalue and reducing its max eigenvalue, thereby significantly enhancing robustness to quantization noise. HeRo-Q requires no architectural modifications, incurs negligible computational overhead, and integrates seamlessly into existing PTQ pipelines. Experiments on Llama and Qwen models show that HeRo Q consistently outperforms state of the art methods including GPTQ, AWQ, and SpinQuant not only achieving superior performance under standard W4A8 settings, but also excelling in the highly challenging W3A16 ultra low bit regime, where it boosts GSM8K accuracy on Llama3 8B to 70.15\% and effectively avoids the logical collapse commonly seen in aggressive quantization.

cs.LG↗

arXiv2026

MoE-DisCo:Low Economy Cost Training Mixture-of-Experts Models

Training large-scale Mixture-of-Experts (MoE) models typically requires high-memory, high-bandwidth GPUs (e.g., A100), and their high cost has become a major barrier to large-model training. In contrast, affordable hardware is low-cost but constrained by memory capacity and bandwidth, making it unsuitable for direct LLM training. To address this, we propose MoE-DisCo (Mixture-of-Experts with Disentangled Clustering and Coordination), a staged training framework. MoE-DisCo decomposes the MoE model into multiple dense submodels, each consisting of a shared backbone and a single expert, and partitions the training data into subsets using unsupervised clustering. Each submodel is trained independently and in parallel on its assigned data subset using low-cost devices, without any inter-device communication. Subsequently, all experts are integrated into a complete MoE model and fine-tuned globally for a short period on high-memory, high-bandwidth GPUs. Experiments show that our method matches or even surpasses full-parameter training in performance across multiple downstream tasks, loss function, and perplexity (PPL), while reducing training cost by 47.6 percent to 69.5 percent on Qwen1.5-MoE-2.7B and Llama-MoE-3.5B across different datasets.

cs.LG↗

arXiv2025

Rethinking Parameter Sharing as Graph Coloring for Structured Compression

Modern deep models have massive parameter sizes, leading to high inference-time memory usage that limits practical deployment. Parameter sharing, a form of structured compression, effectively reduces redundancy, but existing approaches remain heuristic-restricted to adjacent layers and lacking a systematic analysis for cross-layer sharing. However, extending sharing across multiple layers leads to an exponentially expanding configuration space, making exhaustive search computationally infeasible and forming a critical bottleneck for parameter sharing. We recast parameter sharing from a group-theoretic perspective as introducing structural symmetries in the model's parameter space. A sharing configuration can be described by a coloring function $\alpha:L\rightarrow C$ (L: layer indices and C: sharing classes), which determines inter-layer sharing groups while preserving structural symmetry. To determine the coloring function, we propose a second-order geometric criterion based on Taylor expansion and the Hessian spectrum. By projecting perturbations onto the Hessian's low-curvature eigensubspace, the criterion provides an analytic rule for selecting sharing groups that minimize performance impact, yielding a principled and scalable configuration procedure. Across diverse architectures and tasks, Geo-Sharing consistently outperforms state-of-the-art heuristic sharing strategies, achieving higher compression ratios with smaller accuracy degradation.

cs.LG↗

arXiv2025

MoQE: Improve Quantization Model performance via Mixture of Quantization Experts

Quantization method plays a crucial role in improving model efficiency and reducing deployment costs, enabling the widespread application of deep learning models on resource-constrained devices. However, the quantization process inevitably introduces accuracy degradation. In this paper, we propose Mixture of Quantization Experts( abbr. MoQE), a quantization inference framework based on the Mixture-of-Experts (MoE) architecture, aiming to jointly improve the performance of quantization models. MoQE combines multiple quantization variants of one full-precision model as specialized "quantization experts" and dynamically routes input data to the most suitable expert based on its characteristics. MoQE alleviates the performance degradation commonly seen in single quantization models through specialization quantization expert models. We design lightweight, structure-aware router models tailored for both CV and NLP tasks. Experimental evaluations on ResNet, LLaMA, and Qwen model families across benchmark datasets including ImageNet, WikiText, C4, and OpenWebText demonstrate that MoQE achieves performance comparable to SOTA quantization model, without incurring significant increases in inference latency.

cs.LG↗

arXiv2025

Exploiting Block Coordinate Descent for Cost-Effective LLM Model Training

Training large language models typically demands extensive GPU memory and substantial financial investment, which poses a barrier for many small- to medium-sized teams. In this paper, we propose a full-parameter pre-training and fine-tuning framework based on block coordinate descent (BCD), enhanced with engineering optimizations, to enable efficient training of large-scale models on cost-effective RTX 4090, A100 and A800 GPU clusters. Under identical hardware configurations, we reduce the training cost of a 7B model to 33% on A100/A800 and only 2.6% on RTX 4090, compared to standard full-parameter training. It also enables large models previously restricted to A100 clusters to be trained on RTX 4090 without degrading performance. BCD achieves comparable or better accuracy than full-parameter and fine-tuning methods at most cases, with lower GPU consumption and improved hardware utilization.

cs.LG↗

arXiv2025

Can the capability of Large Language Models be described by human ability? A Meta Study

Users of Large Language Models (LLMs) often perceive these models as intelligent entities with human-like capabilities. However, the extent to which LLMs' capabilities truly approximate human abilities remains a topic of debate. In this paper, to characterize the capabilities of LLMs in relation to human capabilities, we collected performance data from over 80 models across 37 evaluation benchmarks. The evaluation benchmarks are categorized into 6 primary abilities and 11 sub-abilities in human aspect. Then, we then clustered the performance rankings into several categories and compared these clustering results with classifications based on human ability aspects. Our findings lead to the following conclusions: 1. We have confirmed that certain capabilities of LLMs with fewer than 10 billion parameters can indeed be described using human ability metrics; 2. While some abilities are considered interrelated in humans, they appear nearly uncorrelated in LLMs; 3. The capabilities possessed by LLMs vary significantly with the parameter scale of the model.

cs.CL↗

arXiv2025

A General Error-Theoretical Analysis Framework for Constructing Compression Strategies

The exponential growth in parameter size and computational complexity of deep models poses significant challenges for efficient deployment. The core problem of existing compression methods is that different layers of the model have significant differences in their tolerance to compression levels. For instance, the first layer of a model can typically sustain a higher compression level compared to the last layer without compromising performance. Thus, the key challenge lies in how to allocate compression levels across layers in a way that minimizes performance loss while maximizing parameter reduction. To address this challenge, we propose a Compression Error Theory (CET) framework, designed to determine the optimal compression level for each layer. Taking quantization as an example, CET leverages differential expansion and algebraic geometry to reconstruct the quadratic form of quantization error as ellipsoids and hyperbolic paraboloids, and utilizes their geometric structures to define an error subspace. To identify the error subspace with minimal performance loss, by performing orthogonal decomposition of the geometric space, CET transforms the optimization process of the error subspace into a complementary problem. The final theoretical analysis shows that constructing the quantization subspace along the major axis results in minimal performance degradation. Through experimental verification of the theory, CET can greatly retain performance while compressing. Specifically, on the ResNet-34 model, CET achieves nearly 11$\times$ parameter compression while even surpassing performance comparable to the original model.

cs.LG↗

arXiv2024

FP=xINT:Representing Neural Networks via Low-Bit Series Basis Functions

Post-Training Quantization (PTQ) converts pre-trained Full-Precision (FP) models into quantized versions without training. While existing methods reduce size and computational costs, they also significantly degrade performance and quantization efficiency at extremely low settings due to quantization noise. We introduce a deep model series expansion framework to address this issue, enabling rapid and accurate approximation of unquantized models without calibration sets or fine-tuning. This is the first use of series expansion for neural network quantization. Specifically, our method expands the FP model into multiple low-bit basis models. To ensure accurate quantization, we develop low-bit basis model expansions at different granularities (tensor, layer, model), and theoretically confirm their convergence to the dense model, thus restoring FP model accuracy. Additionally, we design AbelianAdd/Mul operations between isomorphic models in the low-bit expansion, forming an Abelian group to ensure operation parallelism and commutativity. The experiments show that our algorithm achieves state-of-the-art performance in low-bit settings; for example, 4-bit quantization of ResNet-50 surpasses the original accuracy, reaching 77.03%. The code will be made public.

cs.LG↗

arXiv2024

Lossless Model Compression via Joint Low-Rank Factorization Optimization

Low-rank factorization is a popular model compression technique that minimizes the error $\delta$ between approximated and original weight matrices. Despite achieving performances close to the original models when $\delta$ is optimized, a performance discrepancy remains due to the separate optimization processes for low-rank factorization and model performance, resulting in unavoidable losses. We address this issue by introducing a novel joint optimization strategy for lossless low-rank weight factorization, which, for the first time, enhances the model's performance beyond the original. Our approach begins with a theoretical analysis of the relationship between low-rank factorization and model optimization objectives, establishing a precise perturbation range for matrix factorization errors on model performance. This challenge is then reformulated as a numerical rank deficiency problem with inequality constraints and develop a joint objective that simultaneously addresses factorization error and model performance. Based on the above analysis, we propose two optimization algorithms: \textbf{a lossless optimization algorithm} that maximizes model accuracy while ensuring compression, and \textbf{a compact optimization algorithm} that minimizes model size while preserving performance. These algorithms do not require fine-tuning and can directly compress numerous deep models to achieve lossless results. Our methods demonstrate robust efficacy across various vision and language tasks. For example, the compressed model reduced by 70\% on ResNext50 outperforms the original. Our code will be made public.

cs.LG↗

arXiv2024

Compression for Better: A General and Stable Lossless Compression Framework

This work focus on how to stabilize and lossless model compression, aiming to reduce model complexity and enhance efficiency without sacrificing performance due to compression errors. A key challenge is effectively leveraging compression errors and defining the boundaries for lossless compression to minimize model loss. i.e., compression for better. Currently, there is no systematic approach to determining this error boundary or understanding its specific impact on model performance. We propose a general \textbf{L}oss\textbf{L}ess \textbf{C}ompression theoretical framework (\textbf{LLC}), which further delineates the compression neighborhood and higher-order analysis boundaries through the total differential, thereby specifying the error range within which a model can be compressed without loss. To verify the effectiveness of LLC, we apply various compression techniques, including quantization and decomposition. Specifically, for quantization, we reformulate the classic quantization search problem as a grouped knapsack problem within the lossless neighborhood, achieving lossless quantization while improving computational efficiency. For decomposition, LLC addresses the approximation problem under low-rank constraints, automatically determining the rank for each layer and producing lossless low-rank models. We conduct extensive experiments on multiple neural network architectures on different datasets. The results show that without fancy tricks, LLC can effectively achieve lossless model compression. Our code will be made publicly.

cs.CV↗

arXiv2022

Mixed-Precision Inference Quantization: Radically Towards Faster inference speed, Lower Storage requirement, and Lower Loss

Based on the model's resilience to computational noise, model quantization is important for compressing models and improving computing speed. Existing quantization techniques rely heavily on experience and "fine-tuning" skills. In the majority of instances, the quantization model has a larger loss than a full precision model. This study provides a methodology for acquiring a mixed-precise quantization model with a lower loss than the full precision model. In addition, the analysis demonstrates that, throughout the inference process, the loss function is mostly affected by the noise of the layer inputs. In particular, we will demonstrate that neural networks with massive identity mappings are resistant to the quantization method. It is also difficult to improve the performance of these networks using quantization.

cs.LG↗

arXiv2022

Quantization in Layer's Input is Matter

In this paper, we will show that the quantization in layer's input is more important than parameters' quantization for loss function. And the algorithm which is based on the layer's input quantization error is better than hessian-based mixed precision layout algorithm.

cs.LG↗

arXiv2019

The Scalability for Parallel Machine Learning Training Algorithm: Dataset Matters

To gain a better performance, many researchers put more computing resource into an application. However, in the AI area, there is still a lack of a successful large-scale machine learning training application: The scalability and performance reproducibility of parallel machine learning training algorithm are limited and there are a few pieces of research focusing on why these indexes are limited but there are very few research efforts explaining the reasons in essence. In this paper, we propose that the sample difference in dataset plays a more prominent role in parallel machine learning algorithm scalability. Dataset characters can measure sample difference. These characters include the variance of the sample in a dataset, sparsity, sample diversity and similarity in sampling sequence. To match our proposal, we choose four kinds of parallel machine learning training algorithms as our research objects: (1) Asynchronous parallel SGD algorithm (Hogwild! algorithm) (2) Parallel model average SGD algorithm (Mini-batch SGD algorithm) (3) Decenterilization optimization algorithm, (4) Dual Coordinate Optimization (DADM algorithm). These algorithms cover different types of machine learning optimization algorithms. We present the analysis of their convergence proof and design experiments. Our results show that the characters datasets decide the scalability of the machine learning algorithm. What is more, there is an upper bound of parallel scalability for machine learning algorithms.

cs.DC↗