arXiv subjects

Tongtian Zhu

Publications and source records attributed to Tongtian Zhu.

12 recordsLinked to original sources

arXiv2026

The Hidden Ratio in Adam: Stable Structure, Compression, and Sign Dynamics

Adam is the default optimizer for training modern deep neural networks, yet its adaptive behavior remains poorly understood due to the complex interaction between its first- and second-moment exponential moving averages (EMAs). We study Adam in the tied-$β$ regime, where the two EMA decay rates are equal, and show that its adaptive dynamics can be expressed through a transformed ratio with approximately scale-stable behavior. Empirically, this transformed ratio exhibits a stable, heavy-tailed distribution across tasks, model scales, and training stages, in contrast to the variability of raw moment magnitudes. This empirical stability has both practical and conceptual consequences. First, we derive a recurrence for the transformed ratio, yielding a reparameterization of Adam that replaces the second moment with a compressible state. Leveraging its stable distribution, we show that a fixed 4-bit codebook is sufficient in our experiments to store this state without auxiliary scaling, achieving performance competitive with full-precision Adam. Second, the transformed ratio view clarifies Adam's connection to sign-based methods: Adam reduces to sign-based momentum modulated by the transformed ratio, and replacing it with a constant recovers Signum as a limiting case. This perspective further provides a simple rule for transferring learning rates between the two methods. Together, these results suggest that tied-$β$ Adam admits a simple and approximately stable ratio structure underlying its adaptive behavior and demonstrate its utility for both analysis and efficient implementation.

cs.LG↗

arXiv2026

Distributed Team Orchestration via Supervisor Networks: Convergence, Optimality, and Resilience

In this paper, we study zero-sum potential team games with a supervisor network, where agents rely on supervisor-provided belief information rather than accurate common beliefs. The main challenge is that such belief information can be inaccurate because of supervisors' belief-estimation errors and the misreporting of joint actions by Byzantine teams. We propose the distributed team-orchestrating algorithm (DTOA), which combines team fictitious play with supervisor-based distributed belief learning. We prove the convergence of supervisors' belief estimates and establish that the induced learning dynamics converge to a near team-Nash equilibrium (TNE) in terms of the team-Nash gap (TNG). In the Byzantine setting, we consider a misreporting attack model and develop a Byzantine-resilient DTOA. We further provide probabilistic guarantees for Byzantine-team identification and establish an asymptotic bound on the honest TNG. Numerical experiments illustrate the theoretical findings, compare DTOA with baseline learning methods, and evaluate its performance in a Markov decision process setting.

cs.MA↗

arXiv2026

Mobius Learning: Cyclic Depth Folding in Transformers

Transformer-based language models organize computation along an ordered depth axis, where shallow and deep blocks often develop distinct representational roles. We challenge the conventional view that these roles must remain tied to a block's position in the ordered sequence. We introduce Mobius Learning, a training architecture based on cyclic depth folding, in which different data streams follow cyclically shifted block orders. The same block group is therefore applied early in the block sequence for some data streams and late for others, so it is optimized in both shallow and deep roles, a phenomenon we call depth-role superposition. Surprisingly, in four-worker experiments with a modded GPT-2 small (124M) model trained on 2.5B FineWeb tokens using Muon, Mobius Learning achieves lower validation loss than a fixed-order looped Transformer at larger numbers of Transformer block-sequence passes. This counterintuitive result shows that a block group need not remain confined to one fixed shallow or deep role within the block sequence and opens a new design space based on cyclic depth folding. Crucially, this structure makes Mobius Learning particularly well suited to memory-constrained distributed training: raw training data remain local, while each worker stores one block group rather than the complete Transformer block stack.

cs.LG↗

arXiv2026

On the Surprising Effectiveness of a Single Global Merging in Decentralized Learning

Decentralized learning provides a scalable alternative to parameter-server-based training, yet its performance is often hindered by limited peer-to-peer communication. In this paper, we study how communication should be scheduled over time, including determining when and how frequently devices synchronize. Counterintuitive empirical results show that concentrating communication budgets in the later stages of decentralized training remarkably improves global test performance. Surprisingly, we uncover that fully connected communication at the final step, implemented by a single global merging, can significantly improve the performance of decentralized learning under high data heterogeneity. Our theoretical contributions, which explain these phenomena, are the first to establish that the globally merged model of decentralized SGD can match the convergence rate of parallel SGD. Technically, we reinterpret part of the discrepancy among local models, which were previously considered as detrimental noise, as constructive components essential for matching this rate. This work provides evidence that decentralized learning is able to generalize under high data heterogeneity and limited communication, while offering broad new avenues for model merging research.

cs.LG↗

arXiv2025

DICE: Data Influence Cascade in Decentralized Learning

Decentralized learning offers a promising approach to crowdsource data consumptions and computational workloads across geographically distributed compute interconnected through peer-to-peer networks, accommodating the exponentially increasing demands. However, proper incentives are still in absence, considerably discouraging participation. Our vision is that a fair incentive mechanism relies on fair attribution of contributions to participating nodes, which faces non-trivial challenges arising from the localized connections making influence ``cascade'' in a decentralized network. To overcome this, we design the first method to estimate \textbf{D}ata \textbf{I}nfluence \textbf{C}ascad\textbf{E} (DICE) in a decentralized environment. Theoretically, the framework derives tractable approximations of influence cascade over arbitrary neighbor hops, suggesting the influence cascade is determined by an interplay of data, communication topology, and the curvature of loss landscape. DICE also lays the foundations for applications including selecting suitable collaborators and identifying malicious behaviors. Project page is available at https://raiden-zhu.github.io/blog/2025/DICE/.

cs.LG↗

arXiv2025

Lie Symmetry Net: Preserving Conservation Laws in Modelling Financial Market Dynamics via Differential Equations

This paper employs a novel Lie symmetries-based framework to model the intrinsic symmetries within financial market. Specifically, we introduce Lie symmetry net (LSN), which characterises the Lie symmetries of the differential equations (DE) estimating financial market dynamics, such as the Black-Scholes equation. To simulate these differential equations in a symmetry-aware manner, LSN incorporates a Lie symmetry risk derived from the conservation laws associated with the Lie symmetry operators of the target differential equations. This risk measures how well the Lie symmetries are realised and guides the training of LSN under the structural risk minimisation framework. Extensive numerical experiments demonstrate that LSN effectively realises the Lie symmetries and achieves an error reduction of more than one order of magnitude compared to state-of-the-art methods. The code is available at https://github.com/Jxl163/LSN_code.

math.AP↗

arXiv2025

Topology-aware Generalization of Decentralized SGD

This paper studies the algorithmic stability and generalizability of decentralized stochastic gradient descent (D-SGD). We prove that the consensus model learned by D-SGD is $\mathcal{O}{(N^{-1}+m^{-1} +λ^2)}$-stable in expectation in the non-convex non-smooth setting, where $N$ is the total sample size, $m$ is the worker number, and $1+λ$ is the spectral gap that measures the connectivity of the communication topology. These results then deliver an $\mathcal{O}{(N^{-(1+α)/2}+ m^{-(1+α)/2}+λ^{1+α} + ϕ_{\mathcal{S}})}$ in-average generalization bound, which is non-vacuous even when $λ$ is closed to $1$, in contrast to vacuous as suggested by existing literature on the projected version of D-SGD. Our theory indicates that the generalizability of D-SGD is positively correlated with the spectral gap, and can explain why consensus control in initial training phase can ensure better generalization. Experiments of VGG-11 and ResNet-18 on CIFAR-10, CIFAR-100 and Tiny-ImageNet justify our theory. To our best knowledge, this is the first work on the topology-aware generalization of vanilla D-SGD. Code is available at https://github.com/Raiden-Zhu/Generalization-of-DSGD.

cs.LG↗

arXiv2023

Decentralized SGD and Average-direction SAM are Asymptotically Equivalent

Decentralized stochastic gradient descent (D-SGD) allows collaborative learning on massive devices simultaneously without the control of a central server. However, existing theories claim that decentralization invariably undermines generalization. In this paper, we challenge the conventional belief and present a completely new perspective for understanding decentralized learning. We prove that D-SGD implicitly minimizes the loss function of an average-direction Sharpness-aware minimization (SAM) algorithm under general non-convex non-$β$-smooth settings. This surprising asymptotic equivalence reveals an intrinsic regularization-optimization trade-off and three advantages of decentralization: (1) there exists a free uncertainty evaluation mechanism in D-SGD to improve posterior estimation; (2) D-SGD exhibits a gradient smoothing effect; and (3) the sharpness regularization effect of D-SGD does not decrease as total batch size increases, which justifies the potential generalization benefit of D-SGD over centralized SGD (C-SGD) in large-batch scenarios. The code is available at https://github.com/Raiden-Zhu/ICML-2023-DSGD-and-SAM.

cs.LG↗

arXiv2023

Lookaround Optimizer: $k$ steps around, 1 step average

Weight Average (WA) is an active research topic due to its simplicity in ensembling deep networks and the effectiveness in promoting generalization. Existing weight average approaches, however, are often carried out along only one training trajectory in a post-hoc manner (i.e., the weights are averaged after the entire training process is finished), which significantly degrades the diversity between networks and thus impairs the effectiveness. In this paper, inspired by weight average, we propose Lookaround, a straightforward yet effective SGD-based optimizer leading to flatter minima with better generalization. Specifically, Lookaround iterates two steps during the whole training period: the around step and the average step. In each iteration, 1) the around step starts from a common point and trains multiple networks simultaneously, each on transformed data by a different data augmentation, and 2) the average step averages these trained networks to get the averaged network, which serves as the starting point for the next iteration. The around step improves the functionality diversity while the average step guarantees the weight locality of these networks during the whole training, which is essential for WA to work. We theoretically explain the superiority of Lookaround by convergence analysis, and make extensive experiments to evaluate Lookaround on popular benchmarks including CIFAR and ImageNet with both CNNs and ViTs, demonstrating clear superiority over state-of-the-arts. Our code is available at https://github.com/Ardcy/Lookaround.

cs.CV↗

arXiv2023

Adversarial Erasing with Pruned Elements: Towards Better Graph Lottery Ticket

Graph Lottery Ticket (GLT), a combination of core subgraph and sparse subnetwork, has been proposed to mitigate the computational cost of deep Graph Neural Networks (GNNs) on large input graphs while preserving original performance. However, the winning GLTs in exisiting studies are obtained by applying iterative magnitude-based pruning (IMP) without re-evaluating and re-considering the pruned information, which disregards the dynamic changes in the significance of edges/weights during graph/model structure pruning, and thus limits the appeal of the winning tickets. In this paper, we formulate a conjecture, i.e., existing overlooked valuable information in the pruned graph connections and model parameters which can be re-grouped into GLT to enhance the final performance. Specifically, we propose an adversarial complementary erasing (ACE) framework to explore the valuable information from the pruned components, thereby developing a more powerful GLT, referred to as the ACE-GLT. The main idea is to mine valuable information from pruned edges/weights after each round of IMP, and employ the ACE technique to refine the GLT processing. Finally, experimental results demonstrate that our ACE-GLT outperforms existing methods for searching GLT in diverse tasks. Our code will be made publicly available.

cs.LG↗

arXiv2023

Improving Expressivity of GNNs with Subgraph-specific Factor Embedded Normalization

Graph Neural Networks (GNNs) have emerged as a powerful category of learning architecture for handling graph-structured data. However, existing GNNs typically ignore crucial structural characteristics in node-induced subgraphs, which thus limits their expressiveness for various downstream tasks. In this paper, we strive to strengthen the representative capabilities of GNNs by devising a dedicated plug-and-play normalization scheme, termed as SUbgraph-sPEcific FactoR Embedded Normalization (SuperNorm), that explicitly considers the intra-connection information within each node-induced subgraph. To this end, we embed the subgraph-specific factor at the beginning and the end of the standard BatchNorm, as well as incorporate graph instance-specific statistics for improved distinguishable capabilities. In the meantime, we provide theoretical analysis to support that, with the elaborated SuperNorm, an arbitrary GNN is at least as powerful as the 1-WL test in distinguishing non-isomorphism graphs. Furthermore, the proposed SuperNorm scheme is also demonstrated to alleviate the over-smoothing phenomenon. Experimental results related to predictions of graph, node, and link properties on the eight popular datasets demonstrate the effectiveness of the proposed method. The code is available at https://github.com/chenchkx/SuperNorm.

cs.LG↗

arXiv2023

Contrastive Identity-Aware Learning for Multi-Agent Value Decomposition

Value Decomposition (VD) aims to deduce the contributions of agents for decentralized policies in the presence of only global rewards, and has recently emerged as a powerful credit assignment paradigm for tackling cooperative Multi-Agent Reinforcement Learning (MARL) problems. One of the main challenges in VD is to promote diverse behaviors among agents, while existing methods directly encourage the diversity of learned agent networks with various strategies. However, we argue that these dedicated designs for agent networks are still limited by the indistinguishable VD network, leading to homogeneous agent behaviors and thus downgrading the cooperation capability. In this paper, we propose a novel Contrastive Identity-Aware learning (CIA) method, explicitly boosting the credit-level distinguishability of the VD network to break the bottleneck of multi-agent diversity. Specifically, our approach leverages contrastive learning to maximize the mutual information between the temporal credits and identity representations of different agents, encouraging the full expressiveness of credit assignment and further the emergence of individualities. The algorithm implementation of the proposed CIA module is simple yet effective that can be readily incorporated into various VD architectures. Experiments on the SMAC benchmarks and across different VD backbones demonstrate that the proposed method yields results superior to the state-of-the-art counterparts. Our code is available at https://github.com/liushunyu/CIA.

cs.LG↗