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Yue Song

Publications and source records attributed to Yue Song.

At least 19 recordsLinked to original sources
arXiv2026

Opinion Leader Dynamics: How Sparse Attention Shapes Token Clustering

Sparse attention reduces the quadratic cost of global self-attention while retaining strong empirical performance, but how its restricted interactions shape the evolution of token representations remains theoretically underexplored. Modeling tokens as particles on the unit sphere, we introduce opinion leader dynamics, a framework that identifies two mechanisms through which token groups converge internally while maintaining distinct limiting directions. In the explicit model, fixed representatives induce a potential that attracts tokens toward distinct local maxima. In the implicit model, disconnected interaction groups evolve toward separate consensus directions. We formulate both models as reverse Wasserstein gradient flows and establish exponential convergence under suitable conditions. We further connect these theoretical predictions to token evolution in frontier sparse-attention LLMs that motivate our framework. Across four benchmarks, Kimi-K3, MiniMax-M3, and DeepSeek-V4-Flash consistently exhibit clearer cluster separation and higher clustering scores than the dense-attention model GLM-4.7-Flash in projected token representations. These observations support the relevance of the predicted multiple-group structure to trained frontier LLMs, while finite-particle simulations illustrate the theoretical convergence behavior. Together, our results connect restricted token interactions to distinct group-level attractors, providing a dynamical account of how sparse attention can support alignment within groups while preserving separation between them.

cs.LG↗
arXiv2026

Robust Optimization Under Objective Functional Uncertainty

This paper proposes a new robust optimization (RO) formulation namely the RO under objective functional uncertainty (ObRO). The ObRO adopts a min-max structure where the inner problem finds the worst-case objective function in a continuous function space to maximize the cost, and the outer problem finds the optimal decision in a Euclidean space to minimize the cost. A solution algorithm is designed to alternately generate the worst-case objective function at the current decision and the optimal decision for the current collection of objective functions. Using operator theory, we prove that this algorithm converges to the defined ``semi-global'' saddle point of the ObRO problem. In addition, we propose a numerical solver based on the piece-wise linearization (PWL) approximation of objective functions. The PWL approximate problem is proved to be numerically consistent with the original ObRO problem. The obtained results are applied to the degradation-aware battery charging scheduling in distribution networks.

math.OC↗
arXiv2026

Consensusability of Continuous-Time Multi-Agent Systems With Unbounded Heterogeneous Constant Delays: A Signed Laplacian Perspective

The consensus of continuous-time multi-agent systems with unbounded and heterogeneous constant delays is investigated by combining frequency-domain analysis and algebraic graph theory. Several types of signed Laplacians are constructed to characterize consensusability under delays. The core results are established based on the defined delay-embedded signed Laplacian, where a small-delay link creates a cooperative interaction and a possibly unbounded large-delay link creates an antagonistic interaction between the agents. The dividing line between small and large delays is given by $τ_{ij}=π/2λ_{\max}(L_0)$, where $λ_{\max}(L_0)$ refers to the maximum eigenvalue of the conventional graph Laplacian. It is proved that the consensusability is preserved if the delay-embedded signed Laplacian is positive semi-definite with a simple zero eigenvalue. Moreover, we derived some consensus conditions in terms of the extended effective resistance which measures the overall coupling between two sets of agents. The obtained results provide new insights into the mechanism of delayed consensus from the interplay between the small-delay-induced cooperativeness and large-delay-induced antagonism in the underlying network topology.

math.OC↗
arXiv2026

Consensus Tracking of Perturbed Open Multi-Agent Systems with Repelling Antagonistic Interactions

An open multi-agent system (OMAS) features migrating agents which produce a flexible network that is naturally switching and size-varying. Meanwhile, agent migrations also make an OMAS prone to environmental adversities. In this work, we investigate the consensus tracking problem of OMASs suffering migration-induced adversities, including non-vanishing agent dynamics/state perturbations and repelling antagonistic interactions among agents, over an intermittently disconnected signed digraph. The OMAS is interpreted into a perturbed multi-mode multi-dimensional ($M^3D$) system in which unstable subsystems are created when repelling interactions dominate the cooperative ones in the network regardless of its connectivity. To handle the destabilizing effect brought by repelling interactions and non-vanishing perturbations, we extend the stability theory for $M^3D$ systems and apply it to the OMAS to show that ultimately bounded consensus tracking can be achieved if the network switching satisfies the piecewise average dwell time and activation time ratio conditions. Particularly, for vanishing perturbations, asymptotic tracking can be ensured under weaker switching conditions.

eess.SY↗
arXiv2026

LieBN: Batch Normalization over Lie Groups

Manifold-valued measurements are prevalent in various machine learning tasks. Recent advances have extended Deep Neural Networks (DNNs) to operate on manifolds. These extensions have been accompanied by normalization techniques tailored to different geometries, collectively referred to as Riemannian normalization. However, most existing Riemannian normalization methods are either designed for specific manifolds or fail to effectively normalize manifold-valued sample distributions. To address these limitations, we propose LieBN, a framework for Riemannian Batch Normalization (RBN) over Lie groups. Our approach leverages the theoretically convenient left- and right-invariant metrics, which naturally exist in every Lie group, and provides theoretical guarantees for controlling the Riemannian mean and variance. We instantiate LieBN across nine distinct geometries: four on the Symmetric Positive Definite (SPD) manifold, one on the group of rotation matrices, and four on the manifold of full-rank correlation matrices. Notably, among the SPD metrics, we introduce a novel right-invariant metric and extend three existing Lie group structures via matrix power deformation. Experiments on different manifolds validate the effectiveness of our framework. The code is available at https://github.com/GitZH-Chen/LieBN.git.

cs.LG↗
arXiv2026

The Hyperspherical Geometry of CLIP Latent Space: A Semantic Mixture Model

Contrastive Language-Image Pretraining (CLIP) representations form a semantic embedding space governed by cosine similarity, reflecting an intrinsic hyperspherical geometry. However, existing probabilistic interpretations typically rely on Gaussian assumptions, which fail to capture this directional and multimodal structure. We propose a principled density model for the CLIP latent space based on Mixtures of von Mises-Fisher (MovMF) distributions defined on the unit hypersphere. Using the Expectation-Maximization (EM) algorithm, we efficiently learn a probabilistic model in which each mixture component corresponds to a coherent semantic concept. This formulation yields a closed-form likelihood naturally aligned with hyperspherical geometry, enabling accurate and interpretable density estimation. Empirically, our model significantly improves long-tailed and out-of-distribution detection and provides a natural semantic decomposition, representing each embedding as a sparse probabilistic combination of interpretable concepts. These results suggest that CLIP latent space is more faithfully characterized as a hyperspherical semantic mixture rather than an isotropic Gaussian, establishing a simple and geometrically consistent probabilistic framework for modeling and understanding multimodal representations. Project page is available at https://xiaoyuzhizi.github.io/movmf-clip/.

cs.LG↗
arXiv2026

LoopCoder-v2: Only Loop Once for Efficient Test-Time Computation Scaling

Looped Transformers scale latent computation by repeatedly applying shared blocks, but sequential looping increases latency and KV-cache memory with the loop count. Parallel loop Transformers (PLT) alleviate this cost through cross-loop position offsets (CLP) and shared-KV gated sliding-window attention, making loop count a practical design choice. We therefore study PLT loop-count selection through a gain--cost view: an extra loop may refine representations, but CLP also introduces a positional mismatch at each loop boundary. We instantiate this study by training LoopCoder-v2, a family of 7B PLT coders with different loop counts, from scratch on 18T tokens, followed by matched instruction tuning and evaluation. Empirically, the two-loop variant delivers broad gains over the non-looped baseline across code generation, code reasoning, agentic software engineering, and tool-use benchmarks, improving SWE-bench Verified from 43.0 to 64.4 points and Multi-SWE from 14.0 to 31.0 points. In contrast, variants with three or more loops regress, revealing a strongly non-monotonic loop-count effect. Our diagnostics show that loop 2 provides the main productive refinement, while later loops yield diminishing, oscillatory updates and reduced representational diversity. Because the CLP-induced mismatch remains roughly fixed as refinement gains shrink, the offset cost increasingly dominates. This gain--cost trade-off explains PLT's saturation at two loops and provides diagnostics for loop-count selection.

cs.LG↗
arXiv2026

Krause Synchronization Transformers

Self-attention in Transformers relies on globally normalized softmax weights, causing all tokens to compete for influence at every layer. When composed across depth, this interaction pattern induces strong synchronization dynamics that favor convergence toward a dominant mode, a behavior associated with representation collapse and attention sink phenomena. We introduce Krause Attention, a principled attention mechanism inspired by bounded-confidence consensus dynamics. Krause Attention replaces similarity-based global aggregation with distance-based, localized, and selectively sparse interactions, promoting structured local synchronization instead of global mixing. We relate this behavior to recent theory modeling Transformer dynamics as interacting particle systems, and show how bounded-confidence interactions naturally moderate attention concentration and alleviate attention sinks. Restricting interactions to local neighborhoods also reduces runtime complexity from quadratic to linear in sequence length. Empirically, we validate Krause Attention across diverse settings, including vision (ViT on CIFAR/ImageNet), autoregressive image generation (MNIST/CIFAR-10), large language models (Llama/Qwen), and language models trained from scratch at multiple scales (100M/200M). Across these domains, Krause Attention achieves consistent performance gains while improving computational efficiency, highlighting bounded-confidence dynamics as a scalable and effective inductive bias for attention.

cs.LG↗
arXiv2026

Wide-field mid-infrared cavity-enhanced upconversion imaging

Mid-infrared (MIR) spectral imaging enables precise target identification and analysis by capturing rich chemical fingerprints, which calls for high-sensitivity broadband MIR imagers at room temperature. Here, we devise and implement a continuous-wave pumping MIR upconversion imaging system based on external-cavity enhancement, which favors a large field of view, a low cavity loss, and a high spectral resolution. The involved optical cavity is constructed in an integrated fashion by utilizing one crystal facet as a cavity mirror, which allows a 43-fold power enhancement for the single-longitudinal-mode pump at 1064 nm. In combination with the chirped-poled crystal design, high-fidelity and wide-field spectral imaging mapping is permitted to facilitate an acceptance angle up to 28.5$^\circ$ over a spectral coverage of 2.5--5 $μ$m. Moreover, a thermal locking approach is used to stabilize the cavity at the high-power operation, eliminating active feedback and ensuring long-term stability. A proof-of-principle demonstration is presented to showcase real-time observation of CO$_{2}$ gas injection dynamics. The implemented MIR upconversion imager features wide-field operation, high detection sensitivity, and compact footprint, which would benefit subsequent applications including environment monitoring, gas leakage inspection, and medical diagnostics.

physics.optics↗
arXiv2026

Winfree Oscillatory Neural Network

Oscillations and synchronization are widely believed to play a fundamental role in representation and computation. However, existing machine learning approaches based on synchronization dynamics have largely been confined to specialized settings such as object discovery, with limited evidence of scalability to standard vision benchmarks or logic reasoning tasks. We propose the Winfree Oscillatory Neural Network (WONN), a dynamical neural architecture based on generalized Winfree dynamics. WONN evolves representations on the torus $(S^1)^d$ through structured oscillatory interactions, combining phase-based inductive biases with flexible and hierarchical interaction mechanisms instantiated as either fixed trigonometric mappings or learnable neural networks. We evaluate WONN on image recognition and complex reasoning tasks, including CIFAR, ImageNet, Maze-hard, and Sudoku. Across these domains, WONN achieves competitive or superior performance with strong parameter efficiency. In particular, WONN is, to our knowledge, the first synchronization-based oscillatory architecture to scale competitively to ImageNet-1K. Furthermore, on Maze-hard, WONN achieves 80.1% accuracy using only 1% of the parameters of prior state-of-the-art models. These results suggest that structured oscillatory dynamics provide a scalable and parameter-efficient alternative to conventional neural architectures.

cs.LG↗
arXiv2026

Spontaneous symmetry breaking and Goldstone modes for deep information propagation

In physical systems, whenever a continuous symmetry is spontaneously broken, the system possesses excitations called Goldstone modes, which allow coherent information propagation over long distances and times. In this work, we study deep neural networks whose internal layers are equivariant under a continuous symmetry and may therefore support analogous Goldstone-like degrees of freedom. We demonstrate, both analytically and empirically, that these degrees of freedom enable coherent signal propagation across depth and recurrent iterations, providing a mechanism for stable information flow without relying on architectural stabilizers such as residual connections or normalization. In feedforward networks, this results in improved trainability and representational diversity across layers. In recurrent settings, we demonstrate the same mechanism is valuable for long-term memory by propagating information over recurrent iterations, thereby improving performance of RNNs and GRUs on long-sequence modeling tasks.

cs.LG↗
arXiv2026

Higher-Order Equilibrium Tracking for EM-Compressible Online Estimation

We study online estimation in latent-variable models by recasting the problem as tracking a moving empirical equilibrium. Standard online EM and stochastic approximation analyses primarily study convergence toward the population parameter and typically do not isolate the empirical batch optimum from the online tracking error at finite horizon. Our framework decomposes the online estimate into the frozen batch equilibrium at the current running statistic and a tracking lag that captures the algorithm's delay behind this moving target. We prove a batch-to-online transfer theorem: provided $\lVert e_T \rVert_{L^{2}} = o(T^{-1/2})$, the online estimator inherits the batch central limit theorem and the sharp first-order risk constant. Our key observation is that the empirical optimum evolves on a smooth equilibrium manifold indexed by the running statistic. An $m$-th order equilibrium-jet predictor combined with an order-$ν$ frozen corrector yields localized tracking rates $O(T^{-ν(m+1)})$. We formalize EM-compressibility and EM-jet$^R$-compressibility as the structural conditions that make the equilibrium response and the Newton corrector evaluable from a retained streaming statistic. The theory is instantiated in latent linear Gaussian covariance estimation, where the first-order scheme operates on a compressed $d \times d$ statistic with explicit finite-sample risk envelopes and a certified restart rule.

cs.LG↗
arXiv2026

Anisotropic Modality Align

Training multimodal large language models has long been limited by the scarcity of high-quality paired multimodal data. Recent studies show that the shared representation space of pretrained multimodal contrastive models can serve as a bridge, enabling models to perform multimodal training with unimodal data. However, the key premise of this paradigm remains insufficiently understood: can representations from different modalities be reliably interchanged? The core obstacle lies in the persistent Modality Gap in the shared space. In this work, we revisit the geometric nature of the modality gap. We find that modality representations already share compatible dominant semantic geometry. What truly hinders modality interchangeability is not a simple global shift, but an anisotropic residual structure concentrated along a small number of dominant directions. Based on this finding, we further propose the principle of anisotropic modality gap alignment: effective modality alignment should align with the target-modality distribution while preserving the semantic structure of the source modality. Guided by this principle, we propose an anisotropic geometric correction framework, AnisoAlign, for unpaired modality alignment. This framework leverages the internal geometric prior of the target modality and performs bounded correction on source-modality representations, thereby constructing substitute representations in the target modality. Experiments confirm its benefits in both geometric diagnostics and text-only MLLM training. Overall, this work recasts the modality gap from an empirical observation into a correctable, structured geometric phenomenon and provides a new representation alignment perspective for training multimodal models with unimodal data.

cs.MM↗
arXiv2026

A Short Note on Batch-efficient Divide-and-Conquer Algorithm for EigenDecomposition

EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in deep neural networks. Our previous work proposed a dedicated QR-based ED algorithm for batched small matrices (dim${<}32$). This short paper targets the limitation and proposes a batch-efficient Divide-and-Conquer based ED algorithm for larger matrices. The numerical test shows that for a mini-batch of matrices whose dimensions are smaller than $64$, our method can be much faster than the Pytorch SVD function.

cs.LG↗
arXiv2026

Is CLIP ideal? No. Can we fix it? Yes!

Contrastive Language-Image Pre-Training (CLIP) is a popular method for learning multimodal latent spaces with well-organized semantics. Despite its wide range of applications, CLIP's latent space is known to fail at handling complex visual-textual interactions. Recent works attempt to address its shortcomings with data-centric or algorithmic approaches. But what if the problem is more fundamental, and lies in the geometry of CLIP? Toward this end, we rigorously analyze CLIP's latent space properties, and prove that no CLIP-like joint embedding space exists which can correctly do any two of the following at the same time: 1. represent basic descriptions and image content, 2. represent attribute binding, 3. represent spatial location and relationships, 4. represent negation. Informed by this analysis, we propose Dense Cosine Similarity Maps (DCSMs) as a principled and interpretable scoring method for CLIP-like models, which solves the fundamental limitations of CLIP by retaining the semantic topology of the image patches and text tokens. This method improves upon the performance of classical CLIP-like joint encoder models on a wide array of benchmarks. We share our code and data here for reproducibility: https://github.com/Raphoo/DCSM_Ideal_CLIP

cs.LG↗
arXiv2026

Unsupervised Representation Learning from Sparse Transformation Analysis

There is a vast literature on representation learning based on principles such as coding efficiency, statistical independence, causality, controllability, or symmetry. In this paper we propose to learn representations from sequence data by factorizing the transformations of the latent variables into sparse components. Input data are first encoded as distributions of latent activations and subsequently transformed using a probability flow model, before being decoded to predict a future input state. The flow model is decomposed into a number of rotational (divergence-free) vector fields and a number of potential flow (curl-free) fields. Our sparsity prior encourages only a small number of these fields to be active at any instant and infers the speed with which the probability flows along these fields. Training this model is completely unsupervised using a standard variational objective and results in a new form of disentangled representations where the input is not only represented by a combination of independent factors, but also by a combination of independent transformation primitives given by the learned flow fields. When viewing the transformations as symmetries one may interpret this as learning approximately equivariant representations. Empirically we demonstrate that this model achieves state of the art in terms of both data likelihood and unsupervised approximate equivariance errors on datasets composed of sequence transformations.

cs.LG↗
arXiv2026

Morphological-Symmetry-Equivariant Heterogeneous Graph Neural Network for Robotic Dynamics Learning

We present a morphological-symmetry-equivariant heterogeneous graph neural network, namely MS-HGNN, for robotic dynamics learning, that integrates robotic kinematic structures and morphological symmetries into a single graph network. These structural priors are embedded into the learning architecture as constraints, ensuring high generalizability, sample and model efficiency. The proposed MS-HGNN is a versatile and general architecture that is applicable to various multi-body dynamic systems and a wide range of dynamics learning problems. We formally prove the morphological-symmetry-equivariant property of our MS-HGNN and validate its effectiveness across multiple quadruped robot learning problems using both real-world and simulated data. Our code is made publicly available at https://github.com/lunarlab-gatech/MorphSym-HGNN/.

cs.RO↗
arXiv2026

Langevin Flows for Modeling Neural Latent Dynamics

Neural populations exhibit latent dynamical structures that drive time-evolving spiking activities, motivating the search for models that capture both intrinsic network dynamics and external unobserved influences. In this work, we introduce LangevinFlow, a sequential Variational Auto-Encoder where the time evolution of latent variables is governed by the underdamped Langevin equation. Our approach incorporates physical priors -- such as inertia, damping, a learned potential function, and stochastic forces -- to represent both autonomous and non-autonomous processes in neural systems. Crucially, the potential function is parameterized as a network of locally coupled oscillators, biasing the model toward oscillatory and flow-like behaviors observed in biological neural populations. Our model features a recurrent encoder, a one-layer Transformer decoder, and Langevin dynamics in the latent space. Empirically, our method outperforms state-of-the-art baselines on synthetic neural populations generated by a Lorenz attractor, closely matching ground-truth firing rates. On the Neural Latents Benchmark (NLB), the model achieves superior held-out neuron likelihoods (bits per spike) and forward prediction accuracy across four challenging datasets. It also matches or surpasses alternative methods in decoding behavioral metrics such as hand velocity. Overall, this work introduces a flexible, physics-inspired, high-performing framework for modeling complex neural population dynamics and their unobserved influences.

cs.LG↗