Stochastic momentum methods such as heavy ball (HB), Nesterov momentum, and variants of Accelerated SGD (ASGD) [Kidambi et al., 2018] are widely used in modern training, but their stochastic benefits depend on two distinct quantities: serial runtime, the number of iterations needed to reach a target accuracy, and compute efficiency (CE), the inverse total gradient-query or FLOP cost. Larger batches reduce serial runtime without hurting CE only when the contraction gap grows linearly with batch size. We study stochastic HB and ASGD for consistent linear regression with Gaussian covariates and prove finite-dimensional, discrete-time lower bounds on their batch-size tradeoffs. Our first result shows that HB does not improve the CE frontier over SGD for arbitrary spectra; rather, it preserves SGD-level CE over a larger batch-size window, allowing larger batches to reduce serial runtime until HB reaches its deterministic accelerated scale. This window can be a factor $\sqrtκ$ larger than the SGD critical batch size. For ASGD, the picture is more spectrum-dependent: for rapidly decaying power-law spectra, ASGD improves small-batch CE over HB/SGD, but as batch size grows it trades this CE advantage for improved serial runtime. Synthetic linear-regression experiments verify these qualitative regimes, including near-overlap of ASGD and HB for slowly decaying spectra and the predicted CE--serial tradeoff for rapidly decaying spectra.

Understanding how the human brain progresses from processing simple linguistic inputs to performing high-level reasoning is a fundamental challenge in neuroscience. While modern large language models (LLMs) are increasingly used to model neural responses to language, their internal representations are highly "entangled," mixing information about lexicon, syntax, meaning, and reasoning. This entanglement biases conventional brain encoding analyses toward linguistically shallow features (e.g., lexicon and syntax), making it difficult to isolate the neural substrates of cognitively deeper processes. Here, we introduce a residual disentanglement method that computationally isolates these components. By first probing an LM to identify feature-specific layers, our method iteratively regresses out lower-level representations to produce four nearly orthogonal embeddings for lexicon, syntax, meaning, and, critically, reasoning. We used these disentangled embeddings to model intracranial (ECoG) brain recordings from neurosurgical patients listening to natural speech. We show that: 1) This isolated reasoning embedding exhibits unique predictive power, accounting for variance in neural activity not explained by other linguistic features and even extending to the recruitment of visual regions beyond classical language areas.

Clustering is a fundamental task in both machine learning and data mining. Among various methods, edge-colored clustering (ECC) has emerged as a useful approach for handling categorical data. Given a hypergraph with (hyper)edges labeled by colors, ECC aims to assign vertex colors to minimize the number of edges where the vertex color differs from the edge's color. However, traditional ECC has inherent limitations, as it enforces a nonoverlapping and exhaustive clustering. To tackle these limitations, three versions of ECC have been studied: LOCALECC and GLOBALECC, which allow overlapping clusters, and ROBUSTECC, which accounts for vertex outliers.

Model inversion attacks (MIAs) aim to reconstruct class-representative samples from trained models. Recent generative MIAs utilize generative adversarial networks to learn image priors that guide the inversion process, yielding reconstructions with high visual quality and strong fidelity to the private training data. To explore the reason behind their effectiveness, we begin by examining the gradients of inversion loss w.r.t.

Federated Graph Learning (FGL) has been shown to be particularly effective in enabling collaborative training of Graph Neural Networks (GNNs) in decentralized settings. Model-heterogeneous FGL further enhances practical applicability by accommodating client preferences for diverse model architectures. However, existing model-heterogeneous approaches primarily target Euclidean data and fail to account for a crucial aspect of graph-structured data: topological relationships. To address this limitation, we propose TRUST, a novel knowledge distillation-based modelheterogeneous FGL framework. Specifically, we propose Progressive Curriculum Node Scheduler to progressively introduce challenging nodes based on learning difficulty. In Adaptive Curriculum Distillation Modulator, we propose an adaptive temperature modulator that dynamically adjusts knowledge distillation temperature to accommodate varying client capabilities and graph complexity. Moreover, we leverage Wasserstein-Driven Affinity Distillation to enable models to capture crossclass structural relationships through optimal transport. Extensive experiments on multiple graph benchmarks and model-heterogeneous settings show that TRUST outperforms existing methods, achieving an average 3.6% performance gain, particularly under moderate heterogeneity conditions.

Graph neural networks (GNNs) have achieved remarkable success in various domains but typically rely on centralized, static graphs, which limits their applicability in distributed, evolving environments. To address this limitation, we define the task of Federated Continual Graph Learning (FCGL), a paradigm for incremental learning on dynamic graphs distributed across decentralized clients. Existing methods, however, neither preserve graph topology during task transitions nor mitigate parameter conflicts in server-side aggregation. To overcome these challenges, we introduce MOTION, a generalizable FCGL framework that integrates two complementary modules: the Graph Topology-preserving Multi-Sculpt Coarsening (G-TMSC) module, which maintains the structural integrity of past graphs through a multi-expert, similarity-guided fusion process, and the Graph-Aware Evolving Parameter Adaptive Engine (G-EPAE) module, which refines global model updates by leveraging a topology-sensitive compatibility matrix. Extensive experiments on real-world datasets show that our approach improves average accuracy (AA) by an average of 30% over the FedAvg baseline across five datasets while maintaining a negative average forgetting (AF) rate, significantly enhancing generalization and robustness under FCGL settings.

At the core of the Transformer, the softmax normalizes the attention matrix to be right stochastic. Previous research has shown that this often de-stabilizes training and that enforcing the attention matrix to be doubly stochastic (through Sinkhorn's algorithm) consistently improves performance across different tasks, domains and Transformer flavors. However, Sinkhorn's algorithm is iterative, approximative, non-parametric and thus inflexible w.r.t. the obtained doubly stochastic matrix (DSM). Recently, it has been proven that DSMs can be obtained with a parametric quantum circuit, yielding a novel quantum inductive bias for DSMs with no known classical analogue. Motivated by this, we demonstrate the feasibility of a hybrid classical-quantum doubly stochastic Transformer (QDSFormer) that replaces the softmax in the self-attention layer with a variational quantum circuit. We study the expressive power of the circuit and find that it yields more diverse DSMs that better preserve information than classical operators. Across multiple small-scale object recognition tasks, we find that our QDSFormer consistently surpasses both a standard ViT and other doubly stochastic Transformers. Beyond the Sinkformer, this comparison includes a novel quantum-inspired doubly stochastic Transformer (based on QR decomposition) that can be of independent interest. Our QDSFormer also shows improved training stability and lower performance variation suggesting that it may mitigate the notoriously unstable training of ViTs on small-scale data.

Discrete diffusion models (DDMs) have shown powerful generation ability for discrete data modalities like text and molecules. However, their practical application is hindered by inefficient sampling, requiring a large number of sampling steps. Accelerating DDMs by using larger step sizes typically introduces significant problems in generation quality, as it amplifies the impact of both the compounding decoding error due to factorized predictions and discretization error from numerical approximations, leading to a significant decrease in sampling quality. To address these challenges, we propose learnable sampler distillation (LSD), a novel approach to train fast and high-fidelity samplers for DDMs. LSD employs a distillation approach where a student sampler with a few steps learns to align its intermediate score trajectory with that of a high-quality teacher sampler with numerous steps. This alignment is achieved by optimizing learnable sampler coefficients that adaptively adjust sampling dynamics. Additionally, we further propose LSD+, which also learns time schedules that allocate steps non-uniformly. Experiments across text generation, image generation, and synthetic tasks demonstrate that our proposed approaches outperform existing samplers for DDMs, achieving substantially higher sampling quality with significantly fewer sampling steps. Our code is available at https://github.com/feiyangfu/LSD.

Neural collapse [26] is an intuitive observation that happens at the terminal phase of a well-trained model on a balanced dataset that last-layer features converge to within-class mean, and all within-class means and their corresponding classifier vectors converge to ETF as shown in Figure 6. The main results can be concluded as follows: (NC1) Variability of the last-layer features Σ:= Avgi,c{(hic hc)(hic hc)T} collapse within-class: Σ 0, where hic is the last-layer feature of the i-th sample in the c-th class, and hc is the within-class mean of c-th class's features. Last-layer features converge to within-class mean, and all within-class means and their corresponding classifier vectors converge to a simplex ETF. To analyze this phenomenon, some studies simplify deep neural networks as last-layer features and classifier (layer-peeled model)[9, 12, 40, 53] with proper constraints or regularizations. In the view of layer-peeled model (LPM), training W with constraints on the weights can be seen as training the C-class classification head WL = {W1,...,WC} and features H = {h1,...,hN} of all n samples output by last layer of backbone with constraints EW and EH respectively. EH. (6) In the balanced dataset, as described in Lemma 1, any solutions to this model merge neural collapse and form a simplex equiangular tight frame (ETF), which means ETF is optimal classifier in the balanced case of LPM.

Although receiving notable improvements, current multi-view clustering (MVC) techniques generally rely on feature library mechanisms to propagate accumulated knowledge from historical views to newly-arrived data, which overlooks the information pertaining to basis embedding within each view. Moreover, the mapping paradigm inevitably alters the values of learned landmarks and built affinities due to the uninterruption nature, accordingly disarraying the hierarchical cluster structures. To mitigate these two issues, we in the paper provide a named BSTM algorithm. Concretely, we firstly synchronize with the distinct dimensions by introducing a group of specialized projectors, and then establish unified anchors for all views collected so far to capture intrinsic patterns. Afterwards, departing from per-view architectures, we devise a shared bipartite graph construction via indicators to quantify similarity, which not only avoids redundant data-recalculations but alleviates the representation distortion caused by fusion.