Spatial transcriptomics (ST) technologies provide gene expression measurements with spatial resolution, enabling the dissection of tissue structure and function. A fundamental challenge in ST analysis is clustering spatial spots into coherent functional regions. While existing models effectively integrate expression and spatial signals, they largely overlook sequence-level biological priors encoded in the DNA sequences of expressed genes. To bridge this gap, we propose SAINT (Sequence-Aware Integration for Nucleotide-informed Transcriptomics), a unified framework that augments spatial representation learning with nucleotide-derived features. We construct sequence-augmented datasets across 14 tissue sections from three widely used ST benchmarks (DLPFC, HBC, and MBA), retrieving reference DNA sequences for each expressed gene and encoding them using a pretrained Nucleotide Transformer. For each spot, gene-level embeddings are aggregated via expression-weighted and attention-based pooling, then fused with spatial-expression representations through a late fusion module. Extensive experiments demonstrate that SAINT consistently improves clustering performance across multiple datasets.

Due to its powerful capability of self-supervised representation learning and clustering, contrastive attributed graph clustering (CAGC) has achieved great success, which mainly depends on effective data augmentation and contrastive objective setting. However, most CAGC methods utilize edges as auxiliary information to obtain node-level embedding representation and only focus on node-level embedding augmentation. This approach overlooks edge-level embedding augmentation and the interactions between node-level and edge-level embedding augmentations across various granularity. Moreover, they often treat all contrastive sample pairs equally, neglecting the significant differences between hard and easy positivenegative sample pairs, which ultimately limits their discriminative capability. To tackle these issues, a novel robust attributed graph clustering (RAGC), incorporating hybrid-collaborative augmentation (HCA) and contrastive sample adaptivedifferential awareness (CSADA), is proposed. First, node-level and edge-level embedding representations and augmentations are simultaneously executed to establish a more comprehensive similarity measurement criterion for subsequent contrastive learning.

Despite the popularity of the Adam optimizer in practice, most theoretical analyses study Stochastic Gradient Descent (SGD) as a proxy for Adam, and little is known about how the solutions found by Adam differ. In this paper, we show that Adam implicitly reduces a unique form of sharpness measure shaped by its adaptive updates, leading to qualitatively different solutions from SGD. More specifically, when the training loss is small, Adam wanders around the manifold of minimizers and takes semi-gradients to minimize this sharpness measure in an adaptive manner, a behavior we rigorously characterize through a continuous-time approximation using stochastic differential equations. We further demonstrate how this behavior differs from that of SGD in a well-studied setting: when training overparameterized models with label noise, SGD has been shown to minimize the trace of the Hessian matrix, tr(H), whereas we prove that Adam minimizes tr(Diag(H)1/2) instead. In solving sparse linear regression with diagonal linear networks, this distinction enables Adam to achieve better sparsity and generalization than SGD. Finally, our analysis framework extends beyond Adam to a broad class of adaptive gradient methods, including RMSProp, Adam-mini, Adalayer and Shampoo, and provides a unified perspective on how these adaptive optimizers reduce sharpness, which we hope will offer insights for future optimizer design.

We consider the problem of sampling distributions stemming from non-convex potentials with Unadjusted Langevin Algorithm (ULA). We prove the stability of the discrete-time ULA to drift approximations under the assumption that the potential is strongly convex at infinity.

Muscle coordination is fundamental when humans interact with the world. Reliable estimation of hand muscle engagement can serve as a source of internal feedback, supporting the development of embodied intelligence and the acquisition of dexterous skills. However, contemporary electromyography (EMG) sensing techniques either require prohibitively expensive devices or are constrained to gross motor movements, which inherently involve large muscles.

In settings where ML models are used to inform the allocation of resources, agents affected by the allocation decisions might have an incentive to strategically change their features to secure better outcomes. While prior work has studied strategic responses broadly, disentangling misreporting from genuine adaptation remains a fundamental challenge. In this paper, we propose a causally-motivated approach to identify and quantify how much an agent misreports on average by distinguishing deceptive changes in their features from genuine adaptation. Our key insight is that, unlike genuine adaptation, misreported features do not causally affect downstream variables (i.e., causal descendants). We exploit this asymmetry by comparing the causal effect of misreported features on their causal descendants as derived from manipulated datasets against those from unmanipulated datasets. We formally prove identifiability of the misreporting rate and characterize the variance of our estimator. We empirically validate our theoretical results using a semi-synthetic and real Medicare dataset with misreported data, demonstrating that our approach can be employed to identify misreporting in real-world scenarios.

Despite its widespread adoption, Adam's advantage over Stochastic Gradient Descent (SGD) lacks a comprehensive theoretical explanation. This paper investigates Adam's sensitivity to rotations of the parameter space. We observe that Adam's performance in training transformers degrades under random rotations of the parameter space, indicating a crucial sensitivity to the choice of basis in practice. This reveals that conventional rotation-invariant assumptions are insufficient to capture Adam's advantages theoretically. To better understand the rotation-dependent properties that benefit Adam, we also identify structured rotations that preserve or even enhance its empirical performance. We then examine the rotation-dependent assumptions in the literature and find that they fall short in explaining Adam's behaviour across various rotation types. In contrast, we verify the orthogonality of the update as a promising indicator of Adam's basis sensitivity, suggesting it may be the key quantity for developing rotation-dependent theoretical frameworks that better explain its empirical success.

Traditional curriculum learning proceeds from easy to hard samples, yet defining a reliable notion of difficulty remains elusive. Prior work has used submodular functions to induce difficulty scores in curriculum learning. We reinterpret adaptive subset selection and formulate it as a multi-armed bandit problem, where each arm corresponds to a submodular function guiding sample selection. We introduce ONLINESUBMOD, a novel online greedy policy that optimizes a utility-driven reward and provably achieves no-regret performance under various sampling regimes. Empirically, ONLINESUBMOD outperforms both traditional curriculum learning and bi-level optimization approaches across vision and language datasets, showing superior accuracy-efficiency tradeoffs. More broadly, we show that validationdriven reward metrics offer a principled way to guide the curriculum schedule. Our code is publicly available at GitHub 2.

Machine unlearning algorithms aim to efficiently remove data from a model without retraining it from scratch, in order to remove corrupted or outdated data or respect a user's "right to be forgotten." Certified machine unlearning is a strong theoretical guarantee based on differential privacy that quantifies the extent to which an algorithm erases data from the model weights. In contrast to existing works in certified unlearning for convex or strongly convex loss functions, or nonconvex objectives with limiting assumptions, we propose the first, first-order, black-box (i.e., can be applied to models pretrained with vanilla gradient descent) algorithm for unlearning on general nonconvex loss functions, which unlearns by "rewinding" to an earlier step during the learning process before performing gradient descent on the loss function of the retained data points. We prove (ϵ,δ) certified unlearning and performance guarantees that establish the privacy-utility-complexity tradeoff of our algorithm, and we prove generalization guarantees for functions that satisfy the Polyak-Lojasiewicz inequality. Finally, we demonstrate the superior performance of our algorithm compared to existing methods, within a new experimental framework that more accurately reflects unlearning user data in practice.

Understanding how the test risk scales with model complexity is a central question in machine learning. Classical theory is challenged by the learning curves observed for large over-parametrized deep networks. Capacity measures based on parameter count typically fail to account for these empirical observations. To tackle this challenge, we consider norm-based capacity measures and develop our study for random features based estimators, widely used as simplified theoretical models for more complex networks. In this context, we provide a precise characterization of how the estimator's norm concentrates and how it governs the associated test error. Our results show that the predicted learning curve admits a phase transition from under-to over-parameterization, but no double descent behavior. This confirms that more classical U-shaped behavior is recovered considering appropriate capacity measures based on models norms rather than size. From a technical point of view, we leverage deterministic equivalence as the key tool and further develop new deterministic quantities which are of independent interest.