Sparse plus Low-Rank $(\mathbf{S} + \mathbf{L}\mathbf{R})$ decomposition of Large Language Models (LLMs) has emerged as a promising direction in $\textit{model compression}$, aiming to decompose pre-trained model weights into a sum of sparse and low-rank matrices $\mathbf{W} \approx \mathbf{S} + \mathbf{LR}$. Despite recent progress, existing methods often suffer from substantial performance degradation compared to dense models. In this work, we introduce $\texttt{3BASiL-TM}$, an efficient one-shot post-training method for $(\mathbf{S} + \mathbf{L}\mathbf{R})$ decomposition of LLMs that addresses this gap. Our approach first introduces a novel 3-Block Alternating Direction Method of Multipliers (ADMM) method, termed $\texttt{3BASiL}$, to minimize the layer-wise reconstruction error with convergence guarantees.

To alleviate the reliance on costly 3D training data, recent studies have explored zero-shot 3DVG by leveraging the extensive knowledge and powerful reasoning capabilities of pre-trained LLMs and VLMs. However, existing paradigms tend to emphasize either spatial (3D-based) or semantic (2D-based) understanding, limiting their effectiveness in complex real-world applications. In this work, we introduce SPAZER -- a VLM-driven agent that combines both modalities in a progressive reasoning framework. It first holistically analyzes the scene and produces a 3D rendering from the optimal viewpoint. Based on this, anchor-guided candidate screening is conducted to perform a coarse-level localization of potential objects. Furthermore, leveraging retrieved relevant 2D camera images, 3D-2D joint decision-making is efficiently performed to determine the best-matching object. By bridging spatial and semantic reasoning neural streams, SPAZER achieves robust zero-shot grounding without training on 3D-labeled data. Extensive experiments on ScanRefer and Nr3D benchmarks demonstrate that SPAZER significantly outperforms previous state-of-the-art zero-shot methods, achieving notable gains of $\mathbf{9.0\}$% and $\mathbf{10.9\}$% in accuracy.

We study a sequential decision-making problem on a $n$-node graph $\mathcal{G}$ where each node has an unknown label from a finite set $\mathbf{\Omega}$, drawn from a joint distribution $\mathcal{P}$ that is Markov with respect to $\mathcal{G}$. At each step, selecting a node reveals its label and yields a label-dependent reward. The goal is to adaptively choose nodes to maximize expected accumulated discounted rewards. We impose a frontier exploration constraint, where actions are limited to neighbors of previously selected nodes, reflecting practical constraints in settings such as contact tracing and robotic exploration. We design a Gittins index-based policy that applies to general graphs and is provably optimal when $\mathcal{G}$ is a forest.

We introduce a new family of algorithms for detecting and estimating a rank-one signal from a noisy observation under prior information about that signal's direction, focusing on examples where the signal is known to have entries biased to be positive. Given a matrix observation $\mathbf{Y}$, our algorithms construct a *nonlinear Laplacian*, another matrix of the form $\mathbf{Y} + \mathrm{diag}(\sigma(\mathbf{Y1}))$ for a nonlinear $\sigma: \mathbb{R} \to \mathbb{R}$, and examine the top eigenvalue and eigenvector of this matrix. When $\mathbf{Y}$ is the (suitably normalized) adjacency matrix of a graph, our approach gives a class of algorithms that search for unusually dense subgraphs by computing a spectrum of the graph deformed by the degree profile $\mathbf{Y1}$. We study the performance of such algorithms compared to direct spectral algorithms (the case $\sigma = 0$) on models of sparse principal component analysis with biased signals, including the Gaussian planted submatrix problem. For such models, we rigorously characterize the strength of rank-one signal, as a function of the nonlinearity $\sigma$, required for an outlier eigenvalue to appear in the spectrum of a nonlinear Laplacian matrix. While identifying the $\sigma$ that minimizes the required signal strength in closed form seems intractable, we explore three approaches to design $\sigma$ numerically: exhaustively searching over simple classes of $\sigma$, learning $\sigma$ from datasets of problem instances, and tuning $\sigma$ using black-box optimization of the critical signal strength. We find both theoretically and empirically that, if $\sigma$ is chosen appropriately, then nonlinear Laplacian spectral algorithms substantially outperform direct spectral algorithms, while retaining the conceptual simplicity of spectral methods compared to broader classes of computations like approximate message passing or general first order methods.

Zeroth-order Optimization (ZO) has received wide attention in machine learning, especially when computing full gradient is expensive or even impossible. Recently, ZO has emerged as an important paradigm for memory-efficient fine-tuning of large language models (LLMs), circumventing the memory overhead of backpropagation. However, existing ZO gradient estimators exhibit dimension-dependent variance scaling as $\Theta(d)$, leading to dimension-dependent convergence rates without further assumptions on the objective function, which is prohibitive for large-scale LLM parameters.

To enhance controllability in text-to-image generation, ControlNet introduces image-based control signals, while ControlNet++ improves pixel-level cycle consistency between generated images and the input control signal. To avoid the prohibitive cost of back-propagating through the sampling process, ControlNet++ optimizes only low-noise timesteps (e.g., $t < 200$) using a single-step approximation, which not only ignores the contribution of high-noise timesteps but also introduces additional approximation errors. A straightforward alternative for optimizing controllability across all timesteps is Direct Preference Optimization (DPO), a fine-tuning method that increases model preference for more controllable images ($I^{w}$) over less controllable ones ($I^{l}$). However, due to uncertainty in generative models, it is difficult to ensure that win--lose image pairs differ only in controllability while keeping other factors, such as image quality, fixed. To address this, we propose performing preference learning over control conditions rather than generated images.

Motivated by practical applications where stable long-term performance is critical--such as robotics, operations research, and healthcare--we study the problem of distributionally robust (DR) average-reward reinforcement learning. We propose two algorithms that achieve near-optimal sample complexity. The first reduces the problem to a DR discounted Markov decision process (MDP), while the second, Anchored DR Average-Reward MDP, introduces an anchoring state to stabilize the controlled transition kernels within the uncertainty set. Assuming the nominal MDP is uniformly ergodic, we prove that both algorithms attain a sample complexity of $\widetilde{O}\left(|\mathbf{S}||\mathbf{A}| t_{\mathrm{mix}}^2\varepsilon^{-2}\right)$ for estimating the optimal policy as well as the robust average reward under KL and $f_k$-divergence-based uncertainty sets, provided the uncertainty radius is sufficiently small. Here, $\varepsilon$ is the target accuracy, $|\mathbf{S}|$ and $|\mathbf{A}|$ denote the sizes of the state and action spaces, and $t_{\mathrm{mix}}$ is the mixing time of the nominal MDP. This represents the first finite-sample convergence guarantee for DR average-reward reinforcement learning.

The loss landscapes of neural networks contain minima and saddle points that may be connected in flat regions or appear in isolation. We identify and characterize a special structure in the loss landscape: channels along which the loss decreases extremely slowly, while the output weights of at least two neurons, $a_i$ and $a_j$, diverge to $\pm$infinity, and their input weight vectors, $\mathbf{w_i}$ and $\mathbf{w_j}$, become equal to each other.

This paper presents $\mathbf{OLinear}$, a $\mathbf{linear}$-based multivariate time series forecasting model that operates in an $\mathbf{o}$rthogonally transformed domain. Recent forecasting models typically adopt the temporal forecast (TF) paradigm, which directly encode and decode time series in the time domain. However, the entangled step-wise dependencies in series data can hinder the performance of TF. To address this, some forecasters conduct encoding and decoding in the transformed domain using fixed, dataset-independent bases (e.g., sine and cosine signals in the Fourier transform). In contrast, we propose $\mathbf{OrthoTrans}$, a data-adaptive transformation based on an orthogonal matrix that diagonalizes the series' temporal Pearson correlation matrix.

We consider the problem of preprocessing an $n\times n$ matrix $\mathbf{M}$, and supporting queries that, for any vector $v$, returns the matrix-vector product $\mathbf{M} v$. This problem has been extensively studied in both theory and practice: on one side, practitioners have developed algorithms that are highly efficient in practice, whereas on the other side, theoreticians have proven that the problem cannot be solved faster than naive multiplication in the worst-case. This lower bound holds even in the average-case, implying that existing average-case analyses cannot explain this gap between theory and practice. Hence, we study the problem for \emph{structured} matrices. We show that for $n\times n$ Boolean matrices of VC-dimension $d$, the matrix-vector multiplication problem can be solved with $\smash{\tilde{O}(n^2)}$ preprocessing and $\smash{\tilde O(n^{2-1/d})}$ query time.