State-space models (SSMs) have recently emerged as a compelling alternative to Transformers for sequence modeling tasks. This paper presents a theoretical generalization analysis of selective SSMs, the core architectural component behind the Mamba model. We derive a novel covering number-based generalization bound for selective SSMs, building upon recent theoretical advances in the analysis of Transformer models. Using this result, we analyze how the spectral abscissa of the continuous-time state matrix influences the model's stability during training and its ability to generalize across sequence lengths. We empirically validate our findings on a synthetic majority task, the IMDb sentiment classification benchmark, and the ListOps task, demonstrating how our theoretical insights translate into practical model behavior.

Generating high-resolution 3D shapes using volumetric representations such as Signed Distance Functions (SDFs) presents substantial computational and memory challenges. We introduce Direct3D-S2, a scalable 3D generation framework based on sparse volumes that achieves superior output quality with dramatically reduced training costs. Our key innovation is the Spatial Sparse Attention (SSA) mechanism, which greatly enhances the efficiency of Diffusion Transformer (DiT) computations on sparse volumetric data. SSA allows the model to effectively process large token sets within sparse volumes, significantly reducing computational overhead and achieving a 3.9 speedup in the forward pass and a 9.6 speedup in the backward pass. Our framework also includes a variational autoencoder (VAE) that maintains a consistent sparse volumetric format across input, latent, and output stages. Compared to previous methods with heterogeneous representations in 3DVAE, this unified design significantly improves training efficiency and stability. Our model is trained on public datasets, and experiments demonstrate that Direct3D-S2 not only surpasses state-of-the-art methods in generation quality and efficiency, but also enables training at 1024 resolution using only 8 GPUs, a task typically requiring at least 32 GPUs for volumetric representations at 2563 resolution, thus making gigascale 3D generation both practical and accessible.

In this paper, we study the finite-sample statistical rates of distributional temporal difference (TD) learning with linear function approximation. The aim of distributional TD learning is to estimate the return distribution of a discounted Markov decision process for a given policy π. Previous works on statistical analysis of distributional TD learning mainly focus on the tabular case. In contrast, we first consider the linear function approximation setting and derive sharp finite-sample rates. Our theoretical results demonstrate that the sample complexity of linear distributional TD learning matches that of classic linear TD learning. This implies that, with linear function approximation, learning the full distribution of the return from streaming data is no more difficult than learning its expectation (value function). To derive tight sample complexity bounds, we conduct a fine-grained analysis of the linear-categorical Bellman equation and employ the exponential stability arguments for products of random matrices. Our results provide new insights into the statistical efficiency of distributional reinforcement learning algorithms.

In this paper, we propose a novel optimizer state compression algorithm, namely π-Quant, which leverages the properties of irrational numbers (e.g., π) for memoryefficient training. The core idea is based on our mathematical findings, which show that a pair of parameters can be represented by a single rotation angle using the complex rotation scheme. Building on this insight, we map the parameters into a complex space and perform quantization using the corresponding rotation angles. To efficiently integrate it into optimization process, we develop an efficient system of geometric equations that computes the precise rotation angles with linear complexity. We evaluate π-Quant on a wide range of tasks. Our experiments show that it can reduce the bit-width of parameters to 3.32-bit, achieving a 41.8% decrease in GPU memory usage, all while maintaining full accuracy.

Early-Exit Deep Neural Networks enable adaptive inference by allowing prediction at intermediary layers, significantly reducing computational costs and latency. Most of the early exit strategies greedily exit a sample at an intermediary layer if the confidence in class prediction exceeds a predefined threshold that is set using a static validation set. This is problematic as the model might be overconfident in a wrong class. Also, they are not robust to distribution shifts encountered in deployment, which can undermine model trustworthiness and accuracy. To address these challenges, we propose UAT that adapts the threshold for exit decisions using a Multi-Armed Bandit framework, enabling online, unsupervised adjustment of exit decisions. UAT makes decisions based on a new reward function that assesses predictive certainty and its reliability to balance computational efficiency and prediction quality while penalizing unnecessary late exits. We provide guarantees on risk achieved by UAT and validate its performance on diverse tasks spanning vision-language understanding, text generation, and classification. Our framework demonstrates consistent improvements in speedup (1.70 2.10) with a minimal performance drop (< 2%) as compared to full model performance. Our source code is available at https://github.com/Div290/UAT.

Understanding the predictions made by deep learning models remains a central challenge, especially in high-stakes applications. A promising approach is to equip models with the ability to answer counterfactual questions - hypothetical "what if?" scenarios that go beyond the observed data and provide insight into a model reasoning. In this work, we introduce the notion of causal interpretability, which formalizes when counterfactual queries can be evaluated from a specific class of models and observational data. We analyze two common model classes - blackbox and concept-based predictors - and show that neither is causally interpretable in general. To address this gap, we develop a framework for building models that are causally interpretable by design. Specifically, we derive a complete graphical criterion that determines whether a given model architecture supports a given counterfactual query. This leads to a fundamental tradeoff between causal interpretability and predictive accuracy, which we characterize by identifying the unique maximal set of features that yields an interpretable model with maximal predictive expressiveness. Experiments corroborate the theoretical findings.

Machine learning (ML) is transforming modeling and control in the physical, engineering, and biological sciences. However, rapid development has outpaced the creation of standardized, objective benchmarks--leading to weak baselines, reporting bias, and inconsistent evaluations across methods. This undermines reproducibility, misguides resource allocation, and obscures scientific progress. To address this, we develop a Common Task Framework (CTF) for scientific machine learning. The CTF features a curated set of datasets and task-specific metrics spanning forecasting, state reconstruction, and generalization under realistic constraints, including noise and limited data. Inspired by the success of CTFs in fields like natural language processing and computer vision, our framework provides a structured, rigorous foundation for head-to-head evaluation of diverse algorithms.

Large foundation models face challenges in acquiring transferable, structured thinking abilities, especially when supervised with rigid templates or crowd-annotated instruction datasets. Unlike prior approaches, we focus on a thinking-centric data synthesis paradigm that enables models to evolve through self-generated, cognitively guided data. We propose MINDGYM, a structured and scalable framework for question synthesis, composed of: (1) Cognitive Thinking Process Injection, which infuses high-level reasoning objectives to shape the model's synthesis behavior; (2) Seed Single-Hop Question Synthesis, generating atomic questions from diverse semantic types to encourage broader thinking; and (3) Challenging MultiHop QASynthesis, composing more complex multi-hop questions based on QA seeds for deeper reasoning. Detailed analysis shows that synthetic data generated by our method achieves 16.7% higher average quality and 67.91% lower quality variance compared to baseline sources, highlighting that both high-quality and selfcontained data are essential for effective, thinking-oriented finetuning. MINDGYM improves performance on six reasoning benchmarks, achieving gains of up to 16% on MathVision using only 400 data samples, and generalizable improvements across different model sizes and architectures. MINDGYM underscores the viability of self-challenging mechanisms in refining large model capabilities while minimizing human intervention and resource demands. Code and data are released to promote data-centric research into self-evolving foundation models driven by their internal reasoning capabilities.

We study policy optimization in Stackelberg mean field games (MFGs), a hierarchical framework for modeling the strategic interaction between a single leader and an infinitely large population of homogeneous followers. The objective can be formulated as a structured bi-level optimization problem, in which the leader needs to learn a policy maximizing its reward, anticipating the response of the followers. Existing methods for solving these (and related) problems often rely on restrictive independence assumptions between the leader's and followers' objectives, use samples inefficiently due to nested-loop algorithm structure, and lack finite-time convergence guarantees. To address these limitations, we propose AC-SMFG, a single-loop actor-critic algorithm that operates on continuously generated Markovian samples. The algorithm alternates between (semi-)gradient updates for the leader, a representative follower, and the mean field, and is simple to implement in practice. We establish the finite-time and finite-sample convergence of the algorithm to a stationary point of the Stackelberg objective. To our knowledge, this is the first Stackelberg MFG algorithm with non-asymptotic convergence guarantees. Our key assumption is a "gradient alignment" condition, which requires that the full policy gradient of the leader can be approximated by a partial component of it, relaxing the existing leader-follower independence assumption. Simulation results in a range of well-established economics environments demonstrate that AC-SMFG outperforms existing multi-agent and MFG learning baselines in policy quality and convergence speed.

Opaque objects reconstructed by 3DGaussian Splatting (3DGS) often exhibit a falsely transparent surface, leading to inconsistent background and internal patterns under camera motion in interactive viewing. This issue stems from the ill-posed optimization in 3DGS. During training, background and foreground Gaussians are blended via α-compositing and optimized solely against the input RGB images using a photometric loss. As this process lacks an explicit constraint on surface opacity, the optimization may incorrectly assign transparency to opaque regions, resulting in view-inconsistent and falsely transparent output. This issue is difficult to detect in standard evaluation settings (i.e., rendering static images), but becomes particularly evident in object-centric reconstructions under interactive viewing.