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Recent advances in diffusion and flow matching models have highlighted a shift in the preferred prediction target -- moving from noise ($\varepsilon$) and velocity (v) to direct data (x) prediction -- particularly in high-dimensional settings. However, a formal explanation of why the optimal target depends on the specific properties of the data remains elusive. In this work, we provide a theoretical framework based on a generalized prediction formulation $u=kx-(1-k)n$, where $x$ represents clean data and $n$ denotes noise. This formulation accommodates arbitrary targets, of which $\varepsilon$-, v-, and x-prediction are special cases. We derive the analytical relationship between data's geometry and the optimal prediction target, offering a rigorous justification for why x-prediction becomes superior when the ambient dimension significantly exceeds the data's intrinsic dimension. Furthermore, our controlled analysis reveals how time conditioning and loss variations systematically modulate this optimal objective. While our theory identifies dimensionality as the governing factor for the optimal prediction target, the intrinsic dimension of manifold-bound data is typically intractable to estimate in practice. To bridge this gap, we propose k-Diff, a framework that employs a data-driven approach to learn the optimal prediction parameter k directly from data, bypassing the need for explicit dimension estimation. Extensive experiments in both latent-space and pixel-space image generation demonstrate that k-Diff consistently outperforms fixed-target baselines across varying architectures and data scales, providing a principled and automated approach to enhancing generative performance.

Large language models (LLMs) are increasingly being used to support computer science research. To contribute reliably, these systems must be able to work with information distributed across research papers and across different aspects of the research process. However, large-scale resources that systematically organize such information into structured supervision for both model evaluation and post-training remain limited. To address this gap, we propose a systematic paper-to-QA construction pipeline that organizes information from AI research papers into structured QA pairs supported by source evidence. Using this pipeline, we construct CS-54k, a 54k-pair corpus derived from 14,474 openly licensed AI research papers. The corpus covers eight recurring paper components, including research domain, prior work, existing challenges, motivation, findings and assumptions, methods, experimental settings, and experimental results. We further derive two complementary subsets: CS-4k, a benchmark for evaluating LLMs on paper-derived research QA, and CS-50k, a companion corpus for post-training. Extensive evaluations on CS-4k reveal substantial performance differences across existing LLMs and paper components, with experimental settings and results remaining particularly challenging. Moreover, post-training on CS-50k substantially improves Qwen2.5-7B-Instruct on CS-4k, demonstrating the practical utility of structured, paper-derived supervision. Together, CS-4k and CS-50k provide a unified and scalable resource for benchmarking and improving LLMs on research paper question answering.

Visual Question Answering (VQA) imposes substantial computational overhead on vision-language models (VLMs), motivating model-agnostic input reduction methods that can be readily applied across diverse VLMs, including in black-box settings. Simply enforcing a visual-token cap reduces computation, but it can discard information needed to answer the question. A single reduction strategy also struggles to accommodate different scenarios. Our key observation is that cropping and compression are complementary: cropping highlights small targets and local details, whereas whole-image compression better preserves context for large targets or distributed evidence. Based on this observation, we propose C$^2$-Routing, which adaptively selects cropping or compression according to the input image and question. Since both strategies may still discard key information, we further design a safety gate that uses the predicted joint correctness distribution under original and reduced inputs to guide fallback and protect accuracy. To accommodate consumer GPU resource constraints, all training and evaluation experiments run on RTX 3090 GPUs. To measure gains beyond token capping, we use full-image baselines with the same cap of 1,024 visual tokens. We conduct extensive evaluation on three VLMs and 18 datasets spanning local details, global scenes, scene text, and documents. With the visual budget already capped, C$^2$-Routing further reduces end-to-end FLOPs by 36.53% and visual tokens by 42.36% on average, with a mean relative task-score decrease of only 0.77%.

Low-rank adaptation (LoRA) is the de facto method for parameter-efficient fine-tuning of large neural networks, achieving strong task adaptation with minimal trainable parameters and low optimization cost. Beyond this efficiency, practitioners have observed two striking properties: \textit{robustness to catastrophic forgetting} and the ability to \textit{merge independently trained adapters} into a single model that performs competitively across multiple tasks. These properties are central to continual and multi-task learning, yet remain poorly understood. In this work, we provide a theoretical explanation through a unified \textit{margin-based perspective}. We analyze LoRA in multiclass linear classification under a near-orthogonal task regime with $\ell_2$-regularization, and characterize the optimal LoRA adapter across regularization regimes. Our analysis shows that, in an intermediate regime of regularization parameters, the optimal adapter aligns with the \emph{max-margin solution} on the fine-tuning data. Building on this characterization, we derive two key consequences. First, we obtain closed-form expressions for the margins on pre-training and fine-tuning data, revealing a precise margin trade-off: the regularization parameter controls the balance between retention and adaptation. Second, we analyze adapter merging, proving that merged models achieve positive margin on each task and deriving optimal mixing coefficients that balance margins across tasks and maximize the margin over their union. These results lead to a simple, training-free merging rule, which we term \textit{margin-based LoRA merging} (MaLoRA). Experiments on modern architectures and real datasets validate our theoretical predictions, showing that MaLoRA matches or outperforms several adapter-merging baselines across a range of vision and language classification tasks.

System-1 Decision Models directly make structured probabilistic decisions over query-specified options given a state in a single forward pass, without autoregressively generating reasoning trajectories or textual responses. Recent evaluations cover diverse tasks but often rely on existing benchmarks, where prior exposure to test material can obscure generalization. Moreover, real-world decision making often involves long contexts, large option spaces, and complex logical dependencies, challenges that existing benchmarks do not adequately capture together. Thus, we introduce MMDM (Massive Multitask Decision Making), a benchmark of 5,448 high-quality questions across 16 task categories, combining newly constructed tasks with source-grounded recompositions and rewrites for single-select, multi-select, and soft-label decision making in fresh contexts. It covers realistic scenarios such as agent state tracking, tool and skill selection, preference judgments, and rubric scoring, with option spaces ranging from 2 to 1,024 and inputs extending to 64,817 tokens. With MMDM, we conduct a comprehensive quantitative evaluation of 28 decision models, showing that many perform well on common knowledge yet struggle with interdependent options, constrained decisions, and multi-select tasks. For example, Perplexity Decider-V1.2 reaches 78.75% Hard Single-select Accuracy on world knowledge, but only 53.95% on option logic and 47.95% on constraint planning, while the best Hard Multi-select Accuracy across all models is 36.81%. These results highlight joint reasoning, constraint-aware selection, and complete multi-select recovery as key priorities for decision model development, with MMDM providing a testbed for measuring this progress.