Compiler optimization is essential for improving program performance, yet modern compilers still depend on manually crafted transformation rules over intermediate representations (IRs). As compilers grow in complexity, maintaining these rulebased optimizations becomes increasingly labor-intensive and difficult to scale. Recent advances in large language models (LLMs) offer a promising alternative, but their effectiveness in compiler optimization remains limited - primarily due to the lack of IR-oriented datasets that expose models to diverse transformation samples in real-world scenarios (optimization-sensitive samples), hindering LLMs from learning rich and generalizable optimization strategies. In this paper, we introduce IR-OptSet, the first public optimization-sensitive dataset for advancing LLM-based IR optimizers. It comprises 170KLLVMIR samples from open-source repositories across 8 representative optimization domains. IROptSet defines two core tasks: Code Analysis and Optimized Code Generation, and provides tools for correctness verification, performance evaluation, and dataset expansion. In our experiments, fine-tuning three representative LLMs on IROptSet leads to significant accuracy improvements across both tasks. Moreover, the LLM fine-tuned with IR-OptSet outperforms traditional compiler with the -O3 option in 64 test cases in terms of performance. Further analysis reveals that IROptSet provides greater transformation diversity and representativeness than three widely used IR-oriented datasets, highlighting its potential to drive model-based IR optimization.

Diffusion models typically generate image batches from independent Gaussian initial noises. We argue that this independence assumption is only one choice within a broader class of valid joint noise designs. Instead, one can specify a coupling of the initial noises: each noise remains marginally standard Gaussian, so the pretrained diffusion model receives the same single-sample input distribution, while the dependence across samples is chosen by design. This reframes initial-noise control from selecting or optimizing individual seeds to designing the dependence structure of a multi-sample gallery. This view gives a general framework for initial-noise design, covering several existing methods as special cases and leading naturally to new coupled-noise constructions. Coupled noise can improve generation on its own without adding sampling cost, and it is flexible enough to serve as a structured initialization for optimization-based pipelines when additional computation is available. Empirically, repulsive Gaussian coupling improves gallery diversity on SD1.5, SDXL, and SD3 while largely preserving prompt alignment and image quality. It matches or outperforms recent test-time noise-optimization baselines on several diversity metrics at the same sampling cost as independent generation. Subspace couplings also support fixed-object background generation, producing diverse, natural backgrounds compared with specialized inpainting baselines, with a tunable trade-off in foreground fidelity.

The Adam optimization algorithm has proven remarkably effective for optimization problems across machine learning and even traditional tasks in geometry processing. At the same time, the development of equivariant methods, which preserve their output under the action of rotation or some other transformation, has proven to be important for geometry problems across these domains. In this work, we observe that Adam -- when treated as a function that maps initial conditions to optimized results -- is not rotation equivariant for vector-valued parameters due to per-coordinate moment updates. This leads to significant artifacts and biases in practice. We propose to resolve this deficiency with VectorAdam, a simple modification which makes Adam rotation-equivariant by accounting for the vector structure of optimization variables. We demonstrate this approach on problems in machine learning and traditional geometric optimization, showing that equivariant VectorAdam resolves the artifacts and biases of traditional Adam when applied to vector-valued data, with equivalent or even improved rates of convergence.

To validate the effectiveness of SHOT, we conduct empirical tests on standard few-shot learning tasks and qualitatively analyze its dynamics.

Large language models (LLMs) are commonly trained on datasets consisting of fixed-length token sequences.