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NeurIPS 2026

TwinPrune: Density-Aware Two-Phase Token Pruning for Vision-Language Models

Kai Liu, Anqi Li, Junxian Li, Zhixin Wang, Zhikai Chen, Renjing Pei, Yulun Zhang

We propose a unified spatial-density signal that scores token importance for \emph{both} phases of inference, instantiated as a bipartite merge during prefill and a KV eviction during decode, with measurable gains in each phase. To verify the two phases independently, we partition benchmarks into two diagnostic roles by their scoring rule. \emph{Prefill probes} such as MMBench, POPE, and ScienceQA score only the first decoded token, so their accuracy reflects only the argmax of prefill logits, computed before any decode-phase KV eviction takes effect. \emph{Full-pipeline probes} such as TextVQA, DocVQA, and MM-Vet score the full decoded sequence and therefore reveal both phases. We expose a fundamental evaluation flaw: published claims of decode-phase token pruning validated only on prefill probes have measured prefill quality, not decode quality. Empirically, removing all visual KV at decode leaves prefill-probe accuracy essentially unchanged while collapsing TextVQA and MM-Vet by tens of points, and the insensitivity is a property of the scoring rule, not of the compression strength. Across seven model variants from the InternVL-3.5, Qwen3-VL, and LLaVA-1.5 families and the three full-pipeline-probe benchmarks, we deliver an honest three-axis Pareto over compute, memory, and accuracy. Density-based prefill compression is competitive on the accuracy frontier, scales linearly in the visual-token count, and is roughly two orders of magnitude faster in token selection at high resolution. On the decode side, density top-$k$ KV eviction wins every TextVQA and MM-Vet cell against the strongest published baselines H2O, SnapKV, and StreamingLLM across three keep ratios. The advantage widens to $9.6$ percentage points over H2O at $12.5\%$ keep on TextVQA and holds $7$ to $10$ percentage points across the InternVL-3.5 series from 2B to 38B. Compression also scales gracefully with model size: every matched 8B-to-38B transition we measure reduces, rather than amplifies, the accuracy loss. We recommend MM-Vet or DocVQA as the minimum full-pipeline-probe test for any decode-phase claim. Our code and model will be released soon.

NeurIPS 2026

TwinFlux: One-Step Discrete-Continuous Flow for End-to-End Autonomous Driving

Yu Zhu, Qin Guo, Yujia Zhang, Zheng Shen

End-to-end autonomous driving planning requires trajectories that are multimodal, scene-compliant, and efficient to generate. Deterministic regression is fast but often collapses to a single future, while trajectory-vocabulary methods depend on predefined candidate coverage and iterative generative planners incur multi-step inference cost. We propose TwinFlux, a one-step discrete-continuous trajectory generation framework based on SplitMeanFlow. TwinFlux starts from data-driven trajectory prototypes and refines them through parallel heatmap and offset branches. The heatmap branch provides topology-aware coarse localization on a BEV grid, while the offset branch predicts grid-relative geometric refinement. A differentiable trajectory decoupling-and-reconstruction module connects this representation with physical trajectories. During training, TwinFlux enforces piecewise displacement consistency in reconstructed trajectory space, aligning direct one-step prediction with accumulated sub-interval evolution without Jacobian-vector-product computation or inference overhead. Experiments on NAVSIMv1 and NAVSIMv2 show that TwinFlux outperforms recent end-to-end planning baselines while maintaining real-time inference.

NeurIPS 2026

TurtLES: A Large-Scale Benchmark for Turbulent 3D Neural PDE Surrogates

Jarno Platenburg, Armand Kassaï Koupaï, Paola Cinnella, patrick gallinari

Machine-learning surrogates are increasingly used to accelerate computational fluid dynamics (CFD), yet progress is limited by the lack of benchmarks capturing realistic, time-dependent turbulent flows. We introduce TURTLES, a 13 TB dataset of high-fidelity implicit large-eddy simulations of three-dimensional turbulent cylinder wakes in the shear-layer transition regime. The dataset contains 400 trajectories of 400 time steps each, with 3–9 million points per frame sampled on irregular point clouds, spanning variations in geometry, Reynolds number, and angle of attack. Unlike existing datasets, TURTLES captures fully three-dimensional turbulence with an active energy cascade driven by vortex stretching, combining (i) dense irregular meshes, (ii) long-horizon temporal dynamics, and (iii) physically realistic turbulent behavior. We benchmark state-of-the-art neural operators on long autoregressive rollouts and identify key failure modes, including temporal instability, loss of small-scale energy, and challenges in learning on large irregular domains. TURTLES provides a new standard benchmark for evaluating surrogate models in high-resolution, industrial-scale CFD regimes.

NeurIPS 2026

Tuning the Tuner

Jacob Adkins, Michael Bowling, Adam White

Properly tuned hyperparameters are critical for reinforcement learning algorithms to perform well, limiting their use in real world applications. AutoRL aims to to address this by nesting the reinforcement learning problem within an outer optimization loop, where a black-box optimizer tunes the reinforcement learning algorithm's hyperparameters leaving the AutoRL algorithm's hyperparameters (hyper-hyperparameters) fixed. We provide the first empirical study of an AutoRL algorithm's sensitivity with respect to its hyper-hyperparameters. Our results demonstrate that SMAC3 with Hyperband, used to tune PPO, is sensitive to its hyper-hyperparameters, albeit less so than PPO is to its hyperparameters, and this reduction comes at a significant computational cost. The per-environment tuned performance gains do not outperform random search, suggesting the reduction in sensitivity may not justify the substantial compute and engineering overhead AutoRL imposes.

NeurIPS 2026

Tune-Up Open-Weight CLIP: Optimization Framework for Self-Supervised Fine-tuning of CLIP

Anant Mehta, Xiyuan Wei, Xingyu Chen, Tianbao Yang

CLIP has become a cornerstone of multimodal representation learning, yet improving its performance typically requires a prohibitively costly process of training from scratch on billions of samples. We ask a different question: *Can we improve the performance of open-weight CLIP models across various downstream tasks using only existing self-supervised datasets?* Unlike supervised fine-tuning, which adapts a pretrained model to a single downstream task, our setting seeks to improve general performance across various tasks. However, as both our experiments and prior studies reveal, simply applying standard training protocols starting from an open-weight CLIP model often fails, leading to performance degradation. In this paper, we introduce **TuneCLIP**, a self-supervised fine-tuning framework that overcomes the performance degradation. TuneCLIP has two key components: (1) a warm-up stage of recovering optimization statistics to reduce cold-start bias, inspired by theoretical analysis, and (2) a fine-tuning stage of optimizing a new contrastive loss to mitigate the penalization on false negative pairs. Our extensive experiments show that TuneCLIP consistently improves performance across model architectures and scales. Notably, it elevates leading open-weight models like SigLIP (ViT-B/16), achieving gains of up to +2.5% on ImageNet and related out-of-distribution benchmarks, and +1.2% on the highly competitive DataComp benchmark, setting a new strong baseline for efficient post-pretraining adaptation.

NeurIPS 2026

Tunable Latent Generative Priors for Compressed Sensing and Inverse Problems

Sean Gunn, Jorio Cocola, PAul HAnd, Oliver De Candido, Vaggos Chatziafratis

Latent generative models have emerged as powerful priors for solving inverse problems. These models typically represent a class of natural signals at a single, fixed complexity, governed by the latent dimensionality. This can be limiting: depending on the problem, a latent dimensionality that is too small may result in high representation error, while one that is too large may overfit to noise. We develop tunable latent priors for diffusion models, normalizing flows, and variational autoencoders, leveraging nested dropout. Across tasks including compressed sensing, inpainting, denoising, and phase retrieval, we show empirically that tunable priors consistently achieve lower reconstruction errors than fixed-complexity baselines. In the linear denoising setting, we derive the optimal complexity in closed form, showing how it depends on the noise level and the signal spectrum. This work demonstrates the potential of tunable latent generative priors and motivates both the development of supporting theory and their application across a wide range of inverse problems.

NeurIPS 2026

Tuna-2: Pixel Embeddings Beat Vision Encoders for Multimodal Understanding and Generation

Zhiheng Liu, Weiming Ren, Xiaoke Huang, Shoufa Chen, Tianhong Li, Mengzhao Chen, Yatai Ji, Sen He, Jonas Schult, Belinda Zeng, Tao Xiang, Wenhu Chen, Ping Luo, Luke Zettlemoyer, Yuren Cong

Unified multimodal models typically rely on pretrained vision encoders and use separate visual representations for understanding and generation, creating misalignment between the two tasks and preventing fully end-to-end optimization from raw pixels. We introduce Tuna-2, a native unified multimodal model that performs visual understanding and generation directly based on pixel embeddings. Tuna-2 drastically simplifies the model architecture by employing simple patch embedding layers to encode visual input, completely discarding the modular vision encoder designs such as the VAE or the representation encoder. Experiments show that Tuna-2 achieves state-of-the-art performance in multimodal benchmarks, demonstrating that unified pixel-space modelling can fully compete with latent-space approaches for high-quality image generation. Moreover, while the encoder-based variant converges faster in early pretraining, Tuna-2's encoder-free design achieves stronger multimodal understanding at scale, particularly on tasks requiring fine-grained visual perception. These results show that pretrained vision encoders are not necessary for multimodal modelling, and end-to-end pixel-space learning offers a scalable path toward stronger visual representations for both generation and perception.

NeurIPS 2026

Truthful Calibration Errors for Multi-Class Prediction

Yuxuan Lu, Yifan Wu, Jason Hartline, Lunjia Hu

Calibrated predictions are useful because their numerical values can be interpreted as probabilities. Calibration errors are therefore widely used to evaluate and compare probabilistic predictors. Recently, Haghtalab et al. [2024] introduced truthfulness as an additional requirement for such measures. A calibration measure is truthful if a predictor minimizes its expected measured error by reporting the true conditional label distribution. Many standard empirical calibration errors are non-truthful: a predictor may appear better calibrated by distorting its probabilities. We study the implications of truthful and non-truthful calibration errors for practice. First, we introduce perfectly truthful calibration errors for full multiclass calibration and classwise calibration, two standard multiclass notions. More generally, our construction applies to any linear property of the label distribution, generalizing the truthful calibration error for binary predictions in Hartline et al. [2025]. We also identify a truthful correction for confidence calibration. Second, we characterize the decision-theoretic implications of these truthful errors. For calibrated predictors, truthful calibration errors preserve the Blackwell dominance: a more informative calibrated predictor receives no larger expected error. Third, we show that this decision-theoretic interpretation explains and mitigates the well-observed ranking robustness problem of binned calibration errors. Empirically, non-truthful confidence-based errors can reverse model rankings when the number of bins changes, while our truthful classwise error gives more stable rankings across binning choices.

NeurIPS 2026

Trustworthy and Efficient Map-free LiDAR Localization via Scan-Pose Alignment and Flow Matching

Haoze Chang, Dunqiang Liu, Minghang Zhu, Wen Li, Sheng Ao, Siqi Shen, Chenglu Wen, Cheng Wang

Reliable map-free LiDAR relocalization requires not only accurate and efficient pose estimation but also trustworthy confidence estimation for detecting localization failures. However, estimating reliability to ensure trustworthy LiDAR relocalization remains largely unexplored. Also, existing LiDAR pose regression methods suffer from accuracy and efficiency trade-off. To address this limitation, we propose \textbf{SPAR}, a model-agnostic confidence estimator that reformulates localization reliability as scan-pose alignment. Given a query scan and a predicted pose, SPAR measures their compatibility in a learned embedding space and explicitly optimizes confidence scores to correlate scan with pose. In addition, we introduce \textbf{VeLoc}, an efficient and accurate pose regressor based on flow-matching for efficient pose refinement. Experiments on the Oxford and NCLT datasets demonstrate that the proposed framework achieves a favorable balance between efficiency and accuracy for LiDAR relocalization while enabling reliable localization failure detection across different localization backbones.

NeurIPS 2026

Trustworthy Retrosynthesis: Eliminating Hallucinations with a Diverse Ensemble of Reaction Scorers

Michał Sadowski, Tadija Radusinović, Maria Wyrzykowska, Lukasz Sztukiewicz, Jan Rzymkowski, Piotr Kozakowski, Mikolaj Sacha, Ruard van Workum, Stanislaw Jastrzebski

Retrosynthesis is one of the domains transformed by the rise of generative models, and it is one where the problem of nonsensical or erroneous outputs (hallucinations) is particularly insidious: reliable assessment of synthetic plans is time-consuming, with automatic methods lacking. In this work, we present RetroTrim, a retrosynthesis system that successfully avoids nonsensical plans on a set of challenging drug-like targets. Compared to common baselines in the field, our system is not only the sole method that succeeds in filtering out hallucinated reactions, but it also results in the highest number of high-quality paths overall. The key insight behind RetroTrim is the combination of diverse reaction scoring strategies, based on machine learning models and existing chemical databases. We show that our scoring strategies capture different classes of hallucinations by analyzing them on a dataset of labeled retrosynthetic intermediates. To measure the performance of retrosynthesis systems, we propose a novel evaluation protocol for reactions and synthetic paths based on a structured review by expert chemists. Using this protocol, we compare systems on a set of 32 novel targets, curated to reflect recent trends in drug structures. While the insights behind our methodology are broadly applicable to retrosynthesis, our focus is on targets in the drug-like domain. By releasing our benchmark targets and the details of our evaluation protocol, we hope to inspire further research into reliable retrosynthesis.

NeurIPS 2026

TrustMod-SM: A Multi-Axis Benchmark for Evaluating Trustworthiness of LLMs in Social Media Content Moderation

Aizan Zafar, Sreekantam Sai Venkat, Gathik Jindal, Ritu Raj Sharma, Zishan Ahmad, Tulika Saha, Srinath Srinivasa

Large language models have shown remarkable promise for social media content moderation, with recent studies demonstrating performance rivaling human annotators on policy-compliance tasks. However, the trustworthiness of these models beyond aggregate accuracy remains largely unexamined, posing significant risks, a model with high overall accuracy may still exhibit substantial error-rate disparities across demographic groups while remaining vulnerable to adversarial manipulation. In this paper, we introduce **TrustMod-SM** and aim to comprehensively evaluate the trustworthiness of LLM-based content moderators across five dimensions: *trustfulness*, *fairness*, *safety*, *robustness*, and *context integrity*. TrustMod-SM comprises about 29K evaluation instances curated from eight established datasets, and we evaluate thirteen open-weight models (0.5B-14B parameters), including both text-only and vision-language architectures. Our analysis reveals that models consistently exhibit trustworthiness concerns, often displaying greater demographic disparity as detection accuracy improves, complying with both concealment and exaggeration inducements, assigning high confidence to incorrect predictions while rarely escalating ambiguous content for human review, and failing to distinguish hate from counter-speech and reclaimed language, particularly at sub-8B scales. Furthermore, scaling does not uniformly improve trustworthiness, and a cross-dimensional analysis reveals non-trivial associations between axes, challenging the independence assumed by prior benchmarks. We publicly release our benchmark data, evaluation code, and model predictions at https://anonymous.4open.science/r/TrustMod_SM **WARNING:** This paper contains model outputs that may be considered offensive.

NeurIPS 2026

TrustFlow: Adaptive Trust Calibration for Language Model Guided Reinforcement Learning

Hao Chen, Zhiwei Xu, Hu Fu, Yuelin Ma, Hangyu Mao, Yiqun Chen, Bin Zhang, Guoliang Fan

Reinforcement learning (RL) often suffers from low sample efficiency and inefficient exploration in complex environments. Recent work leverages large language models (LLMs) as sources of prior knowledge for sequential decision-making. However, existing LLM-guided RL approaches typically rely on static or loosely coupled integration, failing to account for the evolving competence of the agent during training. As a result, LLM guidance may become redundant or even detrimental, leading to suboptimal learning dynamics, unnecessary dependence at inference time, and increased latency due to frequent LLM interaction. In this work, we propose \textbf{TrustFlow}, a unified framework that formulates LLM–RL integration as adaptive trust calibration. The key idea is to dynamically regulate the influence of LLM guidance based on learning progress, enabling a gradual transition from prior-driven exploration to LLM-free decision-making. Concretely, a preference representation is first constructed to connect sparse LLM rankings with policy representations. Trust calibration then balances LLM guidance with RL exploration. Building on this trust signal, value alignment is enforced, and a trust-modulated optimization scheme is introduced, incorporating preference structure into the learning process. Empirical results show that TrustFlow consistently improves sample efficiency and enables a smooth transition to fully LLM-free policies, eliminating the need for LLM access at inference time across diverse environments.

NeurIPS 2026

Trust, but Don’t Verify: Epistemic Blind Spots in LLM Source Evaluation

Rohan Pradhan, Steve Goley

Language models increasingly act as epistemic proxies, synthesizing evidence from multiple sources to inform decisions. Whether they evaluate the quality of that evidence, or merely aggregate it based on surface presentation, remains poorly understood. We show that models possess the capability to detect fabricated statistics (correct identification rates of $0.76$--$1.00$ for methodology in isolation) but do not recruit this capability during multi-source synthesis, producing similar numeric estimates whether the statistics are fabricated or valid. Specifically, source influence is governed by a methodology-register gate that responds to the distributional register of analytical text but not to numeric validity: for example, statistically impossible confidence intervals receive the same weight as valid ones. The behavioral dissociation replicates across five models from three families (Claude, Qwen, OLMo) and three professional domains. Mechanistic analyses, including causal tracing, linear probes, and component-level attribution, converge on the same account: the model encodes and causally uses a methodology-register representation that transfers across domains (probe AUC $0.83$--$0.92$), while numeric-validity signals, decodable in isolation, are suppressed to chance during multi-source synthesis. Prompting-based mitigations, even an oracle checklist naming the exact statistical checks, produce blanket skepticism rather than selective discernment, and the post-training pipelines we examine reinforce the stylistic shortcut without building numeric verification. Unlike sycophancy, which tracks user preference, this failure tracks whether a source presents as analytically credible, not whether its claims are internally consistent. We term this $\textit{epistemic alignment}$: like preference and safety alignment, the question is not capability but deployment.

NeurIPS 2026

Trust the Direction, Search the Step: Zero-and-First-Order Methods for LLM Fine-Tuning

Cristian McGee, El Houcine Bergou, Aritra Dutta

Step-size selection remains a central challenge in large-scale neural network optimization: conservative steps slow convergence, while aggressive steps can destabilize training. We propose Zero-and-First-Order optimization (ZFO), a lightweight framework that decouples direction selection from step-size selection. ZFO uses a trusted first-order optimizer to determine the direction and performs zeroth-order evaluations only along this one-dimensional subspace to choose how far to move. Using the current forward-backward pass and two additional fixed-batch function evaluations, ZFO constructs a local model of the objective along the proposed direction and selects a curvature-aware step within a bounded search interval. This yields an adaptive step-selection mechanism with lower cost than full line search. We provide theoretical guarantees showing that shared-sample evaluations produce reliable finite-difference curvature estimates, that the induced local model selects a near-optimal step along the search interval, and that ZFO converges to a neighborhood of a stationary point. Across multiple language models and datasets, ZFO improves accuracy and stability over standard first-order fine-tuning algorithms.

NeurIPS 2026

Trust Region Q Adjoint Matching

Yonghoon Dong, Kyungmin Lee, Changyeon Kim, Jaehyuk Kim, Jinwoo Shin

Off-policy reinforcement learning of pretrained flow policies remains challenging due to the instability of optimization arising from the multi-step sampling process. Recently, Q-learning with Adjoint Matching (QAM) addressed this issue by reformulating into a memoryless stochastic optimal control (SOC) problem with a learned critic. However, QAM inherits a fundamental fragility of critic-guided improvement: small critic errors are amplified when critics are ill-conditioned, often leading to model collapse. This paper introduces Trust Region Q-Adjoint Matching (TRQAM), a stable off-policy fine-tuning algorithm that adaptively controls the path-space KL with pretrained flow policies through projected dual descent. Specifically, we optimize the trust-region parameter $\lambda$ in SOC dynamics, and theoretically show that the path-space KL can be represented by a closed-form function of $\lambda$. As a result, our method can precisely control the exact deviation from pretrained flow policies, achieving stable off-policy RL. Through experiments on 50 OGBench tasks, TRQAM consistently outperforms prior arts in both offline RL and offline-to-online RL. In particular, TRQAM achieves an overall success rate of 68\% in offline RL, substantially improves the strongest baseline at 46\%.

NeurIPS 2026

Trust Region Policy Distillation

Zhengpeng Xie, Li Lyna Zhang, Zeke Xie, Mao Yang

Big goals are hard to achieve all at once; breaking them into small steps is wiser. We present Trust Region Policy Distillation (TOP-D), which transforms the notoriously unstable, high-variance On-Policy Distillation (OPD) into a stable training paradigm by dynamically constructing a proximal teacher. Theoretically, we establish a rigorous framework demonstrating that TOP-D inherently controls gradient variance. By providing a formal global convergence analysis alongside a monotonic improvement bound, we mathematically formalize the reliability and stability of the overall training dynamics. Empirically, TOP-D dramatically enhances training stability, sample efficiency, and final performance on mathematical reasoning tasks. More importantly, TOP-D introduces zero additional computational overhead, positioning itself as a promising alternative to the well-established OPD paradigm.

NeurIPS 2026

Trust Region Continual Learning as an Implicit Meta-Learner

Zekun Wang, Anant Gupta, Chris MacLellan

Continual learning aims to acquire tasks sequentially without catastrophic forgetting, yet standard strategies face a core tradeoff: regularization-based methods (e.g., EWC) can overconstrain updates when task optima are weakly overlapping, while replay-based methods can retain performance but drift due to imperfect replay. We study a hybrid perspective: \emph{trust region continual learning} that combines generative replay with a Fisher-metric trust region constraint. We show that, under local approximations, the resulting update admits a MAML-style interpretation with a single implicit inner step: replay supplies an old-task gradient signal (query-like), while the Fisher-weighted penalty provides an efficient offline curvature shaping (support-like). This yields an emergent meta-learning property in continual learning: the model becomes an initialization that rapidly \emph{re-converges} to prior task optima after each task transition, without explicitly optimizing a bilevel objective. Empirically, on task-incremental diffusion image generation and continual diffusion-policy control, trust region continual learning achieves the best final performance and retention, and consistently recovers early-task performance faster than EWC, replay, and continual meta-learning baselines.

NeurIPS 2026

Trust Guided Decision Transformer

Chainesh Gautam, Raghuram Bharadwaj Diddigi, Chandramouli Kamanchi, Pankaj Dayama, Sumanta Mukherjee, Kameshwaran Sampath

Decision Transformer performance degrades on long rollouts because the conditioning context drifts out of the training distribution. We show that this drift is visible through the model's own next state prediction error, which rises during rollout and stays elevated, giving a direct signal of when context has become unreliable. We introduce Trust Guided Decision Transformer (TGDT), which selects context before applying value guidance. At each step, TGDT evaluates several recent context suffixes using rolling next state prediction error, calibrated against held out offline data via split conformal prediction. It keeps only suffixes whose error stays within the calibrated threshold, then uses a frozen critic to choose the highest value action among the trusted suffixes. This reverses the order used by value only elastic selection, where the critic may choose an action generated from a context the model itself has flagged as unreliable. Experiments on D4RL navigation and locomotion tasks show that state prediction, critic guidance, and hard context reset each solve only part of the problem. TGDT reduces persistent high error runs and improves return over vanilla Decision Transformer, reset based context control, and value only context selection.

NeurIPS 2026

Truncated Riemannian (1+1)-ES for Black-Box Optimization with Intrinsic Dimension Guarantees

Zixu Wu, Hualin Zhang, zhiqiang xu

$(1+1)$-evolution strategy (ES) is a classic variant of evolution strategy for black-box optimization via direct and random search while keeping only a single solution per generation in $\mathbb{R}^n$. Despite convergence with different step-size adaptations, it often remains impractical due to dependence on the unfavorable high dimension of the search space $\mathbb{R}^n$. In fact, many modern optimization problems are naturally constrained to low-dimensional manifolds embedded in very high-dimensional ambient spaces. To see the potential of intrinsic dimensionality reduction for improving practicality, we consider the truncated Riemannian $(1+1)$-ES on a compact Riemannian submanifold $\mathcal{M}\subset\mathbb{R}^n$ and establish its non-asymptotic stationarity guarantee at the standard nonconvex zeroth-order rate of $\widetilde{\mathcal{O}}(\varepsilon^{-4})$ function evaluations. The explicit Gaussian second-moment term in the bound scales with the intrinsic tangent dimension $d=\dim\mathcal{M}$ rather than the ambient dimension $n$, while the remaining truncation dependence is captured by an explicit small-ball drift constant $\alpha_d(R/\sigma_0)$. To the best of our knowledge, this gives the first non-asymptotic stationarity analysis for a comparison-based ES-type method on compact nonconvex Riemannian submanifolds under localized pullback smoothness. Numerical illustrations on sparse PCA over spheres and smooth-surrogate stationarity diagnostics illustrate behavior consistent with the theory and its limitations, while additional experimental studies on truncation radius diagnostics, black-box tuning, and classical evolutionary computation benchmarks support the practical relevance of geometry-aware comparison-based search under limited function-evaluation budgets.

NeurIPS 2026

Trivialized Generative Models on Lie Groups

Neil He, Meenal Jhajharia, Qianxi Wu, Chaoran Cheng, Arindam Banerjee, Ge Liu

Many problems in diverse fields involve data that naturally live on Lie groups. However, existing Riemannian and Lie group generative models still face several limitations. Riemannian flow and consistency models often require position-dependent vector fields, and expensive geometric terms such as Euler-Arnold simulation on general Lie groups or covariant derivatives. Existing Lie group flow models are usually tied to collinear exponential paths, while momentum-based Lie group diffusion relies on compactness assumptions and does not naturally extend to non-compact groups. To address these limitations, we propose Trivialized Generative Models (TGM), a family of generative models that learns endpoint-constrained paths in the fixed Lie algebra and lifts them to the Lie group. This yields Trivialized Flow Matching (TFM), Trivialized Consistency Models (TCM), and momentum-based extensions with endpoint correction, enabling flexible path design, simpler few-step objectives, and generation on non-compact Lie groups. We evaluate TGM on compact SO(3) benchmarks, non-compact $\mathrm{Sp}(4,\mathbb{R})$ datasets motivated by continuous quantum systems and paraxial optics, and real-world protein backbone generation. Across these settings, TGM improves sample quality and efficiency over existing Riemannian and Lie group baselines.

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