Test-Time Optimization

Existing methods for single-image 3D indoor scene generation often produce visually plausible results that violate real-world physical constraints, limiting their reliability in robotics, embodied AI, and virtual environment design. To bridge this gap, we introduce a Physics Evaluator that assesses four aspects (geometric priors, contact, stability, and deployability) through nine sub-constraints, establishing a benchmark for evaluating physical consistency. Our analysis reveals that even state-of-the-art methods produce scenes with substantial physical inconsistencies despite their visual plausibility. To address these limitations, we propose a framework that incorporates feedback from the Physics Evaluator into both training and inference to improve the physical plausibility of generated scenes. Specifically, PhyMix comprises two components: (i) implicit alignment via Scene-GRPO, a critic-free group-relative preference optimization strategy that uses physical evaluations to guide the generator toward physically plausible layouts, and (ii) explicit refinement via verifier-guided agentic repair, which translates evaluator diagnostics into executable scene-editing skills to correct residual violations at inference time. PhyMix unifies physical evaluation, preference-based alignment, and agentic inference-time correction to improve physical plausibility while retaining the observed scene content. Experiments show improvements in reconstruction quality and physical plausibility, while qualitative examples on stylized and real-world images illustrate the applicability of the framework beyond synthetic inputs.

We introduce a test-time framework for multiview Transformers (MVTs) that incorporates priors (e.g., camera poses, intrinsics, and depth) to improve 3D tasks without retraining or modifying pre-trained image-only networks. Rather than feeding priors into the architecture, we cast them as constraints on the predictions and optimize the network at inference time. The optimization loss consists of a self-supervised objective and prior penalty terms. The self-supervised objective captures the compatibility among multi-view predictions and is implemented using photometric or geometric loss between renderings from other views and each view itself. Any available priors are converted into penalty terms on the corresponding output modalities. Across a series of 3D vision benchmarks, including point map estimation and camera pose estimation, our method consistently improves performance over base MVTs by a large margin. On the ETH3D, 7-Scenes, and NRGBD datasets, our method reduces the point-map distance error by more than half compared with the base image-only models. Our method also outperforms retrained prior-aware feed-forward methods, demonstrating the effectiveness of our test-time constrained optimization (TCO) framework for incorporating priors into 3D vision tasks.

Recent advances in 3D Gaussian Splatting (3DGS) present two main directions: feed-forward models offer fast inference in sparse-view settings, while per-scene optimization yields high-quality renderings but is computationally expensive. To combine the benefits of both, we introduce Diff3R, a novel framework that explicitly bridges feed-forward prediction and test-time optimization. By incorporating a differentiable 3DGS optimization layer directly into the training loop, our network learns to predict an optimal initialization for test-time optimization rather than a conventional zero-shot result. To overcome the computational cost of backpropagating through the optimization steps, we propose computing gradients via the Implicit Function Theorem and a scalable, matrix-free PCG solver tailored for 3DGS optimization. Additionally, we incorporate a data-driven uncertainty model into the optimization process by adaptively controlling how much the parameters are allowed to change during optimization. This approach effectively mitigates overfitting in under-constrained regions and increases robustness against input outliers. Since our proposed optimization layer is model-agnostic, we show that it can be seamlessly integrated into existing feed-forward 3DGS architectures for both pose-given and pose-free methods, providing improvements for test-time optimization.

Protein interaction modeling is central to protein design, which has been transformed by machine learning with applications in drug discovery and beyond. In this landscape, structure-based de novo binder design is cast as either conditional generative modeling or sequence optimization via structure predictors ("hallucination"). We argue that this is a false dichotomy and propose Proteina-Complexa, a novel fully atomistic binder generation method unifying both paradigms. We extend recent flow-based latent protein generation architectures and leverage the domain-domain interactions of monomeric computationally predicted protein structures to construct Teddymer, a new large-scale dataset of synthetic binder-target pairs for pretraining. Combined with high-quality experimental multimers, this enables training a strong base model. We then perform inference-time optimization with this generative prior, unifying the strengths of previously distinct generative and hallucination methods. Proteina-Complexa sets a new state of the art in computational binder design benchmarks: it delivers markedly higher in-silico success rates than existing generative approaches, and our novel test-time optimization strategies greatly outperform previous hallucination methods under normalized compute budgets. We also demonstrate interface hydrogen bond optimization, fold class-guided binder generation, and extensions to small molecule targets and enzyme design tasks, again surpassing prior methods. Code, models and new data will be publicly released.

Monocular surface normal estimators trained on large-scale RGB-normal data often perform poorly in the edge cases of reflective, textureless, and dark surfaces. Polarization encodes surface orientation independently of texture and albedo, offering a physics-based complement for these cases. Existing polarization methods, however, require multi-view capture or specialized training data, limiting generalization. We introduce Poppy, a training-free framework that refines normals from any frozen RGB backbone using single-shot polarization measurements at test time. Keeping backbone weights frozen, Poppy optimizes per-pixel offsets to the input RGB and output normal along with a learned reflectance decomposition. A differentiable rendering layer converts the refined normals into polarization predictions and penalizes mismatches with the observed signal. Across seven benchmarks and three backbone architectures (diffusion, flow, and feed-forward), Poppy reduces mean angular error by 23-26% on synthetic data and 6-16% on real data. These results show that guiding learned RGB-based normal estimators with polarization cues at test time refines normals on challenging surfaces without retraining.

Human mesh recovery from single images remains challenging due to inherent depth ambiguity and limited generalization across domains. While recent methods combine regression and optimization approaches, they struggle with poor initialization for test-time refinement and inefficient parameter updates during optimization. We propose a novel meta-learning framework that trains models to produce optimization-friendly initializations while incorporating uncertainty-aware adaptive updates during test-time refinement. Our approach introduces three key innovations: (1) a meta-learning strategy that simulates test-time optimization during training to learn better parameter initializations, (2) a selective parameter caching mechanism that identifies and freezes converged joints to reduce computational overhead, and (3) distribution-based adaptive updates that sample parameter changes from learned distributions, enabling robust exploration while quantifying uncertainty. Additionally, we employ stochastic approximation techniques to handle intractable gradients in complex loss landscapes. Extensive experiments on standard benchmarks demonstrate that our method achieves state-of-the-art performance, reducing MPJPE by 10.3 on 3DPW and 8.0 on Human3.6M compared to strong baselines. Our approach shows superior domain adaptation capabilities with minimal performance degradation across different environmental conditions, while providing meaningful uncertainty estimates that correlate with actual prediction errors. Combining meta-learning and adaptive optimization enables accurate mesh recovery and robust generalization to challenging scenarios.

Scaling inference-time compute for Large Language Models (LLMs) has unlocked unprecedented reasoning capabilities. However, existing inference-time scaling methods typically rely on inefficient and suboptimal discrete search algorithms or trial-and-error prompting to improve the online policy. In this paper, we propose $\nabla$-Reasoner, an iterative generation framework that integrates differentiable optimization over token logits into the decoding loop to refine the policy on the fly. Our core component, Differentiable Textual Optimization (DTO), leverages gradient signals from both the LLM's likelihood and a reward model to refine textual representations. $\nabla$-Reasoner further incorporates rejection sampling and acceleration design to robustify and speed up decoding. Theoretically, we show that performing inference-time gradient descent in the sample space to maximize reward is dual to aligning an LLM policy via KL-regularized reinforcement learning. Empirically, $\nabla$-Reasoner achieves over 20% accuracy improvement on a challenging mathematical reasoning benchmark, while reducing number of model calls by approximately 10-40% compared to strong baselines. Overall, our work introduces a paradigm shift from zeroth-order search to first-order optimization at test time, offering a cost-effective path to amplify LLM reasoning.

Test-time training (TTT) adapts large language models (LLMs) during inference using only unlabeled test inputs. Existing methods, however, face two major bottlenecks on hard reasoning tasks: (1) lack of learnable samples, as self-generated pseudo-labels on difficult questions are often noisy and yield unstable rewards; and (2) inefficient exploration, as performance gains depend on repeatedly sampling many rollouts without explicit diagnosis of why previous attempts fail. We propose TTSR (Test-Time Self-Reflection), a self-evolving framework based on a reflect-then-synthesize paradigm. A single pretrained model alternates between a Student role and a Teacher role: the Student solves test questions and updates, while the Teacher analyzes failed trajectories and synthesizes targeted variant questions closer to the Student's capability frontier. TTSR further maintains a cross-iteration weakness memory and compiles persistent weaknesses into a lightweight strategy note prepended to subsequent Student inputs, so diagnostic knowledge can guide exploration and gradually fade as weaknesses are resolved. Experiments on challenging mathematical reasoning benchmarks show consistent test-time improvements, strong cross-backbone generalization, and transfer to general-domain reasoning tasks.