Enhancing large vision-language models (LVLMs) with visual slow-thinking reasoning is crucial for solving complex multimodal tasks. However, since LVLMs are mainly trained with vision-language alignment, it is difficult to adopt on-policy reinforcement learning (RL) to develop the slow thinking ability because the rollout space is restricted by its initial abilities. Off-policy RL offers a way to go beyond the current policy, but directly distilling trajectories from external models may cause visual hallucinations due to mismatched visual perception abilities across models. To address these issues, this paper proposes SOPHIA, a simple and scalable SemiOff-Policy RL for vision-language slow-tHInking reAsoning. SOPHIA builds a semi-off-policy behavior model by combining on-policy visual understanding from a trainable LVLM with off-policy slow-thinking reasoning from a language model, assigns outcome-based rewards to reasoning, and propagates visual rewards backward. Then LVLM learns slow-thinking reasoning ability from the obtained reasoning trajectories using propagated rewards via off-policy RL algorithms.

Enhancing large vision-language models (LVLMs) with visual slow-thinking reasoning is crucial for solving complex multimodal tasks. However, since LVLMs are mainly trained with vision-language alignment, it is difficult to adopt on-policy reinforcement learning (RL) to develop the slow thinking ability because the rollout space is restricted by its initial abilities. Off-policy RL offers a way to go beyond the current policy, but directly distilling trajectories from external models may cause visual hallucinations due to mismatched visual perception abilities across models.

Preconditioned optimizers are central to language model training, but their stochastic update rules are usually treated as direct approximations to population preconditioned descent. We show that this view misses two finite-sample biases. First, the gradient and preconditioner are typically estimated from the same minibatch, introducing gradient--preconditioner coupling bias. Second, even when the preconditioner estimate is unbiased, its inverse or inverse-root is generally biased because inversion is nonlinear. We propose a single-batch bias-correction framework that addresses both effects: cross-fitted preconditioning estimates the numerator and preconditioner from independent microbatch groups, while variance-corrected inversion uses microbatch variability to subtract the leading delta-method bias term. The framework applies to diagonal moment, diagonal curvature, and matrix preconditioning methods, instantiated in AdamW, Sophia, and Shampoo. Bias correction reduces held-out pretraining loss on Qwen2.5-0.5B by $0.15$, $0.07$, and $0.11$ nats, respectively; the effects on mixed-quality pretraining and downstream instruction tuning are consistently neutral-to-positive. Together, these results establish bias correction as a practical mechanism for reducing finite-sample update bias and improving the performance of preconditioned optimizers.

This trend has motivated research on efficient training algorithms designed to improve training, validation, and downstream performance faster than standard training.

In the age of A.I., we endlessly debate what consciousness looks like. Can a camera see things more clearly? Earlier that day, she'd been onstage at the conference I was attending and had been teased for a gesture that looked as though she were flipping off the audience. Now she was in the hotel lobby, in a black gown, holding court. She stepped in front of a bright-orange wall. I had brought an 85-mm. "What are your hopes for the future of humanity?" She wasn't keen to answer, but she responded to the camera.

Enhancing large vision-language models (LVLMs) with visual slow-thinking reasoning is crucial for solving complex multimodal tasks. However, since LVLMs are mainly trained with vision-language alignment, it is difficult to adopt on-policy reinforcement learning (RL) to develop the slow thinking ability because the rollout space is restricted by its initial abilities. Off-policy RL offers a way to go beyond the current policy, but directly distilling trajectories from external models may cause visual hallucinations due to mismatched visual perception abilities across models. To address these issues, this paper proposes SOPHIA, a simple and scalable Semi-Off-Policy RL for vision-language slow-tHInking reAsoning. SOPHIA builds a semi-off-policy behavior model by combining on-policy visual understanding from a trainable LVLM with off-policy slow-thinking reasoning from a language model, assigns outcome-based rewards to reasoning, and propagates visual rewards backward. Then LVLM learns slow-thinking reasoning ability from the obtained reasoning trajectories using propagated rewards via off-policy RL algorithms. Extensive experiments with InternVL2.5 and InternVL3.0 with 8B and 38B sizes show the effectiveness of SOPHIA. Notably, SOPHIA improves InternVL3.0-38B by 8.50% in average, reaching state-of-the-art performance among open-source LVLMs on multiple multimodal reasoning benchmarks, and even outperforms some closed-source models (e.g., GPT-4.1) on the challenging MathVision and OlympiadBench, achieving 49.08% and 49.95% pass@1 accuracy, respectively. Analysis shows SOPHIA outperforms supervised fine-tuning and direct on-policy RL methods, offering a better policy initialization for further on-policy training.

Large Reasoning Models (LRMs) excel in structured tasks by emulating deliberate human reasoning but often suffer from overthinking, degrading performance and wasting resources. One possible baseline is to deploy both LLM and LRM, then route input by predicting whether it requires reasoning and may cause overthinking. However, deploying multiple models can be costly or impractical. We propose a superposed deployment strategy with a lightweight, training-free regulation to optimize inference by switching one model on and off. Instead of routing, we selectively unlearn from LRM at inference, scaling down computation while preserving reasoning. By analyzing the cumulative energy of singular values, we identify optimal low-rank projections to adjust reasoning just right.

This trend has motivated research on efficient training algorithms designed to improve training, validation, and downstream performance faster than standard training.

First-order optimization methods, such as SGD and Adam, are widely used for training large-scale deep neural networks due to their computational efficiency and robust performance. However, relying solely on gradient information, these methods often struggle to navigate complex loss landscapes with flat regions, plateaus, and saddle points. Second-order methods, which use curvature information from the Hessian matrix, can address these challenges but are computationally infeasible for large models. The Dimer method, a first-order technique that constructs two closely spaced points to probe the local geometry of a potential energy surface, efficiently estimates curvature using only gradient information. Inspired by its use in molecular dynamics simulations for locating saddle points, we propose Dimer-Enhanced Optimization (DEO), a novel framework to escape saddle points in neural network training. DEO adapts the Dimer method to explore a broader region of the loss landscape, approximating the Hessian's smallest eigenvector without computing the full matrix. By periodically projecting the gradient onto the subspace orthogonal to the minimum curvature direction, DEO guides the optimizer away from saddle points and flat regions, enhancing training efficiency with non-stepwise updates. Preliminary experiments on a Transformer toy model show DEO achieves competitive performance compared to standard first-order methods, improving navigation of complex loss landscapes. Our work repurposes physics-inspired, first-order curvature estimation to enhance neural network training in high-dimensional spaces.

Optimizers play a decisive role in reducing pre-training times for LLMs and achieving better-performing models. In this study, we compare three major variants: the de-facto standard AdamW, the simpler Lion, developed through an evolutionary search, and the second-order optimizer Sophia. For better generalization, we train with two different base architectures and use a single- and a multiple-epoch approach while keeping the number of tokens constant. Using the Maximal Update Parametrization and smaller proxy models, we tune relevant hyperparameters separately for each combination of base architecture and optimizer. We found that while the results from all three optimizers were in approximately the same range, Sophia exhibited the lowest training and validation loss, Lion was fastest in terms of training GPU hours but AdamW led to the best downstream evaluation results.