Reinforcement learning is a widely adopted component of large language model post-training, especially for reasoning-style tasks such as maths questions. However, as we show, most existing methods will provably fail to learn from questions that are too hard, where the model always fails, or too easy, where the model always succeeds. Much human effort is therefore spent producing datasets of questions of a suitable difficulty for state-of-the-art models. Given this, we consider how to algorithmically identify questions that allow for maximally efficient training. We introduce a method, LILO (Learnability Improves LLMs Optimally), that prioritises training on questions with high variance of success, known as learnability, and we provide theory which shows that LILO enables the expected improvement of the model to be large. We run a wide range of experiments over multiple base models, algorithms and reasoning datasets to demonstrate that LILO consistently reaches a higher final test accuracy, and can do so in 3 fewer training steps. We explore how questions with high learnability can be efficiently identified, and discuss how learnability can be scaled to produce LLM agents that autonomously and open-endedly expand the frontier of human knowledge.

To mitigate the distortions brought by equirectangular projection, existing methods typically divide 360 images into distortion-less perspective patches. However, since these patches are processed independently, depth inconsistencies are often introduced due to scale drift among patches. Recently, video depth estimation (VDE) models have leveraged temporal consistency for stable depth predictions across frames. Inspired by this, we propose to represent a 360 image as a sequence of perspective frames, mimicking the viewpoint adjustments users make when exploring a 360 scenario in virtual reality. Thus, the spatial consistency among perspective depth patches can be enhanced by exploiting the temporal consistency inherent in VDE models. To this end, we introduce a training-free pipeline for 360 monocular depth estimation, called ST2360D.

Equilibrium learning in adversarial games is an important topic widely examined in the fields of game theory and reinforcement learning (RL). Pursuit-evasion game (PEG), as an important class of real-world games from the fields of robotics and security, requires exponential time to be accurately solved. When the underlying graph structure varies, even the state-of-the-art RL methods require recomputation or at least fine-tuning, which can be time-consuming and impair real-time applicability. This paper proposes an Equilibrium Policy Generalization (EPG) framework to effectively learn a generalized policy with robust cross-graph zeroshot performance. In the context of PEGs, our framework is generally applicable to both pursuer and evader sides in both no-exit and multi-exit scenarios.

Mixture-of-Experts (MoE) models enable efficient scaling of large language models (LLMs) by activating only a subset of experts per input. However, we observe that the commonly used auxiliary load balancing loss often leads to expert overlap and overly uniform routing, which hinders expert specialization and degrades overall performance during post-training. To address this, we propose a simple yet effective solution that introduces two complementary objectives: (1) an orthogonality loss to encourage experts to process distinct types of tokens, and (2) a variance loss to encourage more discriminative routing decisions. Gradient-level analysis demonstrates that these objectives are compatible with the existing auxiliary loss and contribute to optimizing the training process. Experimental results over various model architectures and across multiple benchmarks show that our method significantly enhances expert specialization. Notably, our method improves classic MoE baselines with auxiliary loss by up to 23.79%, while also maintaining load balancing in downstream tasks, without any architectural modifications or additional components. Our code is available at this link.

Inferring 3D human motion from video remains a challenging problem with many applications. While traditional methods estimate the human in image coordinates, many applications require human motion to be estimated in world coordinates. This is particularly challenging when there is both human and camera motion. Progress on this topic has been limited by the lack of rich video data with ground truth human and camera movement. We address this with BEDLAM2.0, a new dataset that goes beyond the popular BEDLAM dataset in important ways.

Designing optimal prompts and reasoning processes for large language models (LLMs) on domain-specific tasks is both necessary and challenging in real-world applications. Determining how to integrate domain knowledge, enhance reasoning efficiency, and even provide domain experts with refined knowledge integration hints are particularly crucial yet unresolved tasks. In this research, we propose Evolutionary Graph Optimization for Prompting (EGO-Prompt), an automated framework to designing better prompts, efficient reasoning processes and providing enhanced causal-informed process. EGO-Prompt begins with a general prompt and fault-tolerant initial Semantic Causal Graph (SCG) descriptions, constructed by human experts, which is then automatically refined and optimized to guide LLM reasoning. Recognizing that expert-defined SCGs may be partial or imperfect and that their optimal integration varies across LLMs, EGO-Prompt integrates a novel causal-guided textual gradient process in two steps: first, generating nearly deterministic reasoning guidance from the SCG for each instance, and second, adapting the LLM to effectively utilize the guidance alongside the original input.

We present a systematic theoretical framework that interprets masked diffusion models (MDMs) as solutions to energy minimization problems in discrete optimal transport. Specifically, we prove that three distinct energy formulationskinetic, conditional kinetic, and geodesic energyare mathematically equivalent under the structure of MDMs, and that MDMs minimize all three when the mask schedule satisfies a closed-form optimality condition. This unification not only clarifies the theoretical foundations of MDMs, but also motivates practical improvements in sampling. By parameterizing interpolation schedules via Beta distributions, we reduce the schedule design space to a tractable 2D search, enabling efficient post-training tuning without model modification. Experiments on synthetic and real-world benchmarks demonstrate that our energy-inspired schedules outperform hand-crafted baselines, particularly in low-step sampling settings.

The bisimulation metric (BSM) is a powerful tool for computing state similarities within a Markov decision process (MDP), revealing that states closer in BSM have more similar optimal value functions. While BSM has been successfully utilized in reinforcement learning (RL) for tasks like state representation learning and policy exploration, its application to multiple-MDP scenarios, such as policy transfer, remains challenging. Prior work has attempted to generalize BSM to pairs of MDPs, but a lack of rigorous analysis of its mathematical properties has limited further theoretical progress. In this work, we formally establish a generalized bisimulation metric (GBSM) between pairs of MDPs, which is rigorously proven with the three fundamental properties: GBSM symmetry, inter-MDP triangle inequality, and the distance bound on identical state spaces. Leveraging these properties, we theoretically analyse policy transfer, state aggregation, and sampling-based estimation in MDPs, obtaining explicit bounds that are strictly tighter than those derived from the standard BSM. Additionally, GBSM provides a closed-form sample complexity for estimation, improving upon existing asymptotic results based on BSM. Numerical results validate our theoretical findings and demonstrate the effectiveness of GBSM in multi-MDP scenarios.

KV cache eviction has emerged as an effective solution to alleviate resource constraints faced by LLMs in long-context scenarios. However, existing token-level eviction methods often overlook two critical aspects: (1) their irreversible eviction strategy fails to adapt to dynamic attention patterns during decoding (the saliency shift problem), and (2) they treat both marginally important tokens and truly unimportant tokens equally, despite the collective significance of marginal tokens to model performance (the marginal information over-compression problem). To address these issues, we design two compensation mechanisms based on the high similarity of attention matrices between LLMs of different scales. We propose SmallKV, a small model assisted compensation method for KV cache compression. SmallKV can maintain attention matching between different-scale LLMs to: 1) assist the larger model in perceiving globally important information of attention; and 2) use the smaller model's attention scores to approximate those of marginal tokens in the larger model. Extensive experiments on benchmarks including GSM8K, BBH, MT-Bench, and LongBench demonstrate the effectiveness of SmallKV. Moreover, efficiency evaluations show that SmallKV achieves 1.75 2.56 times higher throughput than baseline methods, highlighting its potential for efficient and performant LLM inference in resource constrained environments.

In this work, we demonstrate that affine mappings between residual streams of language models is a cheap way to effectively transfer represented features between models. We apply this technique to transfer the weights of Sparse Autoencoders (SAEs) between models of different sizes to compare their representations. We find that small and large models learn similar representation spaces, which motivates training expensive components like SAEs on a smaller model and transferring to a larger model at a FLOPs savings. In particular, using a small-to-large transferred SAE as initialization can lead to 50% cheaper training runs when training SAEs on larger models. Next, we show that transferred probes and steering vectors can effectively recover ground truth performance. Finally, we dive deeper into feature-level transferability, finding that semantic and structural features transfer noticeably differently while specific classes of functional features have their roles faithfully mapped. Overall, our findings illustrate similarities and differences in the linear representation spaces of small and large models and demonstrate a method for improving the training efficiency of SAEs.