Looped Transformers with Layer Normalization Provably Learn the Power Method

Transformers have achieved remarkable success across a wide range of applications, and a growing body of work suggests that part of their strength comes from their ability to learn and execute algorithmic procedures. However, our understanding of how transformers learn such algorithms remains limited, especially in the presence of layer normalization (LN). In this work, we study principal component prediction as a concrete testbed for understanding the training dynamics of transformers with LN. We prove that a looped linear transformer with LN, trained by gradient descent, converges to a solution that implements the power method, with each self-attention layer performing one power iteration. Notably, the model is trained only for principal component prediction, rather than being explicitly supervised to implement the power method. Our finding thus reveals an "algorithmic implicit bias" of looped transformers with LN: principal-component prediction can in principle be achieved by many mechanisms, yet gradient descent selects one that realizes the power method. We further provide a concrete comparison between transformers with and without LN: even with layerwise guidance from power iterations, a transformer without LN cannot exactly learn the power method, whereas the corresponding transformer with LN can, leading to a provable performance gap in principal component prediction. Our results provide, to our knowledge, the first theoretical analysis of the training dynamics of looped and single-layer transformers with LN, and shed light on the role of LN in transformer models.

LEIA: Learned Environment for Interactive Architected Materials

World models have enabled interactive exploration of game environments and robotic manipulation, but physical engineering remains beyond their reach: real materials exhibit nonlinear constitutive laws, carry history-dependent internal state, undergo inertial dynamics, and may possess hierarchical structures spanning multiple length scales. We present LEIA (Learned Environment for Interactive Architected materials), a world model that lets engineers apply boundary conditions step by step and observe the resulting deformation and stress fields in real time. LEIA handles large three-dimensional unstructured meshes and generates autoregressive responses to user-specified loading. We introduce MicroPlate, a benchmark of architected plates spanning two regimes of microstructure modeling: architected lattices that resolve microstructure explicitly through three-dimensional geometry, and a homogeneous plate where microstructural change is modeled implicitly through internal degrees of freedom. MicroPlate is used to assess LEIA alongside four baseline methods across both regimes. Finally, we demonstrate that LEIA enables efficient candidate generation and ranking for fast surrogate-guided search for de novo designs of architected materials, with stress-accurate candidate ranking validated by finite element ground truth.

Transformers Efficiently Perform In-Context Logistic Regression via Normalized Gradient Descent

Transformers have demonstrated remarkable in-context learning (ICL) capabilities. The strong ICL performance of transformers is commonly believed to arise from their ability to implicitly execute certain algorithms on the context, thereby enhancing prediction and generation. In this work, we investigate how transformers with softmax attention perform in-context learning on linear classification data. We first construct a class of multi-layer transformers that can perform in-context logistic regression, with each layer exactly performing one step of normalized gradient descent on an in-context loss. Then, we show that our constructed transformer can be obtained through (i) training a single self-attention layer supervised by one-step gradient descent, and (ii) recurrently applying the trained layer to obtain a looped model. Training convergence guarantees of the self-attention layer and out-of-distribution generalization guarantees of the looped model are provided. Our results advance the theoretical understanding of ICL mechanism by showcasing how softmax transformers can effectively act as in-context learners.

Transformers Trained via Gradient Descent Can Provably Learn a Class of Teacher Models

Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile scenarios and tasks, we theoretically investigate utilizing transformers as students to learn from a class of teacher models. Specifically, the teacher models covered in our analysis include convolution layers with average pooling, graph convolution layers, and various classic statistical learning models, including a variant of sparse token selection models [Sanford et al., 2023, Wang et al., 2024] and group-sparse linear predictors [Zhang et al., 2025]. When learning from this class of teacher models, we prove that one-layer transformers with simplified "position-only'' attention can successfully recover all parameter blocks of the teacher models, thus achieving the optimal population loss. Building upon the efficient mimicry of trained transformers towards teacher models, we further demonstrate that they can generalize well to a broad class of out-of-distribution data under mild assumptions. The key in our analysis is to identify a fundamental bilinear structure shared by various learning tasks, which enables us to establish unified learning guarantees for these tasks when treating them as teachers for transformers.

The Anatomy of an Edit: Mechanism-Guided Activation Steering for Knowledge Editing

Large language models (LLMs) are increasingly used as knowledge bases, but keeping them up to date requires targeted knowledge editing (KE). However, it remains unclear how edits are implemented inside the model once applied. In this work, we take a mechanistic view of KE using neuron-level knowledge attribution (NLKA). Unlike prior work that focuses on pre-edit causal tracing and localization, we use post-edit attribution -- contrasting successful and failed edits -- to isolate the computations that shift when an edit succeeds. Across representative KE methods, we find a consistent pattern: mid-to-late attention predominantly promotes the new target, while attention and FFN modules cooperate to suppress the original fact. Motivated by these findings, we propose MEGA, a MEchanism-Guided Activation steering method that performs attention-residual interventions in attribution-aligned regions without modifying model weights. On CounterFact and Popular, MEGA achieves strong editing performance across KE metrics on GPT2-XL and LLaMA2-7B. Overall, our results elevate post-edit attribution from analysis to engineering signal: by pinpointing where and how edits take hold, it powers MEGA to deliver reliable, architecture-agnostic knowledge edits.

An Empirical Study and Theoretical Explanation on Task-Level Model-Merging Collapse

Model merging unifies independently fine-tuned LLMs from the same base, enabling reuse and integration of parallel development efforts without retraining. However, in practice we observe that merging does not always succeed: certain combinations of task-specialist models suffer from catastrophic performance degradation after merging. We refer to this failure mode as merging collapse. Intuitively, collapse arises when the learned representations or parameter adjustments for different tasks are fundamentally incompatible, so that merging forces destructive interference rather than synergy. In this paper, we identify and characterize the phenomenon of task-level merging collapse, where certain task combinations consistently trigger huge performance degradation across all merging methods. Through extensive experiments and statistical analysis, we demonstrate that representational incompatibility between tasks is strongly correlated with merging collapse, while parameter-space conflict metrics show minimal correlation, challenging conventional wisdom in model merging literature. We provide a theoretical explanation on this phenomenon through rate-distortion theory with a dimension-dependent bound, establishing fundamental limits on task mergeability regardless of methodology.

Synergistic Intra- and Cross-Layer Regularization Losses for MoE Expert Specialization

Sparse Mixture-of-Experts (MoE) models scale Transformers efficiently but suffer from expert overlap -- redundant representations across experts and routing ambiguity, resulting in severely underutilized model capacity. While architectural solutions like DeepSeekMoE promote specialization, they require substantial structural modifications and rely solely on intra-layer signals. In this paper, we propose two plug-and-play regularization losses that enhance MoE specialization and routing efficiency without modifying router or model architectures. First, an intra-layer specialization loss penalizes cosine similarity between experts' SwiGLU activations on identical tokens, encouraging experts to specialize in complementary knowledge. Second, a cross-layer coupling loss maximizes joint Top-$k$ routing probabilities across adjacent layers, establishing coherent expert pathways through network depth while reinforcing intra-layer expert specialization. Both losses are orthogonal to the standard load-balancing loss and compatible with both the shared-expert architecture in DeepSeekMoE and vanilla top-$k$ MoE architectures. We implement both losses as a drop-in Megatron-LM module. Extensive experiments across pre-training, fine-tuning, and zero-shot benchmarks demonstrate consistent task gains, higher expert specialization, and lower-entropy routing; together, these improvements translate into faster inference via more stable expert pathways.

GUI-GENESIS: Automated Synthesis of Efficient Environments with Verifiable Rewards for GUI Agent Post-Training

Post-training GUI agents in interactive environments is critical for developing generalization and long-horizon planning capabilities. However, training on real-world applications is hindered by high latency, poor reproducibility, and unverifiable rewards relying on noisy visual proxies. To address the limitations, we present GUI-GENESIS, the first framework to automatically synthesize efficient GUI training environments with verifiable rewards. GUI-GENESIS reconstructs real-world applications into lightweight web environments using multimodal code models and equips them with code-native rewards, executable assertions that provide deterministic reward signals and eliminate visual estimation noise. Extensive experiments show that GUI-GENESIS reduces environment latency by 10 times and costs by over $28,000 per epoch compared to training on real applications. Notably, agents trained with GUI-GENESIS outperform the base model by 14.54% and even real-world RL baselines by 3.27% on held-out real-world tasks. Finally, we observe that models can synthesize environments they cannot yet solve, highlighting a pathway for self-improving agents.

Kimi K2.5: Visual Agentic Intelligence

We introduce Kimi K2.5, an open-source multimodal agentic model designed to advance general agentic intelligence. K2.5 emphasizes the joint optimization of text and vision so that two modalities enhance each other. This includes a series of techniques such as joint text-vision pre-training, zero-vision SFT, and joint text-vision reinforcement learning. Building on this multimodal foundation, K2.5 introduces Agent Swarm, a self-directed parallel agent orchestration framework that dynamically decomposes complex tasks into heterogeneous sub-problems and executes them concurrently. Extensive evaluations show that Kimi K2.5 achieves state-of-the-art results across various domains including coding, vision, reasoning, and agentic tasks. Agent Swarm also reduces latency by up to $4.5\times$ over single-agent baselines. We release the post-trained Kimi K2.5 model checkpoint to facilitate future research and real-world applications of agentic intelligence.

From Classification to Ranking: Enhancing LLM Reasoning Capabilities for MBTI Personality Detection

Personality detection aims to measure an individual's corresponding personality traits through their social media posts. The advancements in Large Language Models (LLMs) offer novel perspectives for personality detection tasks. Existing approaches enhance personality trait analysis by leveraging LLMs to extract semantic information from textual posts as prompts, followed by training classifiers for categorization. However, accurately classifying personality traits remains challenging due to the inherent complexity of human personality and subtle inter-trait distinctions. Moreover, prompt-based methods often exhibit excessive dependency on expert-crafted knowledge without autonomous pattern-learning capacity. To address these limitations, we view personality detection as a ranking task rather than a classification and propose a corresponding reinforcement learning training paradigm. First, we employ supervised fine-tuning (SFT) to establish personality trait ranking capabilities while enforcing standardized output formats, creating a robust initialization. Subsequently, we introduce Group Relative Policy Optimization (GRPO) with a specialized ranking-based reward function. Unlike verification tasks with definitive solutions, personality assessment involves subjective interpretations and blurred boundaries between trait categories. Our reward function explicitly addresses this challenge by training LLMs to learn optimal answer rankings. Comprehensive experiments have demonstrated that our method achieves state-of-the-art performance across multiple personality detection benchmarks.