arXiv subjects

Yuan Cao

Publications and source records attributed to Yuan Cao.

At least 37 records · Page 2Linked to original sources

arXiv2026

Beyond Fixed Representations: The Vocabulary and Verifier Gaps in Open-Ended AI

Modern AI systems are increasingly being evaluated for their ability to reason, code, prove theorems, use tools, and long-horizon research tasks. These are powerful capabilities, but they share a structural limitation: the representational frame within which the model operates, including its conceptual vocabulary, the space of admissible solutions it can search, and the criteria by which success is evaluated, is typically fixed and supplied in advance. This paper argues that building stronger intelligent systems capable of open-ended innovation requires additional classes of operations: the creation, stabilization, and reuse of new representational primitives, which alter the space being searched rather than simply searching within it. We characterize the distance between current AI systems and genuinely open-ended intelligence through two gaps. The first is the vocabulary gap, the difficulty of inventing and stabilizing new representational primitives rather than merely recombining existing ones. The second is the verifier gap, the difficulty of judging the value of a new primitive when its full payoff may be visible only after future reuse. We interpret both gaps through a unified framework of intelligence as cognitive discrepancy reduction. By viewing intelligent behaviors as a sequence of cognitive transformations, we distinguish intra-space transformations which operate within a fixed representational frame, from generative transformations which may modify the frame itself. On this basis, we propose a ladder of innovation autonomy and outline several directions for advancing open-ended AI, including objectives that reward useful representational change, persistent memory architectures for invented primitives, and adaptive verification mechanisms capable of evolving alongside the representations they evaluate.

cs.AI↗

arXiv2026

A Theory on Flow Matching with Neural Networks

In this work, we develop theoretical foundation for flow matching with neural-network-parameterized conditional velocity fields. We establish convergence guarantees for gradient descent in the over-parameterized 2-layered ReLU neural network regime. We derive generalization bounds for the conditional velocity-field matching objective. Building on these results, we provide Wasserstein-distance guarantees for the samples generated by the induced flow. Our analysis is based on generalization bound for multi-task representation learning with unbounded losses, which may be of independent interest beyond flow-based generative modeling. These theoretical results are validated through extensive experiments on both synthetic and real-world image benchmarks.

cs.LG↗

arXiv2026

Towards Simple and Provable Parameter-Free Adaptive Gradient Methods

Optimization algorithms such as AdaGrad and Adam have significantly advanced the training of deep models by dynamically adjusting the learning rate during the optimization process. However, ad-hoc tuning of learning rates poses a challenge and leads to inefficiencies in practice. To address this issue, recent research has focused on developing ``parameter-free'' algorithms that operate effectively without the need for learning rate tuning. Despite these efforts, existing parameter-free variants of AdaGrad and Adam tend to be overly complex and/or lack formal convergence guarantees. In this paper, we present AdaGrad++ and Adam++, novel and simple parameter-free variants of AdaGrad and Adam with convergence guarantees. We prove that AdaGrad++ achieves comparable convergence rates to AdaGrad in convex optimization without predefined learning rate assumptions. Similarly, Adam++ matches the convergence rate of Adam without relying on any conditions on the learning rates. Experimental results across various deep learning tasks validate the competitive performance of Adam++.

cs.LG↗

arXiv2026

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.

cs.LG↗

arXiv2026

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.

cs.LG↗

arXiv2026

TAH-QUANT: Effective Activation Quantization in Pipeline Parallelism over Slow Network

Decentralized training of large language models offers the opportunity to pool computational resources across geographically distributed participants, but is often bottlenecked by network communication, particularly under pipeline parallel settings. While pipeline parallelism partitions model layers across devices to handle large-scale models, it necessitates frequent communication of intermediate activations, creating challenges when network bandwidth is limited. To address these issues, we propose TAH-Quant (Tile-wise Adaptive Hadamard Quantization), a novel activation quantization framework for pipeline parallelism. TAH-Quant integrates fine-grained tile-wise quantization, entropy-guided tile-wise adaptive bit allocation for optimal bit usage, and a Hadamard-based transformation with pivot swapping to effectively suppress outliers. Compared with token-level allocation, the tile-wise allocator assigns precision at the granularity of small channel windows within each token, reducing quantization error under the same bit budget. We prove that pipeline parallel training equipped with TAH-Quant maintains a convergence rate of O(1/sqrt(T)), matching that of vanilla stochastic gradient descent. Extensive experiments demonstrate that TAH-Quant achieves an aggressive activation quantization ratio of 3-4 bits, providing up to 4.3x throughput speedup over uncompressed FP32 and up to 1.33x wall-clock speedup over AQ-SGD, while preserving training convergence, avoiding AQ-SGD's activation-cache overhead, and generalizing well across various training scenarios.

cs.LG↗

arXiv2026

Catch Your Breath: Adaptive Computation for Self-Paced Sequence Production

Within the landscape of inference-time scaling methods for foundation models, a width-based approach to scaling -- which involves the insertion of tokens in the input stream to delay model responses -- offers a unique advantage by increasing model expressivity while remaining highly parallelizable at both training and inference. The existing literature on training models to utilize tokens relies on the standard cross-entropy objective in which the model output is read out and evaluated only at the final step of a pause sequence. This approach provides no mechanism for the model to regulate its own processing or to signal readiness to respond, treating the additional compute steps as a static barrier rather than a resource to be used adaptively. We propose a supervised loss, Catch Your Breath (CYB), framed as a sequential-decision problem, that trains a model to dynamically and autonomously scale the number of compute steps used for each input token. The model indicates the need for additional compute steps by emitting a special output, delaying its response via a pause. The model can abstain multiple times to obtain longer delays. Our experiments demonstrate that CYB significantly outperforms standard cross-entropy when introduced either in pretraining or fine-tuning, reducing perplexity and enhancing downstream accuracy with no additional computational or memory cost.

cs.CL↗

arXiv2026

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.

cs.LG↗

arXiv2026

Through a Compressed Lens: Investigating The Impact of Quantization on Factual Knowledge Recall

Quantization methods are widely used to accelerate inference and streamline the deployment of large language models (LLMs). Although quantization's effects on various LLM capabilities have been extensively studied, one critical area remains underexplored: factual knowledge recall (FKR), the process by which LLMs access stored knowledge. To this end, we conduct comprehensive experiments using three common quantization techniques at distinct bit widths, in conjunction with interpretability-driven analyses on two tasks, knowledge memorization and latent multi-hop reasoning. We show that quantization typically results in information loss within LLMs, consequently diminishing their capacity for FKR. This effect is particularly amplified in smaller models within the same architectural families. However, models quantized at reduced bit precision do not consistently exhibit inferior performance and occasionally quantization may even enhance model FKR. We find that BitSandBytes demonstrates highest preservation of the original full-precision model's FKR. Despite variability across models and methods, quantization causes modest performance degradation and remains an effective compression strategy.

cs.CL↗

arXiv2026

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.

cs.LG↗

arXiv2026

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.

cs.CL↗

arXiv2026

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.

cs.AI↗

arXiv2026

Optical frequency comb double-resonance spectroscopy of the 9030-9175 cm$^{-1}$ states of ethylene

We use optical-optical double-resonance (OODR) spectroscopy to measure for the first time hot-band transitions of ethylene (C${_2}$H${_4}$) between states in the 3000 cm$^{-1}$ and 9000 cm$^{-1}$ energy ranges. A 3.2 $μ$m continuous wave (CW) pump is used to populate selected states in the $ν$${_9}$ vibrational mode. The sub-Doppler OODR transitions are then probed with two different cavity-enhanced probes tunable around 1.7 $μ$m: a frequency comb probe that allows for broadband measurements and simultaneous detection of many OODR lines, and a CW probe that measures individual lines with higher signal-to-noise ratio and better frequency accuracy. We report center frequencies and relative intensities of 90 ladder-type hot-band transitions from three different states in the $ν$${_9}$ vibrational mode. We exploit combination differences and measurements of polarization-dependent intensity ratios to determine the final state rotational quantum numbers J. Comparison to theoretical predictions from ExoMol allows tentative assignments for 28 transitions. We report improved center frequencies for the three pump transitions in the $ν$${_9}$ band. Furthermore, we observe 18 sub-Doppler V-type transitions from the depleted ground state to the 6000 cm$^{-1}$ region and assign 14 of them to the variational line list of Mraidi et al. [J Quant Spectros Radiat Transfer. 2023;310:108734 doi:10.1016/j.jqsrt.2023.108734].

physics.chem-ph↗

arXiv2026

ScaleGNN: Towards Scalable Graph Neural Networks via Adaptive High-order Neighboring Feature Fusion

Graph Neural Networks (GNNs) have demonstrated impressive performance across diverse graph-based tasks by leveraging message passing to capture complex node relationships. However, on large-scale real-world graphs, GNNs face two major challenges: (1) GNNs struggle to ensure scalability and efficiency as repeated aggregation of large neighborhoods incurs significant computational overhead; (2) GNNs suffer from over-smoothing, where excessive propagation makes node representations indistinguishable, hindering model expressiveness. To tackle these, we propose ScaleGNN, which adaptively fuses multi-hop node features for scalable and effective graph learning. We first compute per-hop pure-neighbor matrices to isolate exclusive structural signals, then apply lightweight fusion to balance low- and high-order information, preserving both local detail and global correlations. To curb redundancy and over-smoothing, we introduce Local Contribution Score (LCS)-based masking to prune low-relevance high-order neighbors, and impose learnable sparsity to selectively integrate valuable multi-hop features. Extensive experiments on real-world datasets show that ScaleGNN consistently outperforms state-of-the-art GNNs in both predictive accuracy and computational efficiency.

cs.LG↗

arXiv2026

SAGA: Selective Adaptive Gating for Efficient and Expressive Linear Attention

While Transformer architecture excel at modeling long-range dependencies contributing to its widespread adoption in vision tasks the quadratic complexity of softmax-based attention mechanisms imposes a major bottleneck, particularly when processing high-resolution images. Linear attention presents a promising alternative by reformulating the attention computation from $(QK)V$ to $Q(KV)$, thereby reducing the complexity from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ while preserving the global receptive field. However, most existing methods compress historical key-value (KV) information uniformly, which can lead to feature redundancy and the loss of directional alignment with the query (Q). This uniform compression results in low-rank $KV$ feature maps, contributing to a performance gap compared to softmax attention. To mitigate this limitation, we propose \textbf{S}elective \textbf{A}daptive \textbf{GA}ting for Efficient and Expressive Linear Attention (SAGA) , which introduces input-adaptive learnable gates to selectively modulate information aggregation into the $KV$ feature map. These gates enhance semantic diversity and alleviate the low-rank constraint inherent in conventional linear attention. Additionally, we propose an efficient Hadamard-product decomposition method for gate computation, which introduces no additional memory overhead. Experiments demonstrate that SAGA achieves a 1.76$\times$ improvement in throughput and a 2.69$\times$ reduction in peak GPU memory compared to PVT-T at a resolution of $1280 \times 1280$. Moreover, it improves top-1 accuracy by up to 4.4\% on the ImageNet dataset, demonstrating both computational efficiency and model effectiveness.

cs.CV↗

arXiv2026

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.

cs.AI↗

arXiv2026

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.

cs.LG↗

arXiv2026

KernelBand: Steering LLM-based Kernel Optimization via Hardware-Aware Multi-Armed Bandits

High-performance GPU kernels are critical for efficient LLM serving, yet their optimization remains a bottleneck requiring deep system expertise. While code LLMs show promise in generating functionally correct code, kernel optimization is intrinsically a search problem over a vast optimization space. The fundamental mismatch prevents existing LLM agents from efficiently exploring the optimization space for diverse hardware and compute patterns. To bridge the gap, we present KernelBand, a framework that formulates kernel optimization as a Multi-Armed Bandit (MAB) problem, explicitly balancing exploration and exploitation to unlock the potential of code LLMs. To navigate the infinite arm space of optimization strategies applied to candidate kernels, we design two key mechanisms: a hardware-aware pruning strategy via profiling bounds and a trace-driven clustering algorithm that leverages Lipschitz continuity. Theoretically, we prove that KernelBand reduces the regret bound to depend on the compact covering number of runtime clusters, ensuring sample-efficient discovery of high-performance kernels. Extensive experiments on TritonBench-G with three GPU architectures and four code LLMs show that KernelBand consistently and substantially outperforms state-of-the-art methods with over 33% average improvement.

cs.LG↗