Revisiting DAgger in the Era of LLM-Agents

Long-horizon LM agents learn from multi-turn interaction, where a single early mistake can alter the subsequent state distribution and derail the whole trajectory. Existing recipes fall short in complementary ways: supervised fine-tuning provides dense teacher supervision but suffers from covariate shift because it is trained on off-policy teacher trajectories; while reinforcement learning with verifiable rewards avoids this off-policy mismatch by learning from on-policy rollouts but with only sparse outcome feedback. We address this dilemma by revisiting Dataset Aggregation (DAgger) for multi-turn LM agents: the algorithm collects trajectories through a turn-level interpolation of student and teacher policies, and the student is then trained on these trajectories using supervised labels provided by the teacher. By directly interacting with environments, we expose the model to realistic states likely to be encountered during deployment, thereby effectively mitigating covariate shift. Besides, since the student is learned by mimicking the teacher's behavior, it receives rich feedback during learning. To demonstrate DAgger enjoys the benefits of both worlds, we tested the algorithm to train a software-engineering agent with 4B- and 8B-scale student models. On SWE-bench Verified, our DAgger-style training improves over the strongest post-training baseline by +3.9 points at 4B and +3.6 points at 8B. The resulting 4B agent reaches 27.3%, outperforming representative published 8B SWE-agent systems, while the 8B agent achieves 29.8%, surpassing SWE-Gym-32B and coming within 5 points of stronger 32B-scale agents. Together with consistent gains on the held-out SWE-Gym split, these results suggest the effectiveness of DAgger for modern long-horizon LM agents.

Support Before Frequency in Discrete Diffusion

Discrete diffusion models are increasingly competitive for language modeling, yet it remains unclear how their denoising objectives organize learning. Although these objectives target the full data distribution, we show that the exact reverse process induces a hierarchy between coarse support information and finer frequency information. For uniform and absorbing (a.k.a. masking) diffusion, we prove that, in the small-noise regime of the final denoising steps, each single-token reverse edit decomposes into a leading scale, determined by whether it moves toward the data support (e.g., grammatically valid sentences), and a finer coefficient, determining relative probabilities within the same scale. Thus, recovering validity structure only requires learning the correct order of magnitude of reverse probabilities, whereas recovering data frequencies requires coefficient-level estimation. The separation is mechanism-dependent: uniform diffusion exhibits a trichotomy into validity-improving, validity-preserving, and validity-worsening edits, while absorbing diffusion places its leading-order mass on validity-improving moves. Experiments on a masked language diffusion model and synthetic regular-language tasks support these predictions: support-localization emerges earlier than within-support frequency ranking, and the contrast between uniform and absorbing diffusion matches the predicted rate separation. Together, our results suggest that discrete diffusion models learn data support before data frequencies.

Muown: Row-Norm Control for Muon Optimization

Muon has emerged as a strong competitor to AdamW for language model pre-training, yet its behavior at scale is sensitive to weight decay. Recent work has observed that, for Muon without decoupled weight decay, the spectral norm of weight matrices drifts upward over training. Through a decomposition of the spectral norm into a row-magnitude factor and a row-coherence factor, we identify the former as the empirical driver of this drift under Muon, while the latter remains well-behaved along the trajectory. Motivated by this diagnosis, we introduce Muown, a drop-in replacement for Muon that treats the row-magnitude vector as an explicit optimizer variable, updating it under the $\ell_\infty$ geometry induced by the decomposition, while applying Muon unchanged to the remaining direction component. We prove that Muown attains the optimal non-convex rates in both deterministic and stochastic regimes under a dual norm aligned with the underlying geometries and with a stochastic noise coefficient that empirically remains below that of Muon throughout training. Across GPT-style pre-training on FineWeb-Edu with model sizes from 124M up to 2.7B parameters, Muown improves perplexity over Muon, SOAP, AdamW, and Lion. It also widens the plateau of near-optimal learning rates across model scales, reduces sensitivity to weight decay, and avoids the spectral norm drift at negligible step-time overhead when appropriately sharded.

Select-then-differentiate: Solving Bilevel Optimization with Manifold Lower-level Solution Sets

We study optimistic bilevel optimization when the lower-level problem has a non-isolated manifold of minimizers. In this setting, the hyper-objective may be non-differentiable because the upper-level criterion must choose among multiple lower-level solutions. Under a local Polyak--Łojasiewicz (PŁ) condition, we show that differentiability does not require the lower-level solution set to be a singleton: uniqueness of the optimistic selection is sufficient. This yields an explicit pseudoinverse-based hyper-gradient formula extending the classical singleton-minimizer result. We further characterize the regularity of the hyper-objective: non-degeneracy of the selected minimizer along the solution manifold yields local smoothness, while failure of uniqueness can create many non-differentiable points and failure of non-degeneracy can destroy all positive Hölder regularity of the hyper-gradient. Motivated by this theory, we propose HG-MS, a select-then-differentiate method combining explicit optimistic selection with efficient pseudoinverse-based hyper-gradient computation. Despite the nonconvex nature of optimistic selection over the lower-level solution manifold, we show that HG-MS converges to a stationary point of the optimistic objective with complexity governed by the intrinsic dimension of the solution manifold rather than its ambient dimension. Empirically, we test a practical variant of HG-MS for matched-budget LLM source reweighting. This variant preserves the select-then-differentiate principle and obtains the best GSM8K/MATH scores across the tested backbones, along with competitive or best MT-Bench instruction-following results.

Zeroth-Order Optimization at the Edge of Stability

Zeroth-order (ZO) methods are widely used when gradients are unavailable or prohibitively expensive, including black-box learning and memory-efficient fine-tuning of large models, yet their optimization dynamics in deep learning remain underexplored. In this work, we provide an explicit step size condition that exactly captures the (mean-square) linear stability of a family of ZO methods based on the standard two-point estimator. Our characterization reveals a sharp contrast with first-order (FO) methods: whereas FO stability is governed solely by the largest Hessian eigenvalue, mean-square stability of ZO methods depends on the entire Hessian spectrum. Since computing the full Hessian spectrum is infeasible in practical neural network training, we further derive tractable stability bounds that depend only on the largest eigenvalue and the Hessian trace. Empirically, we find that full-batch ZO methods operate at the edge of stability: ZO-GD, ZO-GDM, and ZO-Adam consistently stabilize near the predicted stability boundary across a range of deep learning training problems. Our results highlight an implicit regularization effect specific to ZO methods, where large step sizes primarily regularize the Hessian trace, whereas in FO methods they regularize the top eigenvalue.

Integrated electro-optic attention nonlinearities for transformers

Transformers have emerged as the dominant neural-network architecture, achieving state-of-the-art performance in language processing and computer vision. At the core of these models lies the attention mechanism, which requires a nonlinear, non-negative mapping using the Softmax function. However, although Softmax operations account for less than 1% of the total operation count, they can disproportionately bottleneck overall inference latency. Here, we use thin-film lithium niobate (TFLN) Mach-Zehnder modulators (MZMs) as analog nonlinear computational elements to drastically reduce the latency of nonlinear computations. We implement electro-optic alternatives to digital Softmax and Sigmoid, and evaluate their performance in Vision Transformers and Large Language Models. Our system maintains highly competitive accuracy, even under aggressive 4-bit input-output quantization of the analog units. We further characterize system noise at encoding speeds up to 10 GBaud and assess model robustness under various noise conditions. Our findings suggest that TFLN modulators can serve as nonlinear function units within hybrid co-packaged hardware, enabling high-speed and energy-efficient nonlinear computation.

Manifold Generalization Provably Proceeds Memorization in Diffusion Models

Diffusion models often generate novel samples even when the learned score is only \emph{coarse} -- a phenomenon not accounted for by the standard view of diffusion training as density estimation. In this paper, we show that, under the \emph{manifold hypothesis}, this behavior can instead be explained by coarse scores capturing the \emph{geometry} of the data while discarding the fine-scale distributional structure of the population measure~$μ_{\scriptscriptstyle\mathrm{data}}$. Concretely, whereas estimating the full data distribution $μ_{\scriptscriptstyle\mathrm{data}}$ supported on a $k$-dimensional manifold is known to require the classical minimax rate $\tilde{\mathcal{O}}(N^{-1/k})$, we prove that diffusion models trained with coarse scores can exploit the \emph{regularity of the manifold support} and attain a near-parametric rate toward a \emph{different} target distribution. This target distribution has density uniformly comparable to that of~$μ_{\scriptscriptstyle\mathrm{data}}$ throughout any $\tilde{\mathcal{O}}\bigl(N^{-β/(4k)}\bigr)$-neighborhood of the manifold, where $β$ denotes the manifold regularity. Our guarantees therefore depend only on the smoothness of the underlying support, and are especially favorable when the data density itself is irregular, for instance non-differentiable. In particular, when the manifold is sufficiently smooth, we obtain that \emph{generalization} -- formalized as the ability to generate novel, high-fidelity samples -- occurs at a statistical rate strictly faster than that required to estimate the full population distribution~$μ_{\scriptscriptstyle\mathrm{data}}$.

A Schrödinger Eigenfunction Method for Long-Horizon Stochastic Optimal Control

High-dimensional stochastic optimal control (SOC) becomes harder with longer planning horizons: existing methods scale linearly in the horizon $T$, with performance often deteriorating exponentially. We overcome these limitations for a subclass of linearly-solvable SOC problems-those whose uncontrolled drift is the gradient of a potential. In this setting, the Hamilton-Jacobi-Bellman equation reduces to a linear PDE governed by an operator $\mathcal{L}$. We prove that, under the gradient drift assumption, $\mathcal{L}$ is unitarily equivalent to a Schrödinger operator $\mathcal{S} = -Δ+ \mathcal{V}$ with purely discrete spectrum, allowing the long-horizon control to be efficiently described via the eigensystem of $\mathcal{L}$. This connection provides two key results: first, for a symmetric linear-quadratic regulator (LQR), $\mathcal{S}$ matches the Hamiltonian of a quantum harmonic oscillator, whose closed-form eigensystem yields an analytic solution to the symmetric LQR with \emph{arbitrary} terminal cost. Second, in a more general setting, we learn the eigensystem of $\mathcal{L}$ using neural networks. We identify implicit reweighting issues with existing eigenfunction learning losses that degrade performance in control tasks, and propose a novel loss function to mitigate this. We evaluate our method on several long-horizon benchmarks, achieving an order-of-magnitude improvement in control accuracy compared to state-of-the-art methods, while reducing memory usage and runtime complexity from $\mathcal{O}(Td)$ to $\mathcal{O}(d)$.

ANCRe: Adaptive Neural Connection Reassignment for Efficient Depth Scaling

Scaling network depth has been a central driver behind the success of modern foundation models, yet recent investigations suggest that deep layers are often underutilized. This paper revisits the default mechanism for deepening neural networks, namely residual connections, from an optimization perspective. Rigorous analysis proves that the layout of residual connections can fundamentally shape convergence behavior, and even induces an exponential gap in convergence rates. Prompted by this insight, we introduce adaptive neural connection reassignment (ANCRe), a principled and lightweight framework that parameterizes and learns residual connectivities from the data. ANCRe adaptively reassigns residual connections with negligible computational and memory overhead ($<1\%$), while enabling more effective utilization of network depth. Extensive numerical tests across pre-training of large language models, diffusion models, and deep ResNets demonstrate consistently accelerated convergence, boosted performance, and enhanced depth efficiency over conventional residual connections.

SALAAD: Sparse And Low-Rank Adaptation via ADMM

Modern large language models are increasingly deployed under compute and memory constraints, making flexible control of model capacity a central challenge. While sparse and low-rank structures naturally trade off capacity and performance, existing approaches often rely on heuristic designs that ignore layer and matrix heterogeneity or require model-specific architectural modifications. We propose SALAAD, a plug-and-play framework applicable to different model architectures that induces sparse and low-rank structures during training. By formulating structured weight learning under an augmented Lagrangian framework and introducing an adaptive controller that dynamically balances the training loss and structural constraints, SALAAD preserves the stability of standard training dynamics while enabling explicit control over the evolution of effective model capacity during training. Experiments across model scales show that SALAAD substantially reduces memory consumption during deployment while achieving performance comparable to ad-hoc methods. Moreover, a single training run yields a continuous spectrum of model capacities, enabling smooth and elastic deployment across diverse memory budgets without the need for retraining.