自适应方法

Effective exploration remains a key challenge in model-based reinforcement learning (MBRL), especially in high-dimensional continuous control tasks where sample efficiency is critical. Recent work addresses this by using learned policies as proposal distributions for Model-Predictive Path Integral (MPPI) planning. Early approaches update the sampling policy independently of the planner, typically via deterministic policy gradients with entropy regularization. However, since the data distribution is induced by the MPPI planner, misalignment between the policy and planner degrades value estimation and long-term performance. To address this, recent methods explicitly align the policy with the planner by minimizing KL divergence to the planner distribution or by incorporating planner-guided regularization. In this work, we unify these approaches under the Policy Optimization–Model Predictive Control (PO-MPC) framework, a family of KL-regularized MBRL methods that treat the planner’s action distribution as a prior in policy optimization. We show how existing methods emerge as special cases of this family and explore previously unstudied variants. Experiments demonstrate that these variants yield significant performance gains, advancing the state of the art in MPPI-based RL.

Adaptive Moment Estimation (Adam) is one of the most popular and often the default stochastic optimizers for deep neural network training. Using first- and second-moment estimation, Adam provides adaptive learning rates for each parameter, significantly outperforming Stochastic Gradient Descent (SGD). However, as deep neural networks become larger, estimating the first and second moments consumes substantial memory. It motivates various methods to reduce memory usage for adaptive optimizers. In this paper, we propose to rethink the first and second moment estimation from a gradient computation perspective. The gradient of the weight matrix is the multiplication of the input and the gradient of the output. Instead of finding low-rank approximations of the first and second moments, as in previous work, we propose tracking the input and output gradients to efficiently estimate moments. We provide analyses of the similarities and differences between our proposed method, the widely used Adam optimizer, and previous memory-efficient optimizers designed to reduce memory usage. We conduct experiments to verify the effectiveness of our method, which reduces memory usage by up to $30$% while preserving similar performance or even improving the performance of Adam.

Large kernel convolutions offer a scalable alternative to vision transformers for high-resolution 3D volumetric analysis, yet naively increasing kernel size often leads to optimization instability. Motivated by the spatial bias inherent in effective receptive fields (ERFs), we theoretically demonstrate that structurally re-parameterized blocks induce spatially varying learning rates that are crucial for convergence. Leveraging this insight, we introduce Rep3D, a framework that employs a lightweight modulation network to generate receptive-biased scaling masks, adaptively re-weighting kernel updates within a plain encoder architecture. This approach unifies spatial inductive bias with optimization-aware learning, avoiding the complexity of multi-branch designs while ensuring robust local-to-global convergence. Extensive evaluations on five 3D segmentation benchmarks demonstrate that Rep3D consistently outperforms state-of-the-art transformer and fixed-prior baselines. The source code is publicly available at https://github.com/leeh43/Rep3D.

Multi-token prediction (MTP) architecture is widely adopted in LLMs. MTP blocks can be appended to the tail of model to predict additional tokens. However, when training with pipeline parallel, MTP leads to more pipeline bubbles and deteriorates the pipeline efficiency. Based on in-depth analysis of MTP architectures and loss functions, we have identified the parallel nature of the MTP blocks, and leverage it for superior pipeline scheduling. We propose AdaHC, an adaptive pipeline scheduling framework for accelerating LLMs training with MTP block(s). AdaHC splits the output heads into chunks and reassembles the chunks to generate balanced pipeline stages, and performs adaptive activation forwarding to preserve the numerical equivalence. Experimental results show that AdaHC improves the training throughput of SOTA LLMs with diverse MTP configurations by 1.35$\times$ on average. This work paves a new direction for practical pipeline training.

The Muon optimizer has recently attracted considerable attention for its strong empirical performance and use of orthogonalized updates on matrix-shaped parameters, yet its underlying mechanisms and relationship to adaptive optimizers such as Adam remain insufficiently understood. In this work, we aim to address these questions through a unified spectral perspective. Specifically, we view Muon as the \( p = 0 \) endpoint of a family of spectral transformations of the form \( \boldsymbol{U} \boldsymbol{\Sigma}^{p} \boldsymbol{V}^{\top} \), and consider additional variants with \( p = \frac{1}{2} \), \( p = \frac{1}{4} \), and \( p = 1 \). These transformations are applied to both first-moment updates, as in momentum SGD, and to root-mean-square (RMS) normalized gradient updates as in Adam. To enable efficient computation, we develop a coupled Newton iteration that avoids explicit singular value decomposition. Across controlled experiments, we find that RMS-normalized updates yield more stable optimization than first-moment updates. Moreover, while spectral compression provides strong stabilization benefits under first-moment updates, the Muon update (\( p = 0 \)) does not consistently outperform Adam. These results suggest that Muon is best understood as an effective form of spectral normalization, but not a universally superior optimization method. Our code is available at \url{https://github.com/Ocram7/BeyondMuon}.

Testing conditional independence is fundamental yet intrinsically difficult: without additional assumptions, Type I error control is impossible in general. The ``Model-X'' paradigm addresses this difficulty by assuming exact knowledge of a relevant conditional distribution. While small deviations from this assumption can sometimes be tolerated in classical one-shot testing, existing sequential conditional independence tests typically require the Model-X conditional to be known exactly, making them fragile when it must instead be estimated. We propose a new approach that is substantially more robust to such estimation error. Our method applies testing-by-betting to an adaptively optimized Kernel Conditional Independence statistic, together with a normalization scheme and a truncate-and-shift calibration strategy. These modifications greatly reduce Type I error inflation while preserving high power across high-dimensional synthetic benchmarks and real-world fairness tasks, outperforming existing sequential Model-X approaches. Code is available at \url{https://github.com/he-zh/SKCI}.

Genomic foundation models increasingly adopt large language model architectures, yet almost universally rely on fixed tokenization schemes such as $k$-mers, BPE, or single nucleotides, which impose arbitrary sequence boundaries that may obscure biologically relevant structure. We present LDARNet, a 120M-parameter hierarchical genomic foundation model that adapts H-Net-style dynamic chunking from autoregressive generation to masked language modeling, combining BiMamba-2 state-space layers with local attention, bidirectional routing, and a ratio-based regularizer to induce adaptive token boundaries without supervision. Fine-tuned on 27 tasks from the Nucleotide Transformer and Genomic Benchmarks suites, LDARNet achieves 11/18 wins among compact models ($<$300M parameters) and state-of-the-art results on 5 histone modification tasks, outperforming models up to 20$\times$ larger. A FLOPs-matched controlled experiment isolates learned routing as the source of these gains: learned boundaries beat fixed-grid boundaries by up to 14 percentage points on histone tasks at identical compute. Nucleotide-resolution analysis further shows that the learned boundaries align with canonical promoter motifs and splice junctions without supervision, providing a biological interpretation for adaptive tokenization in genomic foundation models.

Adam is a widely used optimization algorithm in deep learning, yet the specific class of objective functions where it exhibits inherent advantages remains underexplored. Unlike prior studies requiring external schedulers and $\beta_2$ near 1 for convergence, this work investigates the ``natural'' auto-convergence properties of Adam. We identify a class of highly degenerate polynomials where Adam converges automatically without additional schedulers. Specifically, we derive theoretical conditions for local asymptotic stability on degenerate polynomials and demonstrate strong alignment between theoretical bounds and experimental results. We prove that Adam achieves local linear convergence on these degenerate functions, significantly outperforming the sub-linear convergence of Gradient Descent and Momentum. This acceleration stems from a decoupling mechanism between the second moment $v_t$ and squared gradient $g_t^2$, which exponentially amplifies the effective learning rate. Finally, we characterize Adam's hyperparameter phase diagram, identifying three distinct behavioral regimes: stable convergence, spikes, and SignGD-like oscillation.

Loss spikes remain a persistent obstacle in large-scale language model pretraining. While previous research has attempted to identify the root cause of loss spikes by investigating individual factors, we observe that, in practice, such spikes are typically triggered by the confluence of heterogeneous factors. Empirically, loss spikes may arise from a combination of data outliers, hardware or transient computational faults, numerical precision issues, and hyperparameter settings. Regardless of the underlying cause, these spikes manifest as unstable optimizer updates, as abnormal gradients contaminate both first- and second-moment states. In this paper, we propose a principled gradient-centric remedy: AdaGC, an adaptive per-tensor gradient clipping scheme that mitigates such contamination by bounding gradient norms relative to a tensor-wise exponential moving average of their historical clipped values. AdaGC is optimizer-agnostic, introduces negligible memory overhead, and reduces communication costs compared to GlobalGC, particularly in hybrid-parallel distributed training. Experiments on Llama-2 7B, Mixtral 8×1B, and ERNIE 10B-A1.4B demonstrate that AdaGC robustly eliminates training instabilities, consistently reducing spike scores to zero for all models and improving downstream accuracy over GlobalGC by 1.32\%, 1.27\%, and 2.48\%, respectively. Furthermore, AdaGC seamlessly integrates with optimizers such as Muon and Lion, consistently yielding higher average accuracy and zero spike scores. The code is available at https://github.com/PaddlePaddle/PaddleFleet (see Research/AdaGC).

Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose *STAGE-BO, Sequential Targeting Adaptive Gap-Filling $\varepsilon$-Constraint Bayesian Optimization*: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in $\varepsilon$-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.

We consider problems of parameter estimation where design variables can be actively optimized to maximize information gain. To this end, we introduce JADAI, a framework that jointly amortizes Bayesian adaptive design and inference by training a policy, a history network, and an inference network end-to-end. The networks minimize a generic loss that aggregates incremental reductions in posterior error along experimental sequences without density evaluations. Inference networks are instantiated with diffusion models that can approximate high-dimensional and multimodal posteriors at every experimental step. JADAI achieves superior or competitive performance across adaptive design benchmarks.

Medical time series are central to healthcare, enabling continuous monitoring and supporting timely clinical decisions. Despite recent progress, existing methods struggle to jointly model local-global dynamics and handle nonstationarities like baseline drift, while often failing to capture latent channel interactions. To address these challenges, we propose **MedMamba**, an end-to-end architecture that integrates state space models with domain-specific inductive biases. Specifically, MedMamba first employs multi-scale convolutional embeddings to capture discriminative local morphology. Second, to mitigate nonstationarity, we introduce a tri-branch differential state space encoder that processes raw, temporal-difference, and frequency-domain views, fusing them to emphasize informative patterns while suppressing drift. Furthermore, to uncover latent channel correlations, we design a spatial graph Mamba module that learns a directed dependency structure regularized toward sparsity and acyclicity, which obviates the need for predefined graphs. Extensive experiments on five real-world datasets demonstrate that MedMamba achieves state-of-the-art performance while maintaining linear computational complexity, and ablation studies validate each component's contribution.Code is available at https://github.com/zhangda1018/MedMamba.

Visual AutoRegressive modeling (VAR) suffers from substantial computational cost due to the massive token count involved. Failing to account for the continuous variation in modeling, existing VAR token reduction methods face three key limitations: heuristic stage partition, non-adaptive schedules, and limited acceleration scope, thereby leaving significant acceleration potential untapped. Since entropy variation intrinsically reflects the transition of predictive uncertainty, it offers a principled measure to capture continuous modeling variation. Therefore, we propose NOVA, a training-free token reduction acceleration framework for VAR models via entropy analysis. NOVA adaptively determines the acceleration activation scale during inference by online identifying the inflection point of scale entropy growth. Through scale-linkage and layer-linkage ratio adjustment, NOVA dynamically computes distinct token reduction ratios for each scale and layer, pruning low-entropy tokens while reusing the cache derived from the residuals at the prior scale to accelerate inference and maintain generation quality. Extensive experiments and analyses validate NOVA as a simple yet effective training-free acceleration framework. Code is available.

Distributional learning problems optimize discrepancies between probability measures, including optimal transport or Sinkhorn divergence, yet are typically optimized using Euclidean first-order methods in parameter space. We show this mismatch is structural rather than algorithmic. We introduce geometry-misalignment, a local condition number that measures distortion between Euclidean geometry and the intrinsic geometry induced by a distributional objective. For a broad class of problems, we establish lower bounds demonstrating that Euclidean first-order methods incur an unavoidable convergence slowdown proportional to misalignment, even under intrinsic strong convexity and smoothness. We further prove geometry-aware preconditioned methods attain matching upper bounds independent of misalignment, yielding a sharp separation between Euclidean optimization and geometry-aware optimization. Beyond convergence rates, we show geometry-misalignment induces an optimization-dependent excess risk term under finite budgets, directly linking optimization geometry with statistical efficiency. We develop a geometry-calibrated optimization framework that estimates misalignment and selectively activates geometry-aware updates when necessary. Experiments on distribution matching for domain adaptation validate the theory, with improvements concentrated in high-misalignment regimes and negligible overhead.

Jung et al. (2025) introduce a hypothesis testing framework for guaranteeing agreement between large language models (LLMs) and human judgments, relying on the assumption that the model’s estimated confidence is monotonic with respect to human-disagreement risk. In practice, however, this assumption may be violated, and the generalization behavior of the confidence estimator is not explicitly analyzed. We mitigate these issues by learning a dedicated confidence estimator instead of relying on heuristic confidence signals. Our approach leverages simulated annotator diversity and a margin-based ranking formulation to explicitly model how confidently an LLM distinguishes between human-agreement and human-disagreement cases. We further derive generalization guarantees for this estimator, revealing a margin-dependent trade-off that informs the design of an adaptive estimator training procedure. When integrated into fixed-sequence testing, the learned confidence estimator yields improved ranking accuracy and empirically strengthens the monotonic relationship between confidence and disagreement risk, leading to higher success rates in satisfying target agreement levels across multiple datasets and judge models.

Large language models (LLMs) achieve remarkable generative performance, yet their output quality is dependent on the decoding strategy. While sampling-based methods (e.g., top-k, nucleus) and search-and-select based methods (e.g., beam search, best-of-n, majority voting) can improve upon greedy decoding, both approaches suffer from limitations: sampling generally commits to a single path, while search often expends excessive computation regardless of task complexity. To address these, we introduce Entropy-informed DEcodiNg (EDEN), a plug-and-play, model-agnostic decoding framework that adaptively allocates computation based on the model’s own uncertainty, approximating higher-width beam search with *fewer expansions*. At each generation step, EDEN estimates the entropy of the output token distribution and adjusts the branching factor monotonically with the entropy, expanding more candidates in high-entropy regions and following a greedier path in low-entropy regions, improving token efficiency. Experiments across complex tasks, including mathematical reasoning, code generation, and scientific questions, demonstrate that EDEN consistently improves output quality over existing decoding strategies, achieving better accuracy-expansion trade-offs than fixed-width beam search. By treating next-token selection as a noisy maximisation problem, we prove that branching factors monotone in entropy are guaranteed to find better (i.e. more probable) continuations than any fixed branching factor within the same total expansion budget, and derive explicit regret rates characterising the benefit of the adaptive allocation.

This paper addresses the critical challenges of hyperparameter tuning and communication efficiency in federated learning (FL). Despite recent advancements in parameter-free FL algorithms such as PAdaMFed, significant communication overhead remains a major obstacle to their practical deployment. To tackle these challenges, we propose a novel communication-efficient parameter-free FL algorithm ParFreFL that halves the communication requirements of PAdaMFed while preserving its parameter-free property. Building on this foundation, we introduce a compressed variant, ComParFreFL, which unifies the momentum increment and error feedback into a single parameter, effectively handling biased compression while maintaining the minimal communication cost. Notably, ComParFreFL also operates independent of the compression ratio, representing the first instance of such robustness in the compressed FL literature to our knowledge. Theoretically, our methods are proven to handle arbitrary data heterogeneity, partial client participation, and achieve linear speedup with respect to both local updates and participating clients. Extensive empirical evaluations demonstrate that our approaches match or slightly surpass the performance of carefully tuned alternatives while significantly reducing communication overhead, making FL more accessible and deployable in dynamic, resource-constrained environments.

Finding flat minima in the loss landscape is a key strategy for Domain Generalization (DG). However, its effectiveness is often limited by two crucial challenges. 1) Domain Shift: Existing methods like Sharpness-Aware Minimization (SAM) apply a uniform optimization strategy across all domains, overlooking the differences of the learning difficulties among multiple domains and thus performing poorly on challenging domains. 2) Anisotropic Sharpness: By perturbing parameters along a single gradient direction, SAM and its variants ignore multi-directional flatness, making the model converge to minima that remain sharp in other directions. The combined challenges make it more difficult for the model to find truly robust solutions in multi-domain scenarios. To overcome these limitations, we propose the Dual Adaptive Sharpness-Aware Minimization (DA-SAM), which comprises two key modules: Dynamic Adaptive Scaling (DAS) module and Adaptive Multi-Directional Flattening (AMDF) module. First, to tackle the domain shift problem, the DAS module computes the real-time loss on each domain to adaptively generate domain-specific scaling factors that guide the generation of perturbation directions. Second, the AMDF module calculates local flatness by generating multiple directions to simulate perturbations in the parameter space. Based on the learned local flatness metric, it dynamically adjusts the perturbation step size to guide the model parameters to be away from anisotropic sharp regions. Crucially, DAS provides domain-level guidance that makes AMDF’s multi-directional geometric exploration more targeted and effective. Extensive experiments on five DG benchmarks demonstrate the effectiveness of our DA-SAM algorithm.

Self-speculative decoding (SSD) accelerates LLM inference by skipping layers to create an efficient draft model, yet existing methods often rely on static heuristics that ignore the dynamic computational overhead of attention in long-context scenarios. We propose KnapSpec, a training-free framework that reformulates draft model selection as a knapsack problem to maximize tokens-per-time throughput. By decoupling Attention and MLP layers and modeling their hardware-specific latencies as functions of context length, KnapSpec adaptively identifies optimal draft configurations on the fly via a parallel dynamic programming algorithm. Furthermore, we provide the first rigorous theoretical analysis establishing cosine similarity between hidden states as a mathematically sound proxy for the token acceptance rate. This foundation allows our method to maintain high drafting faithfulness while navigating the shifting bottlenecks of real-world hardware. Our experiments on Qwen3 and Llama3 demonstrate that KnapSpec consistently outperforms state-of-the-art SSD baselines, achieving up to 1.47$\times$ wall-clock speedup across various benchmarks. Our plug-and-play approach ensures high-speed inference for long sequences without requiring additional training or compromising the target model's output distribution.

Modern recommender systems are typically trained offline and deployed with parameters held fixed between periodic refreshes, yet user behavior can evolve substantially during deployment. This can cause ranking utility to degrade over time and makes it difficult to provide formal guarantees about recommendation quality. We propose **CARE**, an adaptive calibration framework that wraps an arbitrary backbone recommender and outputs variable-size recommendation sets with finite-sample performance guarantees over interaction streams. CARE combines (i) a loss-based monitoring module that localizes behavioral changes and triggers threshold recalibration, and (ii) an online aggregation rule that promotes compact recommendation sets by dynamically reweighting candidate set predictors. We provide theoretical results establishing finite-sample guarantees for utility-based risk control and bounds on the expected set size relative to the best constituent predictor. Experiments across multiple datasets and backbone models demonstrate that CARE improves robustness and maintains compact recommendation sets while preserving the desired statistical guarantees. The code and implementation are available in https://github.com/kalpiree/CARE.