Daily Papers

The recent surge in research interest in applying large language models (LLMs) to decision-making tasks has flourished by leveraging the extensive world knowledge embedded in LLMs. While there is a growing demand to tailor LLMs for custom decision-making tasks, finetuning them for specific tasks is resource-intensive and may diminish the model's generalization capabilities. Moreover, state-of-the-art language models like GPT-4 and Claude are primarily accessible through API calls, with their parametric weights remaining proprietary and unavailable to the public. This scenario emphasizes the growing need for new methodologies that allow learning from agent experiences without requiring parametric updates. To address these problems, we introduce the Experiential Learning (ExpeL) agent. Our agent autonomously gathers experiences and extracts knowledge using natural language from a collection of training tasks. At inference, the agent recalls its extracted insights and past experiences to make informed decisions. Our empirical results highlight the robust learning efficacy of the ExpeL agent, indicating a consistent enhancement in its performance as it accumulates experiences. We further explore the emerging capabilities and transfer learning potential of the ExpeL agent through qualitative observations and additional experiments.

Large Language Model (LLM)-based automatic Multi-Agent Systems (MAS) generation has become a crucial frontier for tackling complex tasks. However, existing methods face a dilemma between model capability and experience retention. Inference-time MAS leverages frozen frontier LLMs but repeats identical searches without learning from past experience. Conversely, Training-time MAS internalizes experience via gradient updates but is constrained by the low capability ceiling of smaller models, and is hard to scale to large frontier LLMs. To bridge this gap, we propose Skill-MAS, a novel third path that decouples experience retention from parametric updates by conceptualizing the high-level orchestration capability as an evolvable Meta-Skill. Skill-MAS refines this architectural knowledge through a closed optimization loop: (1) Multi-Trajectory Rollout samples a behavioral distribution for each task under the current Meta-Skill; and (2) Selective Reflection adaptively selects priority tasks and applies hierarchical contrastive analysis to distill systemic experience into generalizable, strategy-level principles. Extensive experiments across four complex benchmarks and four distinct LLMs demonstrate that Skill-MAS not only achieves remarkable performance gains but also maintains a favorable cost-performance trade-off. Further analysis reveals that the evolved Meta-Skills are highly robust and exhibit strong transferability across unseen tasks and different LLMs.

Existing memory-augmented LLM agents store past experience exclusively in prompt space, as textual summaries or retrieved passages, while keeping model parameters frozen throughout a rollout. Such agents can look up what they have seen but cannot learn from it: their policy is unchanged by experience, and any information dropped from the context is permanently lost. We introduce TMEM, a self-evolving parametric memory framework in which the agent not only compresses history into explicit memory but also absorbs distilled supervision into fast LoRA weights Δ_t via lightweight online updates, genuinely altering its future behavior within a single episode. We formalize this as an agentic decision process with fast-weight rollout dynamics: actions are sampled from π_{θ_0+Δ_t}, while extraction actions produce supervision that updates Δ_t for subsequent decisions. This view makes the extraction policy directly optimizable by RL: training θ_0 improves not only task actions but also the quality of the data used for online LoRA adaptation. We further propose SVD-based initialization of the LoRA subspace to accelerate online convergence. Experiments on LoCoMo, LongMemEval-S, multi-objective search, and CL-Bench show that TMEM consistently outperforms summary-based and retrieval-based baselines across different model scales.

Processing video in vision-language models is expensive: each frame occupies hundreds of tokens, and inference cost scales with every frame and every repeated query. We introduce Video2LoRA, a method for parametric video internalization. A perceiver hypernetwork reads the intermediate representations produced layer-by-layer as a frozen VLM encodes a video, and generates a Low-Rank Adaptation (LoRA) adapter in a single forward pass. Unlike standard LoRA fine-tuning, which requires iterative gradient updates, Video2LoRA predicts these weights directly from the video. Trained for SmolVLM2 500M and 2.2B on video summarization and captioning, Video2LoRA enables the same frozen VLM to answer queries from the adapter alone, with zero visual tokens in its context at query time. Video2LoRA is statistically non-inferior and equivalent to direct video-in-context inference across all five captioning benchmarks at both model scales, and across seven of eight video question answering benchmark-scale pairings. Although trained only on 12 frames at 384px, it remains stable up to 1,024 frames and 1024px, where direct video-in-context inference often degenerates. Across this sweep, it reduces answer-time visual-token load by up to 1,500x and query TTFT by 6-80x, while preserving video-faithful outputs. We also find that independently generated adapters for non-overlapping video segments can compose in rank space, suggesting a path toward chunked long-video internalization.

Large Language Models (LLMs) must continuously learn and update knowledge to remain effective in dynamic real-world environments. While Low-Rank Adaptation (LoRA) is widely used for such memory updates, existing studies mainly rely on qualitative downstream evaluations, leaving the quantitative capacity limits and underlying dynamics of exact parametric memory largely unexplored. To bridge this gap, we employ LoRA as a controlled memory capacity probe within the latent space to systematically quantify exact parametric memory. We introduce the Parametric Memory Law, a robust power law linking loss reduction Delta L to effective parameters and sequence length. At the token level, fine-grained analysis reveals a deterministic phase transition, demonstrating that a prediction probability of p > 0.5 constitutes a sufficient condition for verbatim recall under greedy decoding. Driven by these insights, we introduce MemFT, a threshold-guided optimization strategy that dynamically redistributes the training budget toward sub-threshold tokens. Empirical evaluations demonstrate that MemFT can enhance memory fidelity and efficiency. Code will be released at https://github.com/zjunlp/ParametricMemoryLaw.

Parametric Retrieval-Augmented Generation (PRAG) encodes external documents into lightweight parameter modules that can be retrieved and merged at inference time, offering a promising alternative to in-context retrieval augmentation. Despite its potential, many PRAG implementations train document adapters with task-supervised objectives, which may cause each adapter to encode both document-specific facts and reusable task-solving behavior. This entanglement may make adapter composition less reliable: when multiple adapters are merged at inference time, their overlapping task behaviors can accumulate together with document-specific updates, potentially making the merged adapter less stable and less focused on the intended document knowledge. To examine this issue, we explore Orthogonal Subspace Decomposition (OSD), an adapter-training setup that separates reusable task behavior from document-specific knowledge adapters. Concretely, we first train a Task LoRA to capture reusable task behavior, and then train document LoRAs to encode document-specific knowledge in a orthogonal subspace. This setup provides a controlled way to examine how orthogonalizing task and document LoRA updates affects adapter composition in multi-document PRAG. Experiments across multiple knowledge-intensive tasks and model scales suggest that this orthogonalization strategy can improve compositional robustness in parametric RAG, especially when multiple document adapters are merged.

Inspired by the insights in cognitive science with respect to human memory and reasoning mechanism, a novel evolvable LLM-based (Large Language Model) agent framework is proposed as REMEMBERER. By equipping the LLM with a long-term experience memory, REMEMBERER is capable of exploiting the experiences from the past episodes even for different task goals, which excels an LLM-based agent with fixed exemplars or equipped with a transient working memory. We further introduce Reinforcement Learning with Experience Memory (RLEM) to update the memory. Thus, the whole system can learn from the experiences of both success and failure, and evolve its capability without fine-tuning the parameters of the LLM. In this way, the proposed REMEMBERER constitutes a semi-parametric RL agent. Extensive experiments are conducted on two RL task sets to evaluate the proposed framework. The average results with different initialization and training sets exceed the prior SOTA by 4% and 2% for the success rate on two task sets and demonstrate the superiority and robustness of REMEMBERER.

Non-parametric, k-nearest-neighbor algorithms have recently made inroads to assist generative models such as language models and machine translation decoders. We explore whether such non-parametric models can improve machine translation models at the fine-tuning stage by incorporating statistics from the kNN predictions to inform the gradient updates for a baseline translation model. There are multiple methods which could be used to incorporate kNN statistics and we investigate gradient scaling by a gating mechanism, the kNN's ground truth probability, and reinforcement learning. For four standard in-domain machine translation datasets, compared with classic fine-tuning, we report consistent improvements of all of the three methods by as much as 1.45 BLEU and 1.28 BLEU for German-English and English-German translations respectively. Through qualitative analysis, we found particular improvements when it comes to translating grammatical relations or function words, which results in increased fluency of our model.

While Large Language Model (LLM) agents excel at general tasks, they inherently struggle with continual adaptation due to the frozen weights after deployment. Conventional reinforcement learning (RL) offers a solution but incurs prohibitive computational costs and the risk of catastrophic forgetting. We introduce Just-In-Time Reinforcement Learning (JitRL), a training-free framework that enables test-time policy optimization without any gradient updates. JitRL maintains a dynamic, non-parametric memory of experiences and retrieves relevant trajectories to estimate action advantages on-the-fly. These estimates are then used to directly modulate the LLM's output logits. We theoretically prove that this additive update rule is the exact closed-form solution to the KL-constrained policy optimization objective. Extensive experiments on WebArena and Jericho demonstrate that JitRL establishes a new state-of-the-art among training-free methods. Crucially, JitRL outperforms the performance of computationally expensive fine-tuning methods (e.g., WebRL) while reducing monetary costs by over 30 times, offering a scalable path for continual learning agents. The code is available at https://github.com/liushiliushi/JitRL.

LLM-driven agents demonstrate strong performance in sequential decision-making but often rely on on-the-fly reasoning, re-deriving solutions even in recurring scenarios. This insufficient experience reuse leads to computational redundancy and execution instability. To bridge this gap, we propose ProcMEM, a framework that enables agents to autonomously learn procedural memory from interaction experiences without parameter updates. By formalizing a Skill-MDP, ProcMEM transforms passive episodic narratives into executable Skills defined by activation, execution, and termination conditions to ensure executability. To achieve reliable reusability without capability degradation, we introduce Non-Parametric PPO, which leverages semantic gradients for high-quality candidate generation and a PPO Gate for robust Skill verification. Through score-based maintenance, ProcMEM sustains compact, high-quality procedural memory. Experimental results across in-domain, cross-task, and cross-agent scenarios demonstrate that ProcMEM achieves superior reuse rates and significant performance gains with extreme memory compression. Visualized evolutionary trajectories and Skill distributions further reveal how ProcMEM transparently accumulates, refines, and reuses procedural knowledge to facilitate long-term autonomy.

Large language models (LLMs) have significantly impacted many aspects of our lives. However, assessing and ensuring their chronological knowledge remains challenging. Existing approaches fall short in addressing the accumulative nature of knowledge, often relying on a single time stamp. To overcome this, we introduce ChroKnowBench, a benchmark dataset designed to evaluate chronologically accumulated knowledge across three key aspects: multiple domains, time dependency, temporal state. Our benchmark distinguishes between knowledge that evolves (e.g., scientific discoveries, amended laws) and knowledge that remain constant (e.g., mathematical truths, commonsense facts). Building on this benchmark, we present ChroKnowledge (Chronological Categorization of Knowledge), a novel sampling-based framework for evaluating and updating LLMs' non-parametric chronological knowledge. Our evaluation shows: (1) The ability of eliciting temporal knowledge varies depending on the data format that model was trained on. (2) LLMs partially recall knowledge or show a cut-off at temporal boundaries rather than recalling all aspects of knowledge correctly. Thus, we apply our ChroKnowPrompt, an in-depth prompting to elicit chronological knowledge by traversing step-by-step through the surrounding time spans. We observe that our framework successfully updates the overall knowledge across the entire timeline in both the biomedical domain (+11.9%) and the general domain (+2.8%), demonstrating its effectiveness in refining temporal knowledge. This non-parametric approach also enables knowledge updates not only in open-source models but also in proprietary LLMs, ensuring comprehensive applicability across model types. We perform a comprehensive analysis based on temporal characteristics of ChroKnowPrompt and validate the potential of various models to elicit intrinsic temporal knowledge through our method.

Retrieval-augmented generation stores all content indiscriminately, degrading accuracy as noise accumulates. Parametric approaches compress knowledge into weights, precluding selective updates. Neither mirrors biological memory, which gates encoding based on salience and archives rather than deletes superseded information. We introduce write-time gating that filters incoming knowledge objects using composite salience scores (source reputation, novelty, reliability) while maintaining version chains that preserve prior states. Using real LLM evaluation without oracle access to quality labels, write gating achieves 100 percent accuracy versus 13 percent for ungated stores. The critical finding emerges under distractor scaling: at 8:1 distractor ratios, read-time filtering (Self-RAG) collapses to 0 percent while write gating maintains 100 percent, revealing a structural advantage of write-time over read-time curation. Validation on Wikipedia (20 entities), procedurally generated pharmacology data, and 2026 arXiv papers confirms these findings. The gating advantage scales inversely with parametric memory support: +25pp for Wikipedia, +48pp for post-cutoff arXiv, +65pp for procedural data with zero training knowledge. Signal ablation confirms the method does not depend on oracle-correlated metadata. Write gating matches Self-RAG accuracy at one-ninth the query-time cost.

Recently decades have witnessed the empirical success of framing Knowledge Graph (KG) embeddings via language models. However, language model-based KG embeddings are usually deployed as static artifacts, which are challenging to modify without re-training after deployment. To address this issue, we propose a new task of editing language model-based KG embeddings in this paper. The proposed task aims to enable data-efficient and fast updates to KG embeddings without damaging the performance of the rest. We build four new datasets: E-FB15k237, A-FB15k237, E-WN18RR, and A-WN18RR, and evaluate several knowledge editing baselines demonstrating the limited ability of previous models to handle the proposed challenging task. We further propose a simple yet strong baseline dubbed KGEditor, which utilizes additional parametric layers of the hyper network to edit/add facts. Comprehensive experimental results demonstrate that KGEditor can perform better when updating specific facts while not affecting the rest with low training resources. Code and datasets will be available in https://github.com/zjunlp/PromptKG/tree/main/deltaKG.

Diffusion Language Models (DLMs) offer attractive advantages over Auto-Regressive (AR) models, such as full-attention parallel decoding and flexible generation. However, they suffer from a notable train-inference mismatch: DLMs are trained with a static, single-step masked prediction objective, but deployed through a multi-step progressive denoising trajectory. We propose MemDLM (Memory-Enhanced DLM), which narrows this gap by embedding a simulated denoising process into training via Bi-level Optimization. An inner loop updates a set of fast weights, forming a Parametric Memory that captures the local trajectory experience of each sample, while an outer loop updates the base model conditioned on this memory. By offloading memorization pressure from token representations to parameters, MemDLM yields faster convergence and lower training loss. Moreover, the inner loop can be re-enabled at inference time as an adaptation step, yielding additional gains on long-context understanding. We find that, when activated at inference time, this Parametric Memory acts as an emergent in-weight retrieval mechanism, helping MemDLM further reduce token-level attention bottlenecks on challenging Needle-in-a-Haystack retrieval tasks. Code: https://github.com/JarvisPei/MemDLM.

Urban scene reconstruction requires modeling both static infrastructure and dynamic elements while supporting diverse environmental conditions. We present StyledStreets, a multi-style street simulator that achieves instruction-driven scene editing with guaranteed spatial and temporal consistency. Building on a state-of-the-art Gaussian Splatting framework for street scenarios enhanced by our proposed pose optimization and multi-view training, our method enables photorealistic style transfers across seasons, weather conditions, and camera setups through three key innovations: First, a hybrid embedding scheme disentangles persistent scene geometry from transient style attributes, allowing realistic environmental edits while preserving structural integrity. Second, uncertainty-aware rendering mitigates supervision noise from diffusion priors, enabling robust training across extreme style variations. Third, a unified parametric model prevents geometric drift through regularized updates, maintaining multi-view consistency across seven vehicle-mounted cameras. Our framework preserves the original scene's motion patterns and geometric relationships. Qualitative results demonstrate plausible transitions between diverse conditions (snow, sandstorm, night), while quantitative evaluations show state-of-the-art geometric accuracy under style transfers. The approach establishes new capabilities for urban simulation, with applications in autonomous vehicle testing and augmented reality systems requiring reliable environmental consistency. Codes will be publicly available upon publication.

Most deep reinforcement learning (RL) algorithms distill experience into parametric behavior policies or value functions via gradient updates. While effective, this approach has several disadvantages: (1) it is computationally expensive, (2) it can take many updates to integrate experiences into the parametric model, (3) experiences that are not fully integrated do not appropriately influence the agent's behavior, and (4) behavior is limited by the capacity of the model. In this paper we explore an alternative paradigm in which we train a network to map a dataset of past experiences to optimal behavior. Specifically, we augment an RL agent with a retrieval process (parameterized as a neural network) that has direct access to a dataset of experiences. This dataset can come from the agent's past experiences, expert demonstrations, or any other relevant source. The retrieval process is trained to retrieve information from the dataset that may be useful in the current context, to help the agent achieve its goal faster and more efficiently. he proposed method facilitates learning agents that at test-time can condition their behavior on the entire dataset and not only the current state, or current trajectory. We integrate our method into two different RL agents: an offline DQN agent and an online R2D2 agent. In offline multi-task problems, we show that the retrieval-augmented DQN agent avoids task interference and learns faster than the baseline DQN agent. On Atari, we show that retrieval-augmented R2D2 learns significantly faster than the baseline R2D2 agent and achieves higher scores. We run extensive ablations to measure the contributions of the components of our proposed method.

Vision-Language-Action (VLA) models show strong potential for general-purpose robotic manipulation, yet their closed-loop reliability often degrades under local deployment conditions. Existing evaluations typically treat test episodes as independent zero-shot trials. However, real robots often operate repeatedly in the same or slowly changing environments, where successful executions provide environment-verified evidence of reliable behavior patterns. We study this persistent-deployment setting, asking whether a partially competent frozen VLA can improve its reliability by reusing its successful test-time experience. We propose an online success-memory guided test-time adaptation framework for generative VLAs. During deployment, the robot stores progress-calibrated successful observation-action segments in a long-term memory. At inference, it retrieves state-relevant action chunks, filters inconsistent candidates via trajectory-level consistency, and aggregates them into an elite action prior. To incorporate this prior into action generation, we introduce confidence-adaptive prior guidance, which injects the elite prior into an intermediate state of the flow-matching action sampler and adjusts the guidance strength based on retrieval confidence. This design allows the frozen VLA to exploit environment-specific successful experience while preserving observation-conditioned generative refinement. This retrieve-then-steer mechanism enables lightweight, non-parametric test-time adaptation without requiring parameter updates. Simulation and real-world experiments show improved task success and closed-loop stability, especially in long-horizon and multi-stage tasks.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

The Maximal Update Parametrization (muP) aims to make the optimal hyperparameters (HPs) of a model independent of its size, allowing them to be swept using a cheap proxy model rather than the full-size target model. We present a new scheme, u-muP, which improves upon muP by combining it with Unit Scaling, a method for designing models that makes them easy to train in low-precision. The two techniques have a natural affinity: muP ensures that the scale of activations is independent of model size, and Unit Scaling ensures that activations, weights and gradients begin training with a scale of one. This synthesis opens the door to a simpler scheme, whose default values are near-optimal. This in turn facilitates a more efficient sweeping strategy, with u-muP models reaching a lower loss than comparable muP models and working out-of-the-box in FP8.

We introduce a new method of generating Computer Aided Design (CAD) profiles via a sequence of simple geometric constructions including curve offsetting, rotations and intersections. These sequences start with geometry provided by a designer and build up the points and curves of the final profile step by step. We demonstrate that adding construction steps between the designer's input geometry and the final profile improves generation quality in a similar way to the introduction of a chain of thought in language models. Similar to the constraints in a parametric CAD model, the construction sequences reduce the degrees of freedom in the modeled shape to a small set of parameter values which can be adjusted by the designer, allowing parametric editing with the constructed geometry evaluated to floating point precision. In addition we show that applying reinforcement learning to the construction sequences gives further improvements over a wide range of metrics, including some which were not explicitly optimized.

Second-order optimization has been developed to accelerate the training of deep neural networks and it is being applied to increasingly larger-scale models. In this study, towards training on further larger scales, we identify a specific parameterization for second-order optimization that promotes feature learning in a stable manner even if the network width increases significantly. Inspired by a maximal update parameterization, we consider a one-step update of the gradient and reveal the appropriate scales of hyperparameters including random initialization, learning rates, and damping terms. Our approach covers two major second-order optimization algorithms, K-FAC and Shampoo, and we demonstrate that our parameterization achieves higher generalization performance in feature learning. In particular, it enables us to transfer the hyperparameters across models with different widths.

It is often useful to compactly summarize important properties of model parameters and training data so that they can be used later without storing and/or iterating over the entire dataset. As a specific case, we consider estimating the Function Space Distance (FSD) over a training set, i.e. the average discrepancy between the outputs of two neural networks. We propose a Linearized Activation Function TRick (LAFTR) and derive an efficient approximation to FSD for ReLU neural networks. The key idea is to approximate the architecture as a linear network with stochastic gating. Despite requiring only one parameter per unit of the network, our approach outcompetes other parametric approximations with larger memory requirements. Applied to continual learning, our parametric approximation is competitive with state-of-the-art nonparametric approximations, which require storing many training examples. Furthermore, we show its efficacy in estimating influence functions accurately and detecting mislabeled examples without expensive iterations over the entire dataset.

We present Semantify: a self-supervised method that utilizes the semantic power of CLIP language-vision foundation model to simplify the control of 3D morphable models. Given a parametric model, training data is created by randomly sampling the model's parameters, creating various shapes and rendering them. The similarity between the output images and a set of word descriptors is calculated in CLIP's latent space. Our key idea is first to choose a small set of semantically meaningful and disentangled descriptors that characterize the 3DMM, and then learn a non-linear mapping from scores across this set to the parametric coefficients of the given 3DMM. The non-linear mapping is defined by training a neural network without a human-in-the-loop. We present results on numerous 3DMMs: body shape models, face shape and expression models, as well as animal shapes. We demonstrate how our method defines a simple slider interface for intuitive modeling, and show how the mapping can be used to instantly fit a 3D parametric body shape to in-the-wild images.

Power transforms are popular parametric techniques for making data more Gaussian-like, and are widely used as preprocessing steps in statistical analysis and machine learning. However, we find that direct implementations of power transforms suffer from severe numerical instabilities, which can lead to incorrect results or even crashes. In this paper, we provide a comprehensive analysis of the sources of these instabilities and propose effective remedies. We further extend power transforms to the federated learning setting, addressing both numerical and distributional challenges that arise in this context. Experiments on real-world datasets demonstrate that our methods are both effective and robust, substantially improving stability compared to existing approaches.

As language models scale up, it becomes increasingly expensive to verify research ideas because conclusions on small models do not trivially transfer to large ones. A possible solution is to establish a generic system that directly predicts some metrics for large models solely based on the results and hyperparameters from small models. Existing methods based on scaling laws require hyperparameter search on the largest models, which is impractical with limited resources. We address this issue by presenting our discoveries indicating that Maximal Update parametrization (Mup) enables accurate fitting of scaling laws for hyperparameters close to common loss basins, without any search. Thus, different models can be directly compared on large scales with loss prediction even before the training starts. We propose a new paradigm as a first step towards reliable academic research for any model scale without heavy computation. Code is publicly available at https://github.com/cofe-ai/Mu-scaling.

In the training of large language models (LLMs), updating parameters more efficiently and stably has always been an important challenge. To achieve efficient parameter updates, existing methods usually achieve performance comparable to full parameter updates through methods such as low-dimensional decomposition or layer-wise selective updates. In this work, we propose AlphaAdam, an optimization framework for LLM from the perspective of intra-layer parameter updates. By decoupling parameter updates and dynamically adjusting their strength, AlphaAdam accelerates convergence and improves training stability. We construct parameter masks based on the consistency of historical momentum and gradient direction and combine them with an adaptive mask strength strategy to ensure efficient optimization and theoretical convergence guarantees, which is also applicable to most momentum-based optimizers. Extensive experiments show that AlphaAdam outperforms state-of-the-art methods such as AdamW in terms of convergence speed and computational efficiency across tasks, including GPT-2 pre-trained and fine-tuned RoBERTa and Llama-7B. Our AlphaAdam implements an optimizer enhancement framework for LLMs through intra-layer asynchronous masked adaptive updates. Our code is available in this https://github.com/MaeChd/AlphaAdam.

Fine-tuning pre-trained language models for downstream tasks has achieved impressive results in NLP. However, fine-tuning all parameters becomes impractical due to the rapidly increasing size of model parameters. To address this, Parameter Efficient Fine-Tuning (PEFT) methods update only a subset of parameters. Most PEFT methods, such as LoRA, use incremental updates, which involve adding learned weight matrix increments to the original parameters. Although effective, these methods face limitations in capturing complex parameter dynamics and do not maintain a strong correlation between the original and updated parameters. To overcome these challenges, we propose the direct Updated Transformation (UT) paradigm, which constructs a transformation directly from the original to the updated parameters. This approach ensures that the correlation between the original and updated parameters is preserved, leveraging the semantic features learned during pre-training. Building on this paradigm, we present the Hadamard Updated Transformation (HUT) method. HUT efficiently updates the original weight matrix using the Hadamard transformation with two low-rank matrices, offering a more expressive and flexible update mechanism. This allows HUT to capture richer parameter features through functional transformations, reducing computational complexity while maintaining or improving model quality. Theoretical analysis and extensive experiments on RoBERTa and GPT-2 validate the effectiveness of HUT. Results show that HUT performs on par with or better than other PEFT methods in terms of model quality, while significantly reducing computational complexity.

We introduce a unified framework for iterative reasoning that leverages non-Euclidean geometry via Bregman divergences, higher-order operator averaging, and adaptive feedback mechanisms. Our analysis establishes that, under mild smoothness and contractivity assumptions, a generalized update scheme not only unifies classical methods such as mirror descent and dynamic programming but also captures modern chain-of-thought reasoning processes in large language models. In particular, we prove that our accelerated iterative update achieves an O(1/t^2) convergence rate in the absence of persistent perturbations, and we further demonstrate that feedback (iterative) architectures are necessary to approximate certain fixed-point functions efficiently. These theoretical insights bridge classical acceleration techniques with contemporary applications in neural computation and optimization.

A supervised learning algorithm searches over a set of functions A to B parametrised by a space P to find the best approximation to some ideal function fcolon A to B. It does this by taking examples (a,f(a)) in Atimes B, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent---with respect to a fixed step size and an error function satisfying a certain property---defines a monoidal functor from a category of parametrised functions to this category of update rules. This provides a structural perspective on backpropagation, as well as a broad generalisation of neural networks.

Retrieval-augmented generation (RAG) enhances large language models (LLMs) by retrieving relevant documents from external sources and incorporating them into the context. While it improves reliability by providing factual texts, it significantly increases inference costs as context length grows and introduces challenging issue of RAG hallucination, primarily caused by the lack of corresponding parametric knowledge in LLMs. An efficient solution is to enhance the knowledge of LLMs at test-time. Parametric RAG (PRAG) addresses this by embedding document into LLMs parameters to perform test-time knowledge enhancement, effectively reducing inference costs through offline training. However, its high training and storage costs, along with limited generalization ability, significantly restrict its practical adoption. To address these challenges, we propose Dynamic Parametric RAG (DyPRAG), a novel framework that leverages a lightweight parameter translator model to efficiently convert documents into parametric knowledge. DyPRAG not only reduces inference, training, and storage costs but also dynamically generates parametric knowledge, seamlessly enhancing the knowledge of LLMs and resolving knowledge conflicts in a plug-and-play manner at test-time. Extensive experiments on multiple datasets demonstrate the effectiveness and generalization capabilities of DyPRAG, offering a powerful and practical RAG paradigm which enables superior knowledge fusion and mitigates RAG hallucination in real-world applications. Our code is available at https://github.com/Trae1ounG/DyPRAG.

Hyperparameter (HP) tuning in deep learning is an expensive process, prohibitively so for neural networks (NNs) with billions of parameters. We show that, in the recently discovered Maximal Update Parametrization (muP), many optimal HPs remain stable even as model size changes. This leads to a new HP tuning paradigm we call muTransfer: parametrize the target model in muP, tune the HP indirectly on a smaller model, and zero-shot transfer them to the full-sized model, i.e., without directly tuning the latter at all. We verify muTransfer on Transformer and ResNet. For example, 1) by transferring pretraining HPs from a model of 13M parameters, we outperform published numbers of BERT-large (350M parameters), with a total tuning cost equivalent to pretraining BERT-large once; 2) by transferring from 40M parameters, we outperform published numbers of the 6.7B GPT-3 model, with tuning cost only 7% of total pretraining cost. A Pytorch implementation of our technique can be found at github.com/microsoft/mup and installable via `pip install mup`.

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training, which can alleviate storage and communication requirements. In this paper, we show that it is possible to induce a fixed sparse mask on the model's parameters that selects a subset to update over many iterations. Our method constructs the mask out of the k parameters with the largest Fisher information as a simple approximation as to which parameters are most important for the task at hand. In experiments on parameter-efficient transfer learning and distributed training, we show that our approach matches or exceeds the performance of other methods for training with sparse updates while being more efficient in terms of memory usage and communication costs. We release our code publicly to promote further applications of our approach.

We present a reality check on large language models and inspect the promise of retrieval augmented language models in comparison. Such language models are semi-parametric, where models integrate model parameters and knowledge from external data sources to make their predictions, as opposed to the parametric nature of vanilla large language models. We give initial experimental findings that semi-parametric architectures can be enhanced with views, a query analyzer/planner, and provenance to make a significantly more powerful system for question answering in terms of accuracy and efficiency, and potentially for other NLP tasks

Existing polygonal surface reconstruction methods heavily depend on input completeness and struggle with incomplete point clouds. We argue that while current point cloud completion techniques may recover missing points, they are not optimized for polygonal surface reconstruction, where the parametric representation of underlying surfaces remains overlooked. To address this gap, we introduce parametric completion, a novel paradigm for point cloud completion, which recovers parametric primitives instead of individual points to convey high-level geometric structures. Our presented approach, PaCo, enables high-quality polygonal surface reconstruction by leveraging plane proxies that encapsulate both plane parameters and inlier points, proving particularly effective in challenging scenarios with highly incomplete data. Comprehensive evaluations of our approach on the ABC dataset establish its effectiveness with superior performance and set a new standard for polygonal surface reconstruction from incomplete data. Project page: https://parametric-completion.github.io.

Asymmetrical distance structures (quasimetrics) are ubiquitous in our lives and are gaining more attention in machine learning applications. Imposing such quasimetric structures in model representations has been shown to improve many tasks, including reinforcement learning (RL) and causal relation learning. In this work, we present four desirable properties in such quasimetric models, and show how prior works fail at them. We propose Interval Quasimetric Embedding (IQE), which is designed to satisfy all four criteria. On three quasimetric learning experiments, IQEs show strong approximation and generalization abilities, leading to better performance and improved efficiency over prior methods. Project Page: https://www.tongzhouwang.info/interval_quasimetric_embedding Quasimetric Learning Code Package: https://www.github.com/quasimetric-learning/torch-quasimetric

Robust and effective scaling of models from small to large width typically requires the precise adjustment of many algorithmic and architectural details, such as parameterization and optimizer choices. In this work, we propose a new perspective on parameterization by investigating a key assumption in prior work about the alignment between parameters and data and derive new theoretical results under weaker assumptions and a broader set of optimizers. Our extensive empirical investigation includes tens of thousands of models trained with all combinations of three optimizers, four parameterizations, several alignment assumptions, more than a dozen learning rates, and fourteen model sizes up to 26.8B parameters. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work. Our results show that all parameterizations, not just maximal update parameterization (muP), can achieve hyperparameter transfer; moreover, our novel per-layer learning rate prescription for standard parameterization outperforms muP. Finally, we demonstrate that an overlooked aspect of parameterization, the epsilon parameter in Adam, must be scaled correctly to avoid gradient underflow and propose Adam-atan2, a new numerically stable, scale-invariant version of Adam that eliminates the epsilon hyperparameter entirely.

We address the computational challenges of solving parametric PDEs with non parametrized geometric variations and non-reducible problems, such as those involving shocks and discontinuities of variable positions. Traditional dimensionality reduction methods like POD struggle with these scenarios due to slowly decaying Kolmogorov widths. To overcome this, we propose a novel non-linear dimensionality reduction technique to reduce the required modes for representation. The non-linear reduction is obtained through a POD after applying a transformation on the fields, which we call optimal mappings, and is a solution to an optimization problem in infinite dimension. The proposed learning framework combines morphing techniques, non-linear dimensionality reduction, and Gaussian Process Regression (GPR). The problem is reformulated on a reference geometry before applying the dimensionality reduction. Our method learns both the optimal mapping, and the solution fields, using a series of GPR models, enabling efficient and accurate modeling of complex parametric PDEs with geometrical variability. The results obtained concur with current state-of-the-art models. We mainly compare our method with the winning solution of the ML4CFD NeurIPS 2024 competition.

Novel architectures have recently improved generative image synthesis leading to excellent visual quality in various tasks. Much of this success is due to the scalability of these architectures and hence caused by a dramatic increase in model complexity and in the computational resources invested in training these models. Our work questions the underlying paradigm of compressing large training data into ever growing parametric representations. We rather present an orthogonal, semi-parametric approach. We complement comparably small diffusion or autoregressive models with a separate image database and a retrieval strategy. During training we retrieve a set of nearest neighbors from this external database for each training instance and condition the generative model on these informative samples. While the retrieval approach is providing the (local) content, the model is focusing on learning the composition of scenes based on this content. As demonstrated by our experiments, simply swapping the database for one with different contents transfers a trained model post-hoc to a novel domain. The evaluation shows competitive performance on tasks which the generative model has not been trained on, such as class-conditional synthesis, zero-shot stylization or text-to-image synthesis without requiring paired text-image data. With negligible memory and computational overhead for the external database and retrieval we can significantly reduce the parameter count of the generative model and still outperform the state-of-the-art.

We formulate the predicted-updates dynamic model, one of the first beyond-worst-case models for dynamic algorithms, which generalizes a large set of well-studied dynamic models including the offline dynamic, incremental, and decremental models to the fully dynamic setting when given predictions about the update times of the elements. In the most basic form of our model, we receive a set of predicted update times for all of the updates that occur over the event horizon. We give a novel framework that "lifts" offline divide-and-conquer algorithms into the fully dynamic setting with little overhead. Using this, we are able to interpolate between the offline and fully dynamic settings; when the ell_1 error of the prediction is linear in the number of updates, we achieve the offline runtime of the algorithm (up to poly log n factors). Provided a fully dynamic backstop algorithm, our algorithm will never do worse than the backstop algorithm regardless of the prediction error. Furthermore, our framework achieves a smooth linear trade-off between ell_1 error in the predictions and runtime. These correspond to the desiderata of consistency, robustness, and graceful degradation of the algorithms-with-predictions literature. We further extend our techniques to incremental and decremental settings, transforming algorithms in these settings when given predictions of only the deletion and insertion times, respectively. Our framework is general, and we apply it to obtain improved efficiency bounds over the state-of-the-art dynamic algorithms for a variety of problems including triconnectivity, planar digraph all pairs shortest paths, k-edge connectivity, and others, for prediction error of reasonable magnitude.

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Deep learning has revolutionized industries like computer vision, natural language processing, and speech recognition. However, back propagation, the main method for training deep neural networks, faces challenges like computational overhead and vanishing gradients. In this paper, we propose a novel instant parameter update methodology that eliminates the need for computing gradients at each layer. Our approach accelerates learning, avoids the vanishing gradient problem, and outperforms state-of-the-art methods on benchmark data sets. This research presents a promising direction for efficient and effective deep neural network training.

We study recent research advances that improve large language models through efficient pre-training and scaling, and open datasets and tools. We combine these advances to introduce Cerebras-GPT, a family of open compute-optimal language models scaled from 111M to 13B parameters. We train Cerebras-GPT models on the Eleuther Pile dataset following DeepMind Chinchilla scaling rules for efficient pre-training (highest accuracy for a given compute budget). We characterize the predictable power-law scaling and compare Cerebras-GPT with other publicly-available models to show all Cerebras-GPT models have state-of-the-art training efficiency on both pre-training and downstream objectives. We describe our learnings including how Maximal Update Parameterization (muP) can further improve large model scaling, improving accuracy and hyperparameter predictability at scale. We release our pre-trained models and code, making this paper the first open and reproducible work comparing compute-optimal model scaling to models trained on fixed dataset sizes. Cerebras-GPT models are available on HuggingFace: https://huggingface.co/cerebras.

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., |Params(M){-}Params(m)|{<}Delta. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed naturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call Stability -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of Stability as defined by our measure will remain valid after potential ``naturally-occurring'' model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes.

Post-training has emerged as a crucial paradigm for adapting large-scale pre-trained models to various tasks, whose effects are fully reflected by delta parameters (i.e., the disparity between post-trained and pre-trained parameters). While numerous studies have explored delta parameter properties via operations like pruning, quantization, low-rank approximation, and extrapolation, a unified framework for systematically examining these characteristics has been lacking. In this paper, we propose a novel perspective based on Riemann sum approximation of the loss function to elucidate delta parameter editing operations. Our analysis categorizes existing methods into three classes based on their post-editing performance: competitive, decreased, and improved, explaining how they are expressed by the Riemann sum approximation term and how they alter the model performance. Extensive experiments on both visual and language models, including ViT, LLaMA 3, Qwen 2, and Mistral, corroborate our theoretical findings. Furthermore, we introduce extensions to existing techniques like DARE and BitDelta, highlighting their limitations in leveraging the properties of delta parameters and reorganizing them into general expressions to enhance the applicability and effectiveness of delta parameter editing in post-trained models.

We consider the problem of global optimization with noisy zeroth order oracles - a well-motivated problem useful for various applications ranging from hyper-parameter tuning for deep learning to new material design. Existing work relies on Gaussian processes or other non-parametric family, which suffers from the curse of dimensionality. In this paper, we propose a new algorithm GO-UCB that leverages a parametric family of functions (e.g., neural networks) instead. Under a realizable assumption and a few other mild geometric conditions, we show that GO-UCB achieves a cumulative regret of O(T) where T is the time horizon. At the core of GO-UCB is a carefully designed uncertainty set over parameters based on gradients that allows optimistic exploration. Synthetic and real-world experiments illustrate GO-UCB works better than Bayesian optimization approaches in high dimensional cases, even if the model is misspecified.

We present an innovative approach for solving mathematical problems in Bengali, developed for the DL Sprint 3.0 BUET CSE Fest 2024 Competition. Our method uses advanced deep learning models, notably the Qwen 2.5 series, with improvements made through prompt engineering, model quantization, and Tool Integrated Reasoning (TIR) to handle complex calculations. Initially, we explored various model architectures, including fine-tuned Mistral and quantized Qwen models, refining them with translation techniques, Retrieval-Augmented Generation (RAG), and custom dataset curation. Manual hyperparameter tuning optimized parameters like temperature and top-p to enhance model adaptability and accuracy. Removal of RAG and parameter adjustments further improved robustness. Our approach highlights the potential of advanced NLP techniques in solving Bengali mathematical problems.

Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with scalability and handling rich inputs, such as images. To address these issues, we introduce a technique that converts neural networks from weight space to function space, through a dual parameterization. Our parameterization offers: (i) a way to scale function-space methods to large data sets via sparsification, (ii) retention of prior knowledge when access to past data is limited, and (iii) a mechanism to incorporate new data without retraining. Our experiments demonstrate that we can retain knowledge in continual learning and incorporate new data efficiently. We further show its strengths in uncertainty quantification and guiding exploration in model-based RL. Further information and code is available on the project website.

This paper introduces a public dataset of 1.4 million procedurally-generated bicycle designs represented parametrically, as JSON files, and as rasterized images. The dataset is created through the use of a rendering engine which harnesses the BikeCAD software to generate vector graphics from parametric designs. This rendering engine is discussed in the paper and also released publicly alongside the dataset. Though this dataset has numerous applications, a principal motivation is the need to train cross-modal predictive models between parametric and image-based design representations. For example, we demonstrate that a predictive model can be trained to accurately estimate Contrastive Language-Image Pretraining (CLIP) embeddings from a parametric representation directly. This allows similarity relations to be established between parametric bicycle designs and text strings or reference images. Trained predictive models are also made public. The dataset joins the BIKED dataset family which includes thousands of mixed-representation human-designed bicycle models and several datasets quantifying design performance. The code and dataset can be found at: https://github.com/Lyleregenwetter/BIKED_multimodal/tree/main

Recent advancements in implicit 3D representations and generative models have markedly propelled the field of 3D object generation forward. However, it remains a significant challenge to accurately model geometries with defined sharp features under parametric controls, which is crucial in fields like industrial design and manufacturing. To bridge this gap, we introduce a framework that employs Large Language Models (LLMs) to generate text-driven 3D shapes, manipulating 3D software via program synthesis. We present 3D-PreMise, a dataset specifically tailored for 3D parametric modeling of industrial shapes, designed to explore state-of-the-art LLMs within our proposed pipeline. Our work reveals effective generation strategies and delves into the self-correction capabilities of LLMs using a visual interface. Our work highlights both the potential and limitations of LLMs in 3D parametric modeling for industrial applications.

In many neural networks, different values of the parameters may result in the same loss value. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm's success is not well understood. In this paper, we show that teleportation not only speeds up optimization in the short-term, but gives overall faster time to convergence. Additionally, teleporting to minima with different curvatures improves generalization, which suggests a connection between the curvature of the minimum and generalization ability. Finally, we show that integrating teleportation into a wide range of optimization algorithms and optimization-based meta-learning improves convergence. Our results showcase the versatility of teleportation and demonstrate the potential of incorporating symmetry in optimization.

Training and scaling Large Language Models demand enormous computational resources, motivating both efficient sub-quadratic architectures and principled hyperparameter tuning methods. While the Maximal Update Parametrization (μP) has enabled zero-shot hyperparameter transfer for standard Transformers, its extension to linear models, particularly those with structured state transitions and complicated architectures, remains largely unexplored. By rigorously propagating coordinate-size estimates through the forward pass, gating mechanisms, and recurrent state dynamics, we derive the scaling rules for Gated Delta Network. Experiments on language-model pre-training confirm that our configurations enable stable learning-rate transfer across model widths under both AdamW and SGD, whereas standard parametrization fails to transfer, validating the correctness and practical utility of our analysis.

On-policy distillation (OPD) is increasingly used to improve large language model reasoning, but its training dynamics remain poorly understood. We characterize the trajectory of OPD updates in parameter space and compare it with supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR). A suite of parameter-space diagnostics consistently places OPD in a relaxed off-principal regime: compared with SFT, its updates affect fewer weights and avoid principal directions more strongly, while compared with RLVR, they remain less tightly constrained. Beyond this static localization, OPD exhibits subspace locking: its cumulative updates rapidly enter a narrow low-dimensional channel. Constraining training to the update subspace formed early in training preserves OPD performance but substantially degrades SFT, indicating that the locked subspace is functionally sufficient for OPD. Control experiments further show that sparsifying the update tokens and shifting rollout generation off-policy preserve the rank dynamics, whereas mixing the OPD objective with RLVR changes them. Overall, these results suggest that OPD is not merely an intermediate point between SFT and RLVR, but induces its own update geometry in parameter space.

Large language models deliver strong reasoning and tool-use skills, yet their computational demands make them impractical for edge or cost-sensitive deployments. We present Xmodel-2.5, a 1.3-billion-parameter small language model designed as a drop-in agent core. Training with maximal-update parameterization (μP) allows hyper-parameters tuned on a 20M-parameter proxy to transfer directly to the full model, even under the parameter-tied tie-word-embedding architecture. A 1.4T-token Warmup--Stable--Decay curriculum is used, and we further show that switching from AdamW to Muon during the decay phase improves the 13-task reasoning average by 4.58\,\% while keeping every other hyper-parameter fixed, verifying that early AdamW stability can be paired with late Muon sharpening for better downstream performance. FP8-mixed-precision training balances accuracy and throughput. All checkpoints, recipes, and evaluation code are released under the Apache-2.0 license.https://huggingface.co/XiaoduoAILab/Xmodel-2.5 and https://huggingface.co/XiaoduoAILab/Xmodel-2.5-history (training checkpoints). Training code and evaluation harness: https://github.com/XiaoduoAILab/Xmodel-2.5.

Parametric language models (LMs), which are trained on vast amounts of web data, exhibit remarkable flexibility and capability. However, they still face practical challenges such as hallucinations, difficulty in adapting to new data distributions, and a lack of verifiability. In this position paper, we advocate for retrieval-augmented LMs to replace parametric LMs as the next generation of LMs. By incorporating large-scale datastores during inference, retrieval-augmented LMs can be more reliable, adaptable, and attributable. Despite their potential, retrieval-augmented LMs have yet to be widely adopted due to several obstacles: specifically, current retrieval-augmented LMs struggle to leverage helpful text beyond knowledge-intensive tasks such as question answering, have limited interaction between retrieval and LM components, and lack the infrastructure for scaling. To address these, we propose a roadmap for developing general-purpose retrieval-augmented LMs. This involves a reconsideration of datastores and retrievers, the exploration of pipelines with improved retriever-LM interaction, and significant investment in infrastructure for efficient training and inference.

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets and language models.

The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural implicit surfaces to simple parametric domains like spheres and polycubes. Our method allows users to specify the number of cubes in the parametric domain, learning a configuration that closely resembles the target 3D object's geometry. It computes bi-directional deformation between the object and the domain using a forward mapping from the object's zero level set and an inverse deformation for backward mapping. We ensure nearly bijective mapping with a cycle loss and optimize deformation smoothness. The parameterization quality, assessed by angle and area distortions, is guaranteed using a Laplacian regularizer and an optimized learned parametric domain. Our framework integrates with existing neural rendering pipelines, using multi-view images of a single object or multiple objects of similar geometries to reconstruct 3D geometry and compute texture maps automatically, eliminating the need for any prior information. We demonstrate the method's effectiveness on images of human heads and man-made objects.

Learned optimizers (LOs) can significantly reduce the wall-clock training time of neural networks, substantially reducing training costs. However, they often suffer from poor meta-generalization, especially when training networks larger than those seen during meta-training. To address this, we use the recently proposed Maximal Update Parametrization (muP), which allows zero-shot generalization of optimizer hyperparameters from smaller to larger models. We extend muP theory to learned optimizers, treating the meta-training problem as finding the learned optimizer under muP. Our evaluation shows that LOs meta-trained with muP substantially improve meta-generalization as compared to LOs trained under standard parametrization (SP). Notably, when applied to large-width models, our best muLO, trained for 103 GPU-hours, matches or exceeds the performance of VeLO, the largest publicly available learned optimizer, meta-trained with 4000 TPU-months of compute. Moreover, muLOs demonstrate better generalization than their SP counterparts to deeper networks and to much longer training horizons (25 times longer) than those seen during meta-training.

Hyperparameter optimization (HPO) is concerned with the automated search for the most appropriate hyperparameter configuration (HPC) of a parameterized machine learning algorithm. A state-of-the-art HPO method is Hyperband, which, however, has its own parameters that influence its performance. One of these parameters, the maximal budget, is especially problematic: If chosen too small, the budget needs to be increased in hindsight and, as Hyperband is not incremental by design, the entire algorithm must be re-run. This is not only costly but also comes with a loss of valuable knowledge already accumulated. In this paper, we propose incremental variants of Hyperband that eliminate these drawbacks, and show that these variants satisfy theoretical guarantees qualitatively similar to those for the original Hyperband with the "right" budget. Moreover, we demonstrate their practical utility in experiments with benchmark data sets.

The analysis of non-stationary time-series data requires insight into its local and global patterns with physical interpretability. However, traditional smoothing algorithms, such as B-splines, Savitzky-Golay filtering, and Empirical Mode Decomposition (EMD), lack the ability to perform parametric optimization with guaranteed continuity. In this paper, we propose Functional Continuous Decomposition (FCD), a JAX-accelerated framework that performs parametric, continuous optimization on a wide range of mathematical functions. By using Levenberg-Marquardt optimization to achieve up to C^1 continuous fitting, FCD transforms raw time-series data into M modes that capture different temporal patterns from short-term to long-term trends. Applications of FCD include physics, medicine, financial analysis, and machine learning, where it is commonly used for the analysis of signal temporal patterns, optimized parameters, derivatives, and integrals of decomposition. Furthermore, FCD can be applied for physical analysis and feature extraction with an average SRMSE of 0.735 per segment and a speed of 0.47s on full decomposition of 1,000 points. Finally, we demonstrate that a Convolutional Neural Network (CNN) enhanced with FCD features, such as optimized function values, parameters, and derivatives, achieved 16.8% faster convergence and 2.5% higher accuracy over a standard CNN.

Parametric computer-aided design (CAD) tools are the predominant way that engineers specify physical structures, from bicycle pedals to airplanes to printed circuit boards. The key characteristic of parametric CAD is that design intent is encoded not only via geometric primitives, but also by parameterized constraints between the elements. This relational specification can be viewed as the construction of a constraint program, allowing edits to coherently propagate to other parts of the design. Machine learning offers the intriguing possibility of accelerating the design process via generative modeling of these structures, enabling new tools such as autocompletion, constraint inference, and conditional synthesis. In this work, we present such an approach to generative modeling of parametric CAD sketches, which constitute the basic computational building blocks of modern mechanical design. Our model, trained on real-world designs from the SketchGraphs dataset, autoregressively synthesizes sketches as sequences of primitives, with initial coordinates, and constraints that reference back to the sampled primitives. As samples from the model match the constraint graph representation used in standard CAD software, they may be directly imported, solved, and edited according to downstream design tasks. In addition, we condition the model on various contexts, including partial sketches (primers) and images of hand-drawn sketches. Evaluation of the proposed approach demonstrates its ability to synthesize realistic CAD sketches and its potential to aid the mechanical design workflow.

Self-reflection enables language agents to iteratively refine solutions, yet often produces repetitive outputs that limit reasoning performance. Recent studies have attempted to address this limitation through various approaches, among which increasing reflective diversity has shown promise. Our empirical analysis reveals a strong positive correlation between reflective diversity and task success, further motivating the need for diverse reflection signals. We introduce ParamMem, a parametric memory module that encodes cross-sample reflection patterns into model parameters, enabling diverse reflection generation through temperature-controlled sampling. Building on this module, we propose ParamAgent, a reflection-based agent framework that integrates parametric memory with episodic and cross-sample memory. Extensive experiments on code generation, mathematical reasoning, and multi-hop question answering demonstrate consistent improvements over state-of-the-art baselines. Further analysis reveals that ParamMem is sample-efficient, enables weak-to-strong transfer across model scales, and supports self-improvement without reliance on stronger external model, highlighting the potential of ParamMem as an effective component for enhancing language agents.

Integrating Large Language Models (LLMs) with Knowledge Graphs (KGs) results in complex systems with numerous hyperparameters that directly affect performance. While such systems are increasingly common in retrieval-augmented generation, the role of systematic hyperparameter optimization remains underexplored. In this paper, we study this problem in the context of Cognee, a modular framework for end-to-end KG construction and retrieval. Using three multi-hop QA benchmarks (HotPotQA, TwoWikiMultiHop, and MuSiQue) we optimize parameters related to chunking, graph construction, retrieval, and prompting. Each configuration is scored using established metrics (exact match, F1, and DeepEval's LLM-based correctness metric). Our results demonstrate that meaningful gains can be achieved through targeted tuning. While the gains are consistent, they are not uniform, with performance varying across datasets and metrics. This variability highlights both the value of tuning and the limitations of standard evaluation measures. While demonstrating the immediate potential of hyperparameter tuning, we argue that future progress will depend not only on architectural advances but also on clearer frameworks for optimization and evaluation in complex, modular systems.

When considering a model architecture, there are several ways to reduce its memory footprint. Historically, popular approaches included selecting smaller architectures and creating sparse networks through pruning. More recently, randomized parameter-sharing (RPS) methods have gained traction for model compression at start of training. In this paper, we comprehensively assess the trade-off between memory and accuracy across RPS, pruning techniques, and building smaller models. Our findings demonstrate that RPS, which is both data and model-agnostic, consistently outperforms/matches smaller models and all moderately informed pruning strategies, such as MAG, SNIP, SYNFLOW, and GRASP, across the entire compression range. This advantage becomes particularly pronounced in higher compression scenarios. Notably, even when compared to highly informed pruning techniques like Lottery Ticket Rewinding (LTR), RPS exhibits superior performance in high compression settings. This points out inherent capacity advantage that RPS enjoys over sparse models. Theoretically, we establish RPS as a superior technique in terms of memory-efficient representation when compared to pruning for linear models. This paper argues in favor of paradigm shift towards RPS based models. During our rigorous evaluation of RPS, we identified issues in the state-of-the-art RPS technique ROAST, specifically regarding stability (ROAST's sensitivity to initialization hyperparameters, often leading to divergence) and Pareto-continuity (ROAST's inability to recover the accuracy of the original model at zero compression). We provably address both of these issues. We refer to the modified RPS, which incorporates our improvements, as STABLE-RPS.

Revision is a crucial step in scientific writing, where authors refine their work to improve clarity, structure, and academic quality. Existing approaches to automated writing assistance often focus on sentence-level revisions, which fail to capture the broader context needed for effective modification. In this paper, we explore the impact of shifting from sentence-level to paragraph-level scope for the task of scientific text revision. The paragraph level definition of the task allows for more meaningful changes, and is guided by detailed revision instructions rather than general ones. To support this task, we introduce ParaRev, the first dataset of revised scientific paragraphs with an evaluation subset manually annotated with revision instructions. Our experiments demonstrate that using detailed instructions significantly improves the quality of automated revisions compared to general approaches, no matter the model or the metric considered.

Diffusion Transformers have emerged as the foundation for vision generative models, but their scalability is limited by the high cost of hyperparameter (HP) tuning at large scales. Recently, Maximal Update Parametrization (muP) was proposed for vanilla Transformers, which enables stable HP transfer from small to large language models, and dramatically reduces tuning costs. However, it remains unclear whether muP of vanilla Transformers extends to diffusion Transformers, which differ architecturally and objectively. In this work, we generalize standard muP to diffusion Transformers and validate its effectiveness through large-scale experiments. First, we rigorously prove that muP of mainstream diffusion Transformers, including DiT, U-ViT, PixArt-alpha, and MMDiT, aligns with that of the vanilla Transformer, enabling the direct application of existing muP methodologies. Leveraging this result, we systematically demonstrate that DiT-muP enjoys robust HP transferability. Notably, DiT-XL-2-muP with transferred learning rate achieves 2.9 times faster convergence than the original DiT-XL-2. Finally, we validate the effectiveness of muP on text-to-image generation by scaling PixArt-alpha from 0.04B to 0.61B and MMDiT from 0.18B to 18B. In both cases, models under muP outperform their respective baselines while requiring small tuning cost, only 5.5% of one training run for PixArt-alpha and 3% of consumption by human experts for MMDiT-18B. These results establish muP as a principled and efficient framework for scaling diffusion Transformers.

Recently, Large Language Models (LLMs) have achieved significant success, prompting increased interest in expanding their generative capabilities beyond general text into domain-specific areas. This study investigates the generation of parametric sequences for computer-aided design (CAD) models using LLMs. This endeavor represents an initial step towards creating parametric 3D shapes with LLMs, as CAD model parameters directly correlate with shapes in three-dimensional space. Despite the formidable generative capacities of LLMs, this task remains challenging, as these models neither encounter parametric sequences during their pretraining phase nor possess direct awareness of 3D structures. To address this, we present CAD-Llama, a framework designed to enhance pretrained LLMs for generating parametric 3D CAD models. Specifically, we develop a hierarchical annotation pipeline and a code-like format to translate parametric 3D CAD command sequences into Structured Parametric CAD Code (SPCC), incorporating hierarchical semantic descriptions. Furthermore, we propose an adaptive pretraining approach utilizing SPCC, followed by an instruction tuning process aligned with CAD-specific guidelines. This methodology aims to equip LLMs with the spatial knowledge inherent in parametric sequences. Experimental results demonstrate that our framework significantly outperforms prior autoregressive methods and existing LLM baselines.

Solving time-dependent parametric partial differential equations (PDEs) is challenging, as models must adapt to variations in parameters such as coefficients, forcing terms, and boundary conditions. Data-driven neural solvers either train on data sampled from the PDE parameters distribution in the hope that the model generalizes to new instances or rely on gradient-based adaptation and meta-learning to implicitly encode the dynamics from observations. This often comes with increased inference complexity. Inspired by the in-context learning capabilities of large language models (LLMs), we introduce Zebra, a novel generative auto-regressive transformer designed to solve parametric PDEs without requiring gradient adaptation at inference. By leveraging in-context information during both pre-training and inference, Zebra dynamically adapts to new tasks by conditioning on input sequences that incorporate context trajectories or preceding states. This approach enables Zebra to flexibly handle arbitrarily sized context inputs and supports uncertainty quantification through the sampling of multiple solution trajectories. We evaluate Zebra across a variety of challenging PDE scenarios, demonstrating its adaptability, robustness, and superior performance compared to existing approaches.

Updating a truncated Singular Value Decomposition (SVD) is crucial in representation learning, especially when dealing with large-scale data matrices that continuously evolve in practical scenarios. Aligning SVD-based models with fast-paced updates becomes increasingly important. Existing methods for updating truncated SVDs employ Rayleigh-Ritz projection procedures, where projection matrices are augmented based on original singular vectors. However, these methods suffer from inefficiency due to the densification of the update matrix and the application of the projection to all singular vectors. To address these limitations, we introduce a novel method for dynamically approximating the truncated SVD of a sparse and temporally evolving matrix. Our approach leverages sparsity in the orthogonalization process of augmented matrices and utilizes an extended decomposition to independently store projections in the column space of singular vectors. Numerical experiments demonstrate a remarkable efficiency improvement of an order of magnitude compared to previous methods. Remarkably, this improvement is achieved while maintaining a comparable precision to existing approaches.

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning probability measures to the spatial domain, which allows us to treat collocation grids probabilistically as random variables to be marginalised out. Adapting this spatial statistics view, we solve forward and inverse problems for parametric PDEs in a way that leads to the construction of Gaussian process models of solution fields. The implementation of these random grids poses a unique set of challenges for inverse physics informed deep learning frameworks and we propose a new architecture called Grid Invariant Convolutional Networks (GICNets) to overcome these challenges. We further show how to incorporate noisy data in a principled manner into our physics informed model to improve predictions for problems where data may be available but whose measurement location does not coincide with any fixed mesh or grid. The proposed method is tested on a nonlinear Poisson problem, Burgers equation, and Navier-Stokes equations, and we provide extensive numerical comparisons. We demonstrate significant computational advantages over current physics informed neural learning methods for parametric PDEs while improving the predictive capabilities and flexibility of these models.

We propose an algorithm for inexpensive gradient-based hyperparameter optimization that combines the implicit function theorem (IFT) with efficient inverse Hessian approximations. We present results about the relationship between the IFT and differentiating through optimization, motivating our algorithm. We use the proposed approach to train modern network architectures with millions of weights and millions of hyper-parameters. For example, we learn a data-augmentation network - where every weight is a hyperparameter tuned for validation performance - outputting augmented training examples. Jointly tuning weights and hyperparameters with our approach is only a few times more costly in memory and compute than standard training.

Recent advances in reasoning capabilities of large language models (LLMs) are largely driven by reinforcement learning (RL), yet the underlying parameter dynamics during RL training remain poorly understood. This work identifies two fundamental properties of RL-induced parameter updates in LLMs: (1) Rank-1 Dominance, where the top singular subspace of the parameter update matrix nearly fully determines reasoning improvements, recovering over 99\% of performance gains; and (2) Rank-1 Linear Dynamics, where this dominant subspace evolves linearly throughout training, enabling accurate prediction from early checkpoints. Extensive experiments across 8 LLMs and 7 algorithms validate the generalizability of these properties. More importantly, based on these findings, we propose AlphaRL, a plug-in acceleration framework that extrapolates the final parameter update using a short early training window, achieving up to 2.5 speedup while retaining \textgreater 96\% of reasoning performance without extra modules or hyperparameter tuning. This positions our finding as a versatile and practical tool for large-scale RL, opening a path toward principled, interpretable, and efficient training paradigm for LLMs.

The factuality of large language model (LLMs) tends to decay over time since events posterior to their training are "unknown" to them. One way to keep models up-to-date could be factual update: the task of inserting, replacing, or removing certain simple (atomic) facts within the model. To study this task, we present WikiFactDiff, a dataset that describes the evolution of factual knowledge between two dates as a collection of simple facts divided into three categories: new, obsolete, and static. We describe several update scenarios arising from various combinations of these three types of basic update. The facts are represented by subject-relation-object triples; indeed, WikiFactDiff was constructed by comparing the state of the Wikidata knowledge base at 4 January 2021 and 27 February 2023. Those fact are accompanied by verbalization templates and cloze tests that enable running update algorithms and their evaluation metrics. Contrary to other datasets, such as zsRE and CounterFact, WikiFactDiff constitutes a realistic update setting that involves various update scenarios, including replacements, archival, and new entity insertions. We also present an evaluation of existing update algorithms on WikiFactDiff.

Large Language Models (LLMs) are frequently updated due to data or architecture changes to improve their performance. When updating models, developers often focus on increasing overall performance metrics with less emphasis on being compatible with previous model versions. However, users often build a mental model of the functionality and capabilities of a particular machine learning model they are interacting with. They have to adapt their mental model with every update -- a draining task that can lead to user dissatisfaction. In practice, fine-tuned downstream task adapters rely on pretrained LLM base models. When these base models are updated, these user-facing downstream task models experience instance regression or negative flips -- previously correct instances are now predicted incorrectly. This happens even when the downstream task training procedures remain identical. Our work aims to provide seamless model updates to a user in two ways. First, we provide evaluation metrics for a notion of compatibility to prior model versions, specifically for generative tasks but also applicable for discriminative tasks. We observe regression and inconsistencies between different model versions on a diverse set of tasks and model updates. Second, we propose a training strategy to minimize the number of inconsistencies in model updates, involving training of a compatibility model that can enhance task fine-tuned language models. We reduce negative flips -- instances where a prior model version was correct, but a new model incorrect -- by up to 40% from Llama 1 to Llama 2.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

Recent work has shown that orthonormal matrix updates speed up neural network optimization, improve training stability, and offer better hyperparameter transfer across model sizes. Applying these updates efficiently when model weights and optimizer states are sharded across a large-scale distributed LLM training system remains a major challenge. We introduce Dion (DIstributed OrthoNormalization), a scalable and communication-efficient orthonormalizing optimizer. Dion leverages low-rank approximation and decoupled momentum buffers, eliminating the need for full gradient synchronization while producing numerically equivalent results. It is compatible with simultaneous DDP, FSDP, and TP parallelism, and it computes an orthonormalized update without unsharding a full parameter matrix on any single device. We evaluate Dion on language models from 120M to 3B parameters and find that its benefits improve with increasing model size and batch size.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

Targeted data selection has emerged as a crucial paradigm for efficient instruction tuning, aiming to identify a small yet influential subset of training examples for a specific target task. In practice, influence is often measured through the effect of an example on parameter updates. To make selection scalable, many approaches leverage optimizer statistics (e.g., Adam states) as an axis-aligned surrogate for update geometry (i.e., diagonal precondition), implicitly treating parameters as coordinate-wise independent. We show that this assumption breaks down in parameter-efficient fine-tuning (PEFT) methods such as LoRA. In this setting, the induced optimization geometry exhibits strong cross-parameter coupling with non-trivial off-diagonal interactions, while the task-relevant update directions are confined to a low-dimensional subspace. Motivated by this mismatch, we propose GIST (Gradient Isometric Subspace Transformation), a simple yet principled alternative that replaces axis-aligned scaling with robust subspace alignment. GIST recovers a task-specific subspace from validation gradients via spectral filtering (SVD), projects training gradients into this coupled subspace, and scores examples by their alignment with target directions.Extensive experiments have demonstrated that GIST matches or outperforms the state-of-the-art baseline with only 0.29% of the storage and 25% of the computational time under the same selection budget.

Large pre-trained models decay over long-term deployment as input distributions shift, user requirements change, or crucial knowledge gaps are discovered. Recently, model editors have been proposed to modify a model's behavior by adjusting its weights during deployment. However, when editing the same model multiple times, these approaches quickly decay a model's performance on upstream data and forget how to fix previous errors. We propose and study a novel Lifelong Model Editing setting, where streaming errors are identified for a deployed model and we update the model to correct its predictions without influencing unrelated inputs without access to training edits, exogenous datasets, or any upstream data for the edited model. To approach this problem, we introduce General Retrieval Adaptors for Continual Editing, or GRACE, which learns to cache a chosen layer's activations in an adaptive codebook as edits stream in, leaving original model weights frozen. GRACE can thus edit models thousands of times in a row using only streaming errors, without influencing unrelated inputs. Experimentally, we show that GRACE improves over recent alternatives and generalizes to unseen inputs. Our code is available at https://www.github.com/thartvigsen/grace.

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and space. Central to our approach is a combination of continuous-time neural networks with two novel neural architectures, i.e., Jump and Attentive Continuous-time Normalizing Flows. This approach allows us to learn complex distributions for both the spatial and temporal domain and to condition non-trivially on the observed event history. We validate our models on data sets from a wide variety of contexts such as seismology, epidemiology, urban mobility, and neuroscience.

While current large language models (LLMs) demonstrate some capabilities in knowledge-intensive tasks, they are limited by relying on their parameters as an implicit storage mechanism. As a result, they struggle with infrequent knowledge and temporal degradation. In addition, the uninterpretable nature of parametric memorization makes it challenging to understand and prevent hallucination. Parametric memory pools and model editing are only partial solutions. Retrieval Augmented Generation (RAG) x2013 though non-parametric x2013 has its own limitations: it lacks structure, complicates interpretability and makes it hard to effectively manage stored knowledge. In this paper, we introduce MemLLM, a novel method of enhancing LLMs by integrating a structured and explicit read-and-write memory module. MemLLM tackles the aforementioned challenges by enabling dynamic interaction with the memory and improving the LLM's capabilities in using stored knowledge. Our experiments indicate that MemLLM enhances the LLM's performance and interpretability, in language modeling in general and knowledge-intensive tasks in particular. We see MemLLM as an important step towards making LLMs more grounded and factual through memory augmentation.

Scaling large models requires optimization strategies that ensure rapid convergence grounded in stability. Maximal Update Parametrization (boldsymbolμP) provides a theoretical safeguard for width-invariant Θ(1) activation control, whereas emerging optimizers like Muon are only ``half-aligned'' with these constraints: they control updates but allow weights to drift. To address this limitation, we introduce the Spectral Sphere Optimizer (SSO), which enforces strict module-wise spectral constraints on both weights and their updates. By deriving the steepest descent direction on the spectral sphere, SSO realizes a fully boldsymbolμP-aligned optimization process. To enable large-scale training, we implement SSO as an efficient parallel algorithm within Megatron. Through extensive pretraining on diverse architectures, including Dense 1.7B, MoE 8B-A1B, and 200-layer DeepNet models, SSO consistently outperforms AdamW and Muon. Furthermore, we observe significant practical stability benefits, including improved MoE router load balancing, suppressed outliers, and strictly bounded activations.

Generative foundation models are increasingly scaled in both width and depth, posing significant challenges for stable feature learning and reliable hyperparameter (HP) transfer across model sizes. While maximal update parameterization (μP) has provided a principled solution to both problems for width scaling, existing extensions to the joint width-depth scaling regime remain fragmented, architecture- and optimizer-specific, and often rely on technically involved theories. In this work, we develop a simple and unified spectral framework for μP under joint width-depth scaling. Considering residual networks of varying block depths, we first introduce a spectral μP condition that precisely characterizes how the norms of weights and their per-step updates should scale with width and depth, unifying previously disparate μP formulations as special cases. Building on this condition, we then derive a general recipe for implementing μP across a broad class of optimizers by mapping the spectral constraints to concrete HP parameterizations. This approach not only recovers existing μP formulations (e.g., for SGD and AdamW) but also naturally extends to a wider range of optimizers. Finally, experiments on GPT-2 style language models demonstrate that the proposed spectral μP condition preserves stable feature learning and enables robust HP transfer under width-depth scaling.

As the open-weight AI landscape continues to proliferate-with model development, significant investment, and user interest-it becomes increasingly important to predict which models will ultimately drive innovation and shape AI ecosystems. Building on parallels with citation dynamics in scientific literature, we propose a framework to quantify how an open-weight model's influence evolves. Specifically, we adapt the model introduced by Wang et al. for scientific citations, using three key parameters-immediacy, longevity, and relative fitness-to track the cumulative number of fine-tuned models of an open-weight model. Our findings reveal that this citation-style approach can effectively capture the diverse trajectories of open-weight model adoption, with most models fitting well and outliers indicating unique patterns or abrupt jumps in usage.

Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. In this work, we (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. We show that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. Our theoretical results provide new insight in understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, we provide an algorithm to compute the metric by leveraging Sinkhorn divergences and validate our findings through a simulation study.

Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. In this paper, we derive the basic mathematical conditions that successful update rules commonly satisfy. Consequently, we propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems. Numerical simulations validate our theoretical findings and demonstrate the superior empirical performance of the proposed L2O model.

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable training. These challenges arise particularly from the ill-conditioning of the optimization problem caused by the differential terms in the loss function. To address these issues, we propose learning a solver, i.e., solving PDEs using a physics-informed iterative algorithm trained on data. Our method learns to condition a gradient descent algorithm that automatically adapts to each PDE instance, significantly accelerating and stabilizing the optimization process and enabling faster convergence of physics-aware models. Furthermore, while traditional physics-informed methods solve for a single PDE instance, our approach extends to parametric PDEs. Specifically, we integrate the physical loss gradient with PDE parameters, allowing our method to solve over a distribution of PDE parameters, including coefficients, initial conditions, and boundary conditions. We demonstrate the effectiveness of our approach through empirical experiments on multiple datasets, comparing both training and test-time optimization performance. The code is available at https://github.com/2ailesB/neural-parametric-solver.

Prototyping complex computer-aided design (CAD) models in modern softwares can be very time-consuming. This is due to the lack of intelligent systems that can quickly generate simpler intermediate parts. We propose Text2CAD, the first AI framework for generating text-to-parametric CAD models using designer-friendly instructions for all skill levels. Furthermore, we introduce a data annotation pipeline for generating text prompts based on natural language instructions for the DeepCAD dataset using Mistral and LLaVA-NeXT. The dataset contains sim170K models and sim660K text annotations, from abstract CAD descriptions (e.g., generate two concentric cylinders) to detailed specifications (e.g., draw two circles with center (x,y) and radius r_{1}, r_{2}, and extrude along the normal by d...). Within the Text2CAD framework, we propose an end-to-end transformer-based auto-regressive network to generate parametric CAD models from input texts. We evaluate the performance of our model through a mixture of metrics, including visual quality, parametric precision, and geometrical accuracy. Our proposed framework shows great potential in AI-aided design applications. Our source code and annotations will be publicly available.

The ubiquity of large-scale Pre-Trained Models (PTMs) is on the rise, sparking interest in model hubs, and dedicated platforms for hosting PTMs. Despite this trend, a comprehensive exploration of the challenges that users encounter and how the community leverages PTMs remains lacking. To address this gap, we conducted an extensive mixed-methods empirical study by focusing on discussion forums and the model hub of HuggingFace, the largest public model hub. Based on our qualitative analysis, we present a taxonomy of the challenges and benefits associated with PTM reuse within this community. We then conduct a quantitative study to track model-type trends and model documentation evolution over time. Our findings highlight prevalent challenges such as limited guidance for beginner users, struggles with model output comprehensibility in training or inference, and a lack of model understanding. We also identified interesting trends among models where some models maintain high upload rates despite a decline in topics related to them. Additionally, we found that despite the introduction of model documentation tools, its quantity has not increased over time, leading to difficulties in model comprehension and selection among users. Our study sheds light on new challenges in reusing PTMs that were not reported before and we provide recommendations for various stakeholders involved in PTM reuse.

Exponential growth in the scale of modern foundation models has led to the widespread adoption of Low-Rank Adaptation (LoRA) as a parameter-efficient fine-tuning technique. However, standard LoRA implementations disregard the varying intrinsic dimensionality of model layers and enforce a uniform rank, leading to parameter redundancy. We propose Post-Optimization Adaptive Rank Allocation (PARA), a data-free compression method for LoRA that integrates seamlessly into existing fine-tuning pipelines. PARA leverages Singular Value Decomposition to prune LoRA ranks using a global threshold over singular values across all layers. This results in non-uniform rank allocation based on layer-wise spectral importance. As a post-hoc method, PARA circumvents the training modifications and resulting instabilities that dynamic architectures typically incur. We empirically demonstrate that PARA reduces parameter count by 75-90\% while preserving the predictive performance of the original, uncompressed LoRA across multiple vision and language benchmarks. Code will be published upon acceptance.

In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines, in this work, are made to be bounded by introducing a parametric nonlinear term that is positive. The straight lines are transformed into bounded nonlinear curves that become unbounded at a much slower rate than the independent variable. This transforming equation can be expressed as a continued fraction of straight lines. The continued fraction is real-valued and converges to the solutions of the transforming equation. Following Euler's method, the continued fraction has been reduced into an infinite series. The usefulness of the bounding nature of continued fraction is demonstrated by solving the problem of image classification. Parameters estimated on the Fashion-MNIST dataset of greyscale images using continued fraction of regression lines have less variance, converge quickly and are more accurate than the linear counterpart. Moreover, this multi-dimensional parametric estimation problem can be expressed on xy- plane using the parameters of the continued fraction and patterns emerge on planar plots.

Hypernetworks, neural networks that predict the parameters of another neural network, are powerful models that have been successfully used in diverse applications from image generation to multi-task learning. Unfortunately, existing hypernetworks are often challenging to train. Training typically converges far more slowly than for non-hypernetwork models, and the rate of convergence can be very sensitive to hyperparameter choices. In this work, we identify a fundamental and previously unidentified problem that contributes to the challenge of training hypernetworks: a magnitude proportionality between the inputs and outputs of the hypernetwork. We demonstrate both analytically and empirically that this can lead to unstable optimization, thereby slowing down convergence, and sometimes even preventing any learning. We present a simple solution to this problem using a revised hypernetwork formulation that we call Magnitude Invariant Parametrizations (MIP). We demonstrate the proposed solution on several hypernetwork tasks, where it consistently stabilizes training and achieves faster convergence. Furthermore, we perform a comprehensive ablation study including choices of activation function, normalization strategies, input dimensionality, and hypernetwork architecture; and find that MIP improves training in all scenarios. We provide easy-to-use code that can turn existing networks into MIP-based hypernetworks.

We present AlphaApollo, a self-evolving agentic reasoning system that aims to address two bottlenecks in foundation model (FM) reasoning-limited model-intrinsic capacity and unreliable test-time iteration. AlphaApollo orchestrates multiple models with professional tools to enable deliberate, verifiable reasoning. It couples (i) a computation tool (Python with numerical and symbolic libraries) and (ii) a retrieval tool (task-relevant external information) to execute exact calculations and ground decisions. The system further supports multi-round, multi-model solution evolution via a shared state map that records candidates, executable checks, and feedback for iterative refinement. In evaluations on AIME 2024/2025 across multiple models, AlphaApollo delivers consistent gains: +5.15% Average@32 and +23.34% Pass@32 for Qwen2.5-14B-Instruct, and +8.91% Average@32 with +26.67% Pass@32 for Llama-3.3-70B-Instruct. Tool-use analysis shows that more than 80% of tool calls are successfully executed, with consistent outperformance of non-tool baselines, thereby lifting the capability ceiling of FMs. More empirical results and implementation details will be updated at https://github.com/tmlr-group/AlphaApollo.

Our goal is to assess if AutoML system changes - i.e., to the search space or hyperparameter optimization - will improve the final model's performance on production tasks. However, we cannot test the changes on production tasks. Instead, we only have access to limited descriptors about tasks that our AutoML system previously executed, like the number of data points or features. We also have a set of development tasks to test changes, ex., sampled from OpenML with no usage constraints. However, the development and production task distributions are different leading us to pursue changes that only improve development and not production. This paper proposes a method to leverage descriptor information about AutoML production tasks to select a filtered subset of the most relevant development tasks. Empirical studies show that our filtering strategy improves the ability to assess AutoML system changes on holdout tasks with different distributions than development.

Despite significant progress in model editing methods, their application in real-world scenarios remains challenging as they often cause large language models (LLMs) to collapse. Among them, ROME is particularly concerning, as it could disrupt LLMs with only a single edit. In this paper, we study the root causes of such collapse. Through extensive analysis, we identify two primary factors that contribute to the collapse: i) inconsistent handling of prefixed and unprefixed keys in the parameter update equation may result in very small denominators, causing excessively large parameter updates; ii) the subject of collapse cases is usually the first token, whose unprefixed key distribution significantly differs from the prefixed key distribution in autoregressive transformers, causing the aforementioned issue to materialize. To validate our findings, we propose a simple yet effective approach: uniformly using prefixed keys during editing phase and adding prefixes during testing phase to ensure the consistency between training and testing. The experimental results show that the proposed solution can prevent model collapse while maintaining the effectiveness of the edits.

Numerical simulations in climate, chemistry, or astrophysics are computationally too expensive for uncertainty quantification or parameter-exploration at high-resolution. Reduced-order or surrogate models are multiple orders of magnitude faster, but traditional surrogates are inflexible or inaccurate and pure machine learning (ML)-based surrogates too data-hungry. We propose a hybrid, flexible surrogate model that exploits known physics for simulating large-scale dynamics and limits learning to the hard-to-model term, which is called parametrization or closure and captures the effect of fine- onto large-scale dynamics. Leveraging neural operators, we are the first to learn grid-independent, non-local, and flexible parametrizations. Our multiscale neural operator is motivated by a rich literature in multiscale modeling, has quasilinear runtime complexity, is more accurate or flexible than state-of-the-art parametrizations and demonstrated on the chaotic equation multiscale Lorenz96.

Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact best-response for a shallow linear network with L2-regularized Jacobian can be represented by a similar gating mechanism. We fit this model using a gradient-based hyperparameter optimization algorithm which alternates between approximating the best-response around the current hyperparameters and optimizing the hyperparameters using the approximate best-response function. Unlike other gradient-based approaches, we do not require differentiating the training loss with respect to the hyperparameters, allowing us to tune discrete hyperparameters, data augmentation hyperparameters, and dropout probabilities. Because the hyperparameters are adapted online, our approach discovers hyperparameter schedules that can outperform fixed hyperparameter values. Empirically, our approach outperforms competing hyperparameter optimization methods on large-scale deep learning problems. We call our networks, which update their own hyperparameters online during training, Self-Tuning Networks (STNs).

Despite strong performance on existing benchmarks, it remains unclear whether large language models can reason over genuinely novel scientific information. Most evaluations score end-to-end RAG pipelines, where reasoning is confounded with retrieval and toolchain choices, and the signal is further contaminated by parametric memorization and open-web volatility. We introduce DeR2, a controlled deep-research sandbox that isolates document-grounded reasoning while preserving core difficulties of deep search: multi-step synthesis, denoising, and evidence-based conclusion making. DeR2 decouples evidence access from reasoning via four regimes--Instruction-only, Concepts (gold concepts without documents), Related-only (only relevant documents), and Full-set (relevant documents plus topically related distractors)--yielding interpretable regime gaps that operationalize retrieval loss vs. reasoning loss and enable fine-grained error attribution. To prevent parametric leakage, we apply a two-phase validation that requires parametric failure without evidence while ensuring oracle-concept solvability. To ensure reproducibility, each instance provides a frozen document library (drawn from 2023-2025 theoretical papers) with expert-annotated concepts and validated rationales. Experiments across a diverse set of state-of-the-art foundation models reveal substantial variation and significant headroom: some models exhibit mode-switch fragility, performing worse with the Full-set than with Instruction-only, while others show structural concept misuse, correctly naming concepts but failing to execute them as procedures.

We conduct an extended analysis of dark energy constraints, in support of the findings of the DESI DR2 cosmology key paper, including DESI data, Planck CMB observations, and three different supernova compilations. Using a broad range of parametric and non-parametric methods, we explore the dark energy phenomenology and find consistent trends across all approaches, in good agreement with the w_0w_aCDM key paper results. Even with the additional flexibility introduced by non-parametric approaches, such as binning and Gaussian Processes, we find that extending LambdaCDM to include a two-parameter w(z) is sufficient to capture the trends present in the data. Finally, we examine three dark energy classes with distinct dynamics, including quintessence scenarios satisfying w geq -1, to explore what underlying physics can explain such deviations. The current data indicate a clear preference for models that feature a phantom crossing; although alternatives lacking this feature are disfavored, they cannot yet be ruled out. Our analysis confirms that the evidence for dynamical dark energy, particularly at low redshift (z lesssim 0.3), is robust and stable under different modeling choices.

We consider a family of convex quadratic programs in which the coefficients of the linear objective term and the righthand side of the constraints are affine functions of a parameter. It is well known that the solution of such a parametrized quadratic program is a piecewise affine function of the parameter. The number of (polyhedral) regions in the solution map can grow exponentially in problem size, but when the number of regions is moderate, a so-called explicit solver is practical. Such a solver computes the coefficients of the affine functions and the linear inequalities defining the polyhedral regions offline; to solve a problem instance online it simply evaluates this explicit solution map. Potential advantages of an explicit solver over a more general purpose iterative solver can include transparency, interpretability, reliability, and speed. In this paper we describe how code generation can be used to automatically generate an explicit solver from a high level description of a parametrized quadratic program. Our method has been implemented in the open-source software CVXPYgen, which is part of CVXPY, a domain specific language for general convex optimization.

Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model parameters is available. Here we study the common opposite situation, where direct screening or random sampling of model parameters leads to exhaustive training times and evaluations at unphysical parameter values. Our solution is to decouple uncertainty quantification from network architecture. Instead of sampling network weights, we introduce the model-parameter distribution as an input to network training via Markov chain Monte Carlo (MCMC). In this way, the surrogate achieves the same uncertainty quantification as the underlying physical model, but with substantially reduced computation time. The approach is fully agnostic with respect to the neural network choice. In our examples, we present a quantile emulator for prediction and a novel autoencoder-based ODE network emulator that can flexibly estimate different trajectory paths corresponding to different ODE model parameters. Moreover, we present a mathematical analysis that provides a transparent way to relate potential performance loss to measurable distribution mismatch.

We introduce a model-based asynchronous multi-fidelity method for hyperparameter and neural architecture search that combines the strengths of asynchronous Hyperband and Gaussian process-based Bayesian optimization. At the heart of our method is a probabilistic model that can simultaneously reason across hyperparameters and resource levels, and supports decision-making in the presence of pending evaluations. We demonstrate the effectiveness of our method on a wide range of challenging benchmarks, for tabular data, image classification and language modelling, and report substantial speed-ups over current state-of-the-art methods. Our new methods, along with asynchronous baselines, are implemented in a distributed framework which will be open sourced along with this publication.

A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation. Linear parameter decomposition -- a framework that has been proposed to resolve several issues with current decomposition methods -- decomposes neural network parameters into a sum of sparsely used vectors in parameter space. However, the current main method in this framework, Attribution-based Parameter Decomposition (APD), is impractical on account of its computational cost and sensitivity to hyperparameters. In this work, we introduce Stochastic Parameter Decomposition (SPD), a method that is more scalable and robust to hyperparameters than APD, which we demonstrate by decomposing models that are slightly larger and more complex than was possible to decompose with APD. We also show that SPD avoids other issues, such as shrinkage of the learned parameters, and better identifies ground truth mechanisms in toy models. By bridging causal mediation analysis and network decomposition methods, this demonstration opens up new research possibilities in mechanistic interpretability by removing barriers to scaling linear parameter decomposition methods to larger models. We release a library for running SPD and reproducing our experiments at https://github.com/goodfire-ai/spd.

The performance of an algorithm often critically depends on its parameter configuration. While a variety of automated algorithm configuration methods have been proposed to relieve users from the tedious and error-prone task of manually tuning parameters, there is still a lot of untapped potential as the learned configuration is static, i.e., parameter settings remain fixed throughout the run. However, it has been shown that some algorithm parameters are best adjusted dynamically during execution, e.g., to adapt to the current part of the optimization landscape. Thus far, this is most commonly achieved through hand-crafted heuristics. A promising recent alternative is to automatically learn such dynamic parameter adaptation policies from data. In this article, we give the first comprehensive account of this new field of automated dynamic algorithm configuration (DAC), present a series of recent advances, and provide a solid foundation for future research in this field. Specifically, we (i) situate DAC in the broader historical context of AI research; (ii) formalize DAC as a computational problem; (iii) identify the methods used in prior-art to tackle this problem; (iv) conduct empirical case studies for using DAC in evolutionary optimization, AI planning, and machine learning.

ML-augmented algorithms utilize predictions to achieve performance beyond their worst-case bounds. Producing these predictions might be a costly operation -- this motivated Im et al. '22 to introduce the study of algorithms which use predictions parsimoniously. We design parsimonious algorithms for caching and MTS with action predictions, proposed by Antoniadis et al. '20, focusing on the parameters of consistency (performance with perfect predictions) and smoothness (dependence of their performance on the prediction error). Our algorithm for caching is 1-consistent, robust, and its smoothness deteriorates with the decreasing number of available predictions. We propose an algorithm for general MTS whose consistency and smoothness both scale linearly with the decreasing number of predictions. Without the restriction on the number of available predictions, both algorithms match the earlier guarantees achieved by Antoniadis et al. '20.

We address the problem of uncertainty calibration and introduce a novel calibration method, Parametrized Temperature Scaling (PTS). Standard deep neural networks typically yield uncalibrated predictions, which can be transformed into calibrated confidence scores using post-hoc calibration methods. In this contribution, we demonstrate that the performance of accuracy-preserving state-of-the-art post-hoc calibrators is limited by their intrinsic expressive power. We generalize temperature scaling by computing prediction-specific temperatures, parameterized by a neural network. We show with extensive experiments that our novel accuracy-preserving approach consistently outperforms existing algorithms across a large number of model architectures, datasets and metrics.

Creating a 360{\deg} parametric model of a human head is a very challenging task. While recent advancements have demonstrated the efficacy of leveraging synthetic data for building such parametric head models, their performance remains inadequate in crucial areas such as expression-driven animation, hairstyle editing, and text-based modifications. In this paper, we build a dataset of artist-designed high-fidelity human heads and propose to create a novel parametric 360{\deg} renderable parametric head model from it. Our scheme decouples the facial motion/shape and facial appearance, which are represented by a classic parametric 3D mesh model and an attached neural texture, respectively. We further propose a training method for decompositing hairstyle and facial appearance, allowing free-swapping of the hairstyle. A novel inversion fitting method is presented based on single image input with high generalization and fidelity. To the best of our knowledge, our model is the first parametric 3D full-head that achieves 360{\deg} free-view synthesis, image-based fitting, appearance editing, and animation within a single model. Experiments show that facial motions and appearances are well disentangled in the parametric space, leading to SOTA performance in rendering and animating quality. The code and SynHead100 dataset are released at https://nju-3dv.github.io/projects/Head360.

In this paper, we consider the problem of Iterative Machine Teaching (IMT), where the teacher provides examples to the learner iteratively such that the learner can achieve fast convergence to a target model. However, existing IMT algorithms are solely based on parameterized families of target models. They mainly focus on convergence in the parameter space, resulting in difficulty when the target models are defined to be functions without dependency on parameters. To address such a limitation, we study a more general task -- Nonparametric Iterative Machine Teaching (NIMT), which aims to teach nonparametric target models to learners in an iterative fashion. Unlike parametric IMT that merely operates in the parameter space, we cast NIMT as a functional optimization problem in the function space. To solve it, we propose both random and greedy functional teaching algorithms. We obtain the iterative teaching dimension (ITD) of the random teaching algorithm under proper assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the greedy teaching algorithm has a significantly lower ITD, which reaches a tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our theoretical findings with extensive experiments in nonparametric scenarios.

We study the problem of designing models for machine learning tasks defined on sets. In contrast to traditional approach of operating on fixed dimensional vectors, we consider objective functions defined on sets that are invariant to permutations. Such problems are widespread, ranging from estimation of population statistics poczos13aistats, to anomaly detection in piezometer data of embankment dams Jung15Exploration, to cosmology Ntampaka16Dynamical,Ravanbakhsh16ICML1. Our main theorem characterizes the permutation invariant functions and provides a family of functions to which any permutation invariant objective function must belong. This family of functions has a special structure which enables us to design a deep network architecture that can operate on sets and which can be deployed on a variety of scenarios including both unsupervised and supervised learning tasks. We also derive the necessary and sufficient conditions for permutation equivariance in deep models. We demonstrate the applicability of our method on population statistic estimation, point cloud classification, set expansion, and outlier detection.

This paper presents MathBode, a dynamic diagnostic for mathematical reasoning in large language models (LLMs). Instead of one-shot accuracy, MathBode treats each parametric problem as a system: we drive a single parameter sinusoidally and fit first-harmonic responses of model outputs and exact solutions. This yields interpretable, frequency-resolved metrics -- gain (amplitude tracking) and phase (lag) -- that form Bode-style fingerprints. Across five closed-form families (linear solve, ratio/saturation, compound interest, 2x2 linear systems, similar triangles), the diagnostic surfaces systematic low-pass behavior and growing phase lag that accuracy alone obscures. We compare several models against a symbolic baseline that calibrates the instrument (G approx 1, phi approx 0). Results separate frontier from mid-tier models on dynamics, providing a compact, reproducible protocol that complements standard benchmarks with actionable measurements of reasoning fidelity and consistency. We open-source the dataset and code to enable further research and adoption.

We introduce BézierFlow, a lightweight training approach for few-step generation with pretrained diffusion and flow models. BézierFlow achieves a 2-3x performance improvement for sampling with leq 10 NFEs while requiring only 15 minutes of training. Recent lightweight training approaches have shown promise by learning optimal timesteps, but their scope remains restricted to ODE discretizations. To broaden this scope, we propose learning the optimal transformation of the sampling trajectory by parameterizing stochastic interpolant (SI) schedulers. The main challenge lies in designing a parameterization that satisfies critical desiderata, including boundary conditions, differentiability, and monotonicity of the SNR. To effectively meet these requirements, we represent scheduler functions as Bézier functions, where control points naturally enforce these properties. This reduces the problem to learning an ordered set of points in the time range, while the interpretation of the points changes from ODE timesteps to Bézier control points. Across a range of pretrained diffusion and flow models, BézierFlow consistently outperforms prior timestep-learning methods, demonstrating the effectiveness of expanding the search space from discrete timesteps to Bézier-based trajectory transformations.

In this paper we develop a dynamic form of Bayesian optimization for machine learning models with the goal of rapidly finding good hyperparameter settings. Our method uses the partial information gained during the training of a machine learning model in order to decide whether to pause training and start a new model, or resume the training of a previously-considered model. We specifically tailor our method to machine learning problems by developing a novel positive-definite covariance kernel to capture a variety of training curves. Furthermore, we develop a Gaussian process prior that scales gracefully with additional temporal observations. Finally, we provide an information-theoretic framework to automate the decision process. Experiments on several common machine learning models show that our approach is extremely effective in practice.

Many state-of-the-art hyperparameter optimization (HPO) algorithms rely on model-based optimizers that learn surrogate models of the target function to guide the search. Gaussian processes are the de facto surrogate model due to their ability to capture uncertainty but they make strong assumptions about the observation noise, which might not be warranted in practice. In this work, we propose to leverage conformalized quantile regression which makes minimal assumptions about the observation noise and, as a result, models the target function in a more realistic and robust fashion which translates to quicker HPO convergence on empirical benchmarks. To apply our method in a multi-fidelity setting, we propose a simple, yet effective, technique that aggregates observed results across different resource levels and outperforms conventional methods across many empirical tasks.

Maximizing a monotone submodular function under cardinality constraint k is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction, exemplar clustering, and coverage problems. We study this classic problem in the fully dynamic model where a stream of insertions and deletions of elements of an underlying ground set is given and the goal is to maintain an approximate solution using a fast update time. A recent paper at NeurIPS'20 by Lattanzi, Mitrovic, Norouzi{-}Fard, Tarnawski, Zadimoghaddam claims to obtain a dynamic algorithm for this problem with a 1{2} -epsilon approximation ratio and a query complexity bounded by poly(log(n),log(k),epsilon^{-1}). However, as we explain in this paper, the analysis has some important gaps. Having a dynamic algorithm for the problem with polylogarithmic update time is even more important in light of a recent result by Chen and Peng at STOC'22 who show a matching lower bound for the problem -- any randomized algorithm with a 1{2}+epsilon approximation ratio must have an amortized query complexity that is polynomial in n. In this paper, we develop a simpler algorithm for the problem that maintains a (1{2}-epsilon)-approximate solution for submodular maximization under cardinality constraint k using a polylogarithmic amortized update time.

Sharpness Aware Minimization (SAM) enhances performance across various neural architectures and datasets. As models are continually scaled up to improve performance, a rigorous understanding of SAM's scaling behaviour is paramount. To this end, we study the infinite-width limit of neural networks trained with SAM, using the Tensor Programs framework. Our findings reveal that the dynamics of standard SAM effectively reduce to applying SAM solely in the last layer in wide neural networks, even with optimal hyperparameters. In contrast, we identify a stable parameterization with layerwise perturbation scaling, which we call Maximal Update and Perturbation Parameterization (μP^2), that ensures all layers are both feature learning and effectively perturbed in the limit. Through experiments with MLPs, ResNets and Vision Transformers, we empirically demonstrate that μP^2 achieves hyperparameter transfer of the joint optimum of learning rate and perturbation radius across model scales. Moreover, we provide an intuitive condition to derive μP^2 for other perturbation rules like Adaptive SAM and SAM-ON, also ensuring balanced perturbation effects across all layers.

We develop a continual learning method for pretrained models that requires no access to old-task data, addressing a practical barrier in foundation model adaptation where pretraining distributions are often unavailable. Our key observation is that pretrained networks exhibit substantial geometric redundancy, and that this redundancy can be exploited in two complementary ways. First, redundant neurons provide a proxy for dominant pretraining-era feature directions, enabling the construction of approximately protected update subspaces directly from pretrained weights. Second, redundancy offers a natural bias for where to place plasticity: by restricting updates to a subset of redundant neurons and constraining the remaining degrees of freedom, we obtain update families with reduced functional drift on the old-data distribution and improved worst-case retention guarantees. These insights lead to PLATE (Plasticity-Tunable Efficient Adapters), a continual learning method requiring no past-task data that provides explicit control over the plasticity-retention trade-off. PLATE parameterizes each layer with a structured low-rank update ΔW = B A Q^top, where B and Q are computed once from pretrained weights and kept frozen, and only A is trained on the new task. The code is available at https://github.com/SalesforceAIResearch/PLATE.

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to improve the parameterization of structural optimization. Rather than directly optimizing densities on a grid, we instead optimize the parameters of a neural network which outputs those densities. This reparameterization leads to different and often better solutions. On a selection of 116 structural optimization tasks, our approach produces the best design 50% more often than the best baseline method.

We discuss methods for modeling eclipsing binary stars using the "physical", "simplified" and "phenomenological" models. There are few realizations of the "physical" Wilson-Devinney (1971) code and its improvements, e.g. Binary Maker, Phoebe. A parameter search using the Monte-Carlo method was realized by Zola et al. (2010), which is efficient in expense of too many evaluations of the test function. We compare existing algorithms of minimization of multi-parametric functions and propose to use a "combined" algorithm, depending on if the Hessian matrix is positively determined. To study methods, a simply fast-computed function resembling the "complete" test function for the physical model. Also we adopt a simplified model of an eclipsing binary at a circular orbit assuming spherical components with an uniform brightness distribution. This model resembles more advanced models in a sense of correlated parameter estimates due to a similar topology of the test function. Such a model may be applied to detached Algol-type systems, where the tidal distortion of components is negligible.

Automatic analysis of the enormous sets of images is a critical task in life sciences. This faces many challenges such as: algorithms are highly parameterized, significant human input is intertwined, and lacking a standard meta-visualization approach. This paper proposes an alternative iterative approach for optimizing input parameters, saving time by minimizing the user involvement, and allowing for understanding the workflow of algorithms and discovering new ones. The main focus is on developing an interactive visualization technique that enables users to analyze the relationships between sampled input parameters and corresponding output. This technique is implemented as a prototype called Veni Vidi Vici, or "I came, I saw, I conquered." This strategy is inspired by the mathematical formulas of numbering computable functions and is developed atop ImageJ, a scientific image processing program. A case study is presented to investigate the proposed framework. Finally, the paper explores some potential future issues in the application of the proposed approach in parameter space analysis in visualization.

We show that time series foundation models scale: a single training recipe produces reliable forecast-quality improvements from 4M to 2.5B parameters. We release Toto 2.0, a family of five open-weights forecasting models trained under this recipe. The Toto 2.0 family sets a new state of the art on three forecasting benchmarks: BOOM, our observability benchmark; GIFT-Eval, the standard general-purpose benchmark; and the recent contamination-resistant TIME benchmark. This report describes our experimental results and details the design decisions behind Toto 2.0: its architecture and training recipe, training data, and the u-muP hyperparameter transfer pipeline. All five base checkpoints are released under Apache 2.0.