Daily Papers

Generalized Category Discovery (GCD) aims to discover novel categories in unlabelled datasets using knowledge learned from labelled samples. Previous studies argued that parametric classifiers are prone to overfitting to seen categories, and endorsed using a non-parametric classifier formed with semi-supervised k-means. However, in this study, we investigate the failure of parametric classifiers, verify the effectiveness of previous design choices when high-quality supervision is available, and identify unreliable pseudo-labels as a key problem. We demonstrate that two prediction biases exist: the classifier tends to predict seen classes more often, and produces an imbalanced distribution across seen and novel categories. Based on these findings, we propose a simple yet effective parametric classification method that benefits from entropy regularisation, achieves state-of-the-art performance on multiple GCD benchmarks and shows strong robustness to unknown class numbers. We hope the investigation and proposed simple framework can serve as a strong baseline to facilitate future studies in this field. Our code is available at: https://github.com/CVMI-Lab/SimGCD.

Many recent machine learning tasks focus to develop models that can generalize to unseen distributions. Domain generalization (DG) has become one of the key topics in various fields. Several literatures show that DG can be arbitrarily hard without exploiting target domain information. To address this issue, test-time adaptive (TTA) methods are proposed. Existing TTA methods require offline target data or extra sophisticated optimization procedures during the inference stage. In this work, we adopt Non-Parametric Classifier to perform the test-time Adaptation (AdaNPC). In particular, we construct a memory that contains the feature and label pairs from training domains. During inference, given a test instance, AdaNPC first recalls K closed samples from the memory to vote for the prediction, and then the test feature and predicted label are added to the memory. In this way, the sample distribution in the memory can be gradually changed from the training distribution towards the test distribution with very little extra computation cost. We theoretically justify the rationality behind the proposed method. Besides, we test our model on extensive numerical experiments. AdaNPC significantly outperforms competitive baselines on various DG benchmarks. In particular, when the adaptation target is a series of domains, the adaptation accuracy of AdaNPC is 50% higher than advanced TTA methods. The code is available at https://github.com/yfzhang114/AdaNPC.

Neural net classifiers trained on data with annotated class labels can also capture apparent visual similarity among categories without being directed to do so. We study whether this observation can be extended beyond the conventional domain of supervised learning: Can we learn a good feature representation that captures apparent similarity among instances, instead of classes, by merely asking the feature to be discriminative of individual instances? We formulate this intuition as a non-parametric classification problem at the instance-level, and use noise-contrastive estimation to tackle the computational challenges imposed by the large number of instance classes. Our experimental results demonstrate that, under unsupervised learning settings, our method surpasses the state-of-the-art on ImageNet classification by a large margin. Our method is also remarkable for consistently improving test performance with more training data and better network architectures. By fine-tuning the learned feature, we further obtain competitive results for semi-supervised learning and object detection tasks. Our non-parametric model is highly compact: With 128 features per image, our method requires only 600MB storage for a million images, enabling fast nearest neighbour retrieval at the run time.

The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities, for example the normal, while not losing much in precision when the true density is far from the parametric class. The idea is to multiply an initial parametric density estimate with a kernel type estimate of the necessary correction factor. This works well in cases where the correction factor function is less rough than the original density itself. Extensive comparisons with the kernel estimator are carried out, including exact analysis for the class of all normal mixtures. The new method, with a normal start, wins quite often, even in many cases where the true density is far from normal. Procedures for choosing the smoothing parameter of the estimator are also discussed. The new estimator should be particularly useful in higher dimensions, where the usual nonparametric methods have problems. The idea is also spelled out for nonparametric regression.

Neural network classifiers have become the de-facto choice for current "pre-train then fine-tune" paradigms of visual classification. In this paper, we investigate k-Nearest-Neighbor (k-NN) classifiers, a classical model-free learning method from the pre-deep learning era, as an augmentation to modern neural network based approaches. As a lazy learning method, k-NN simply aggregates the distance between the test image and top-k neighbors in a training set. We adopt k-NN with pre-trained visual representations produced by either supervised or self-supervised methods in two steps: (1) Leverage k-NN predicted probabilities as indications for easy vs. hard examples during training. (2) Linearly interpolate the k-NN predicted distribution with that of the augmented classifier. Via extensive experiments on a wide range of classification tasks, our study reveals the generality and flexibility of k-NN integration with additional insights: (1) k-NN achieves competitive results, sometimes even outperforming a standard linear classifier. (2) Incorporating k-NN is especially beneficial for tasks where parametric classifiers perform poorly and / or in low-data regimes. We hope these discoveries will encourage people to rethink the role of pre-deep learning, classical methods in computer vision. Our code is available at: https://github.com/KMnP/nn-revisit.

Multi-representation diffusion models can improve visual synthesis by denoising complementary views of an image, but their performance depends critically on the asynchronous schedule that determines when each representation is denoised. We propose to learn this schedule. Our method formulates asynchronous flow matching over multiple representation spaces and uses a schedule-corrected objective that keeps each representation's local noising-time weights fixed as the schedule changes. We instantiate the schedule with a flexible parametric class that is convex and monotone by construction, and learn it using a fast joint probe with less than 1% additional training compute. On ImageNet 256x256, the learned schedule substantially improves both convergence speed and final quality under a matched 675M-parameter XL backbone. With AutoGuidance, our 200-epoch model reaches FID 1.05, matching the 800-epoch SFD-XL baseline with 4x less training. Training to 600 epochs further improves to FID 1.02, outperforming the 1B-parameter SFD-XXL result of FID 1.04 while using a smaller model. In the unguided setting, our 200-epoch model reaches FID 2.37, already below the best 800-epoch SFD-XL result (2.54) at 4x less training, and improves to FID 2.14 at 600 epochs. Code is available at https://github.com/bsq532087/LWD

We consider the question of learning Q-function in a sample efficient manner for reinforcement learning with continuous state and action spaces under a generative model. If Q-function is Lipschitz continuous, then the minimal sample complexity for estimating ε-optimal Q-function is known to scale as Ω(1{ε^{d_1+d_2 +2}}) per classical non-parametric learning theory, where d_1 and d_2 denote the dimensions of the state and action spaces respectively. The Q-function, when viewed as a kernel, induces a Hilbert-Schmidt operator and hence possesses square-summable spectrum. This motivates us to consider a parametric class of Q-functions parameterized by its "rank" r, which contains all Lipschitz Q-functions as r to infty. As our key contribution, we develop a simple, iterative learning algorithm that finds ε-optimal Q-function with sample complexity of O(1{ε^{max(d_1, d_2)+2}}) when the optimal Q-function has low rank r and the discounting factor γ is below a certain threshold. Thus, this provides an exponential improvement in sample complexity. To enable our result, we develop a novel Matrix Estimation algorithm that faithfully estimates an unknown low-rank matrix in the ell_infty sense even in the presence of arbitrary bounded noise, which might be of interest in its own right. Empirical results on several stochastic control tasks confirm the efficacy of our "low-rank" algorithms.

Generalized category discovery (GCD) is a pragmatic but underexplored problem, which requires models to automatically cluster and discover novel categories by leveraging the labeled samples from old classes. The challenge is that unlabeled data contain both old and new classes. Early works leveraging pseudo-labeling with parametric classifiers handle old and new classes separately, which brings about imbalanced accuracy between them. Recent methods employing contrastive learning neglect potential positives and are decoupled from the clustering objective, leading to biased representations and sub-optimal results. To address these issues, we introduce a unified and unbiased prototype learning framework, namely ProtoGCD, wherein old and new classes are modeled with joint prototypes and unified learning objectives, {enabling unified modeling between old and new classes}. Specifically, we propose a dual-level adaptive pseudo-labeling mechanism to mitigate confirmation bias, together with two regularization terms to collectively help learn more suitable representations for GCD. Moreover, for practical considerations, we devise a criterion to estimate the number of new classes. Furthermore, we extend ProtoGCD to detect unseen outliers, achieving task-level unification. Comprehensive experiments show that ProtoGCD achieves state-of-the-art performance on both generic and fine-grained datasets. The code is available at https://github.com/mashijie1028/ProtoGCD.

The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between inference speed and accuracy. Existing approximate nearest neighbor solutions accelerate retrieval but often degrade classification precision and lack adaptability in selecting the optimal neighborhood size (k). Here, we present an adaptive graph model that decouples inference latency from computational complexity. By integrating a Hierarchical Navigable Small World (HNSW) graph with a pre-computed voting mechanism, our framework completely transfers the computational burden of neighbor selection and weighting to the training phase. Within this topological structure, higher graph layers enable rapid navigation, while lower layers encode precise, node-specific decision boundaries with adaptive neighbor counts. Benchmarking against eight state-of-the-art baselines across six diverse datasets, we demonstrate that this architecture significantly accelerates inference speeds, achieving real-time performance, without compromising classification accuracy. These findings offer a scalable, robust solution to the long-standing inference bottleneck of kNN, establishing a new structural paradigm for graph-based nonparametric learning.

Direct alignment algorithms such as Direct Preference Optimization (DPO) fine-tune models based on preference data, using only supervised learning instead of two-stage reinforcement learning with human feedback (RLHF). We show that DPO encodes a statistical estimation problem over reward functions induced by a parametric policy class. When the true reward function that generates preferences cannot be realized via the policy class, DPO becomes misspecified, resulting in failure modes such as preference order reversal, worsening of policy reward, and high sensitivity to the input preference data distribution. On the other hand, we study the local behavior of two-stage RLHF for a parametric class and relate it to a natural gradient step in policy space. Our fine-grained geometric characterization allows us to propose AuxDPO, which introduces additional auxiliary variables in the DPO loss function to help move towards the RLHF solution in a principled manner and mitigate the misspecification in DPO. We empirically demonstrate the superior performance of AuxDPO on didactic bandit settings as well as LLM alignment tasks.

The prevalence of sarcasm in social media, conveyed through text-image combinations, presents significant challenges for sentiment analysis and intention mining. Current multi-modal sarcasm detection methods have been proven to struggle with biases from spurious cues, leading to a superficial understanding of the complex interactions between text and image. To address these issues, we propose InterCLIP-MEP, a robust framework for multi-modal sarcasm detection. InterCLIP-MEP introduces a refined variant of CLIP, Interactive CLIP (InterCLIP), as the backbone, enhancing sample representations by embedding cross-modality information in each encoder. Furthermore, a novel training strategy is designed to adapt InterCLIP for a Memory-Enhanced Predictor (MEP). MEP uses dynamic dual-channel memory to store valuable historical knowledge of test samples and then leverages this memory as a non-parametric classifier to derive the final prediction. By using InterCLIP to encode text-image interactions more effectively and incorporating MEP, InterCLIP-MEP offers a more robust recognition of multi-modal sarcasm. Experiments demonstrate that InterCLIP-MEP achieves state-of-the-art performance on the MMSD2.0 benchmark. Code and data are available at [https://github.com/CoderChen01/InterCLIP-MEP](https://github.com/CoderChen01/InterCLIP-MEP).

Wasserstein gradient flow has emerged as a promising approach to solve optimization problems over the space of probability distributions. A recent trend is to use the well-known JKO scheme in combination with input convex neural networks to numerically implement the proximal step. The most challenging step, in this setup, is to evaluate functions involving density explicitly, such as entropy, in terms of samples. This paper builds on the recent works with a slight but crucial difference: we propose to utilize a variational formulation of the objective function formulated as maximization over a parametric class of functions. Theoretically, the proposed variational formulation allows the construction of gradient flows directly for empirical distributions with a well-defined and meaningful objective function. Computationally, this approach replaces the computationally expensive step in existing methods, to handle objective functions involving density, with inner loop updates that only require a small batch of samples and scale well with the dimension. The performance and scalability of the proposed method are illustrated with the aid of several numerical experiments involving high-dimensional synthetic and real datasets.

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.

This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the "standard" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude -- including full LTL model checking, analysis with user-defined analysis strategies, and even statistical model checking -- for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Romeo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Romeo in many cases.

Large, pretrained models are commonly finetuned with imagery that is heavily augmented to mimic different conditions and scales, with the resulting models used for various tasks with imagery from a range of spatial scales. Such models overlook scale-specific information in the data for scale-dependent domains, such as remote sensing. In this paper, we present Scale-MAE, a pretraining method that explicitly learns relationships between data at different, known scales throughout the pretraining process. Scale-MAE pretrains a network by masking an input image at a known input scale, where the area of the Earth covered by the image determines the scale of the ViT positional encoding, not the image resolution. Scale-MAE encodes the masked image with a standard ViT backbone, and then decodes the masked image through a bandpass filter to reconstruct low/high frequency images at lower/higher scales. We find that tasking the network with reconstructing both low/high frequency images leads to robust multiscale representations for remote sensing imagery. Scale-MAE achieves an average of a 2.4 - 5.6% non-parametric kNN classification improvement across eight remote sensing datasets compared to current state-of-the-art and obtains a 0.9 mIoU to 1.7 mIoU improvement on the SpaceNet building segmentation transfer task for a range of evaluation scales.

Federated optimization studies the problem of collaborative function optimization among multiple clients (e.g. mobile devices or organizations) under the coordination of a central server. Since the data is collected separately by each client and always remains decentralized, federated optimization preserves data privacy and allows for large-scale computing, which makes it a promising decentralized machine learning paradigm. Though it is often deployed for tasks that are online in nature, e.g., next-word prediction on keyboard apps, most works formulate it as an offline problem. The few exceptions that consider federated bandit optimization are limited to very simplistic function classes, e.g., linear, generalized linear, or non-parametric function class with bounded RKHS norm, which severely hinders its practical usage. In this paper, we propose a new algorithm, named Fed-GO-UCB, for federated bandit optimization with generic non-linear objective function. Under some mild conditions, we rigorously prove that Fed-GO-UCB is able to achieve sub-linear rate for both cumulative regret and communication cost. At the heart of our theoretical analysis are distributed regression oracle and individual confidence set construction, which can be of independent interests. Empirical evaluations also demonstrate the effectiveness of the proposed algorithm.

We introduce 3D Gaussian blendshapes for modeling photorealistic head avatars. Taking a monocular video as input, we learn a base head model of neutral expression, along with a group of expression blendshapes, each of which corresponds to a basis expression in classical parametric face models. Both the neutral model and expression blendshapes are represented as 3D Gaussians, which contain a few properties to depict the avatar appearance. The avatar model of an arbitrary expression can be effectively generated by combining the neutral model and expression blendshapes through linear blending of Gaussians with the expression coefficients. High-fidelity head avatar animations can be synthesized in real time using Gaussian splatting. Compared to state-of-the-art methods, our Gaussian blendshape representation better captures high-frequency details exhibited in input video, and achieves superior rendering performance.

We present PIRATR, an end-to-end 3D object detection framework for robotic use cases in point clouds. Extending PI3DETR, our method streamlines parametric 3D object detection by jointly estimating multi-class 6-DoF poses and class-specific parametric attributes directly from occlusion-affected point cloud data. This formulation enables not only geometric localization but also the estimation of task-relevant properties for parametric objects, such as a gripper's opening, where the 3D model is adjusted according to simple, predefined rules. The architecture employs modular, class-specific heads, making it straightforward to extend to novel object types without re-designing the pipeline. We validate PIRATR on an automated forklift platform, focusing on three structurally and functionally diverse categories: crane grippers, loading platforms, and pallets. Trained entirely in a synthetic environment, PIRATR generalizes effectively to real outdoor LiDAR scans, achieving a detection mAP of 0.919 without additional fine-tuning. PIRATR establishes a new paradigm of pose-aware, parameterized perception. This bridges the gap between low-level geometric reasoning and actionable world models, paving the way for scalable, simulation-trained perception systems that can be deployed in dynamic robotic environments. Code available at https://github.com/swingaxe/piratr.

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

Posterior sampling allows the exploitation of prior knowledge of the environment's transition dynamics to improve the sample efficiency of reinforcement learning. The prior is typically specified as a class of parametric distributions, a task that can be cumbersome in practice, often resulting in the choice of uninformative priors. In this work, we propose a novel posterior sampling approach in which the prior is given as a (partial) causal graph over the environment's variables. The latter is often more natural to design, such as listing known causal dependencies between biometric features in a medical treatment study. Specifically, we propose a hierarchical Bayesian procedure, called C-PSRL, simultaneously learning the full causal graph at the higher level and the parameters of the resulting factored dynamics at the lower level. For this procedure, we provide an analysis of its Bayesian regret, which explicitly connects the regret rate with the degree of prior knowledge. Our numerical evaluation conducted in illustrative domains confirms that C-PSRL strongly improves the efficiency of posterior sampling with an uninformative prior while performing close to posterior sampling with the full causal graph.

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of parametric PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed supervision: (i) labeled data from analytical solutions generated via the Method of Manufactured Solutions (MMS), and (ii) unlabeled samples optimized using physics-informed objectives. The model maps PDE parametrizations to target Physics-Informed Neural Networks (PINNs) and can handle linear elliptic, hyperbolic, and parabolic equations in two dimensions with varying source terms, geometries, and mixed Dirichlet/Neumann boundary conditions, including interior boundaries. HyPINO achieves strong zero-shot accuracy on seven benchmark problems from PINN literature, outperforming U-Nets, Poseidon, and Physics-Informed Neural Operators (PINO). Further, we introduce an iterative refinement procedure that compares the physics of the generated PINN to the requested PDE and uses the discrepancy to generate a "delta" PINN. Summing their contributions and repeating this process forms an ensemble whose combined solution progressively reduces the error on six benchmarks and achieves over 100x gain in average L_2 loss in the best case, while retaining forward-only inference. Additionally, we evaluate the fine-tuning behavior of PINNs initialized by HyPINO and show that they converge faster and to lower final error than both randomly initialized and Reptile-meta-learned PINNs on five benchmarks, performing on par on the remaining two. Our results highlight the potential of this scalable approach as a foundation for extending neural operators toward solving increasingly complex, nonlinear, and high-dimensional PDE problems with significantly improved accuracy and reduced computational cost.

Neutron/gamma discrimination has been intensively researched in recent years, due to its unique scientific value and widespread applications. With the advancement of detection materials and algorithms, nowadays we can achieve fairly good discrimination. However, further improvements rely on better utilization of detector raw signals, especially energy-independent pulse characteristics. We begin by discussing why figure-of-merit (FoM) is not a comprehensive criterion for high-precision neutron/gamma discriminators, and proposing a new evaluation method based on adversarial sampling. Inspired by frequency-domain analysis in existing literature, parametric linear/nonlinear models with minimum complexity are created, upon the discrete spectrum, with tunable parameters just as neural networks. We train the models on an open-source neutron/gamma dataset (CLYC crystals with silicon photomultipliers) preprocessed by charge normalization to discover and exploit energy-independent features. The performance is evaluated on different sampling rates and noise levels, in comparison with the frequency classification index and conventional methods. The frequency-domain parametric models show higher accuracy and better adaptability to variations of data integrity than other discriminators. The proposed method is also promising for online inference on economical hardware and portable devices.

Modern techniques like contrastive learning have been effectively used in many areas, including computer vision, natural language processing, and graph-structured data. Creating positive examples that assist the model in learning robust and discriminative representations is a crucial stage in contrastive learning approaches. Usually, preset human intuition directs the selection of relevant data augmentations. Due to patterns that are easily recognized by humans, this rule of thumb works well in the vision and language domains. However, it is impractical to visually inspect the temporal structures in time series. The diversity of time series augmentations at both the dataset and instance levels makes it difficult to choose meaningful augmentations on the fly. In this study, we address this gap by analyzing time series data augmentation using information theory and summarizing the most commonly adopted augmentations in a unified format. We then propose a contrastive learning framework with parametric augmentation, AutoTCL, which can be adaptively employed to support time series representation learning. The proposed approach is encoder-agnostic, allowing it to be seamlessly integrated with different backbone encoders. Experiments on univariate forecasting tasks demonstrate the highly competitive results of our method, with an average 6.5\% reduction in MSE and 4.7\% in MAE over the leading baselines. In classification tasks, AutoTCL achieves a 1.2% increase in average accuracy.

We introduce a Parametric Information Maximization (PIM) model for the Generalized Category Discovery (GCD) problem. Specifically, we propose a bi-level optimization formulation, which explores a parameterized family of objective functions, each evaluating a weighted mutual information between the features and the latent labels, subject to supervision constraints from the labeled samples. Our formulation mitigates the class-balance bias encoded in standard information maximization approaches, thereby handling effectively both short-tailed and long-tailed data sets. We report extensive experiments and comparisons demonstrating that our PIM model consistently sets new state-of-the-art performances in GCD across six different datasets, more so when dealing with challenging fine-grained problems.

The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The Fourier neural operator is the first ML-based method to successfully model turbulent flows with zero-shot super-resolution. It is up to three orders of magnitude faster compared to traditional PDE solvers. Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution.

We present PEAM, a Parametric Embodied Agent Memory framework in Minecraft that transforms agent memory from inference-time retrieval into parameter-resident skills internalized through experience. PEAM pairs a slow deliberative LLM for open-ended reasoning with a fast parametric module for reflexive execution of consolidated skills. The fast module is a multimodal Mixture-of-Experts LoRA architecture with per-category physically isolated adapters, enabling parameter-level continual learning without catastrophic forgetting. We treat failure as a first-class training signal: failure--correction trajectory pairs are internalized through a joint behavioral-cloning and contrastive objective, so the agent learns not only what succeeds but also how corrected actions differ from failed ones. To govern consolidation, PEAM introduces a parameterization-worthiness score for deciding which experience should be internalized, and a scale-free self-triggered consolidation mechanism for deciding when to internalize without task-specific hand-tuned thresholds, making the agent self-evolving as the trigger transfers across task distributions without re-tuning. Experiments in Minecraft show that PEAM improves long-horizon task performance, mitigates forgetting on previously consolidated skills, and improves parametric-versus-retrieval efficiency over retrieval-based embodied agents and parametric memory variants.

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.

Properties such as composability and automatic differentiation made artificial neural networks a pervasive tool in applications. Tackling more challenging problems caused neural networks to progressively become more complex and thus difficult to define from a mathematical perspective. We present a general definition of linear layer arising from a categorical framework based on the notions of integration theory and parametric spans. This definition generalizes and encompasses classical layers (e.g., dense, convolutional), while guaranteeing existence and computability of the layer's derivatives for backpropagation.

Deep neural networks (DNNs) are often used for text classification tasks as they usually achieve high levels of accuracy. However, DNNs can be computationally intensive with billions of parameters and large amounts of labeled data, which can make them expensive to use, to optimize and to transfer to out-of-distribution (OOD) cases in practice. In this paper, we propose a non-parametric alternative to DNNs that's easy, light-weight and universal in text classification: a combination of a simple compressor like gzip with a k-nearest-neighbor classifier. Without any training, pre-training or fine-tuning, our method achieves results that are competitive with non-pretrained deep learning methods on six in-distributed datasets. It even outperforms BERT on all five OOD datasets, including four low-resource languages. Our method also performs particularly well in few-shot settings where labeled data are too scarce for DNNs to achieve a satisfying accuracy.

Monitoring machine learning models once they are deployed is challenging. It is even more challenging to decide when to retrain models in real-case scenarios when labeled data is beyond reach, and monitoring performance metrics becomes unfeasible. In this work, we use non-parametric bootstrapped uncertainty estimates and SHAP values to provide explainable uncertainty estimation as a technique that aims to monitor the deterioration of machine learning models in deployment environments, as well as determine the source of model deterioration when target labels are not available. Classical methods are purely aimed at detecting distribution shift, which can lead to false positives in the sense that the model has not deteriorated despite a shift in the data distribution. To estimate model uncertainty we construct prediction intervals using a novel bootstrap method, which improves upon the work of Kumar & Srivastava (2012). We show that both our model deterioration detection system as well as our uncertainty estimation method achieve better performance than the current state-of-the-art. Finally, we use explainable AI techniques to gain an understanding of the drivers of model deterioration. We release an open source Python package, doubt, which implements our proposed methods, as well as the code used to reproduce our experiments.

Iris-based biometric systems are vulnerable to presentation attacks (PAs), where adversaries present physical artifacts (e.g., printed iris images, textured contact lenses) to defeat the system. This has led to the development of various presentation attack detection (PAD) algorithms, which typically perform well in intra-domain settings. However, they often struggle to generalize effectively in cross-domain scenarios, where training and testing employ different sensors, PA instruments, and datasets. In this work, we use adversarial training samples of both bonafide irides and PAs to improve the cross-domain performance of a PAD classifier. The novelty of our approach lies in leveraging transformation parameters from classical data augmentation schemes (e.g., translation, rotation) to generate adversarial samples. We achieve this through a convolutional autoencoder, ADV-GEN, that inputs original training samples along with a set of geometric and photometric transformations. The transformation parameters act as regularization variables, guiding ADV-GEN to generate adversarial samples in a constrained search space. Experiments conducted on the LivDet-Iris 2017 database, comprising four datasets, and the LivDet-Iris 2020 dataset, demonstrate the efficacy of our proposed method. The code is available at https://github.com/iPRoBe-lab/ADV-GEN-IrisPAD.

Supervised learning of image classifiers distills human knowledge into a parametric model through pairs of images and corresponding labels (X,Y). We argue that this simple and widely used representation of human knowledge neglects rich auxiliary information from the annotation procedure, such as the time-series of mouse traces and clicks left after image selection. Our insight is that such annotation byproducts Z provide approximate human attention that weakly guides the model to focus on the foreground cues, reducing spurious correlations and discouraging shortcut learning. To verify this, we create ImageNet-AB and COCO-AB. They are ImageNet and COCO training sets enriched with sample-wise annotation byproducts, collected by replicating the respective original annotation tasks. We refer to the new paradigm of training models with annotation byproducts as learning using annotation byproducts (LUAB). We show that a simple multitask loss for regressing Z together with Y already improves the generalisability and robustness of the learned models. Compared to the original supervised learning, LUAB does not require extra annotation costs. ImageNet-AB and COCO-AB are at https://github.com/naver-ai/NeglectedFreeLunch.

One of the major difficulties in medical image segmentation is the high variability of these images, which is caused by their origin (multi-centre), the acquisition protocols (multi-parametric), as well as the variability of human anatomy, the severity of the illness, the effect of age and gender, among others. The problem addressed in this work is the automatic semantic segmentation of lumbar spine Magnetic Resonance images using convolutional neural networks. The purpose is to assign a class label to each pixel of an image. Classes were defined by radiologists and correspond to different structural elements like vertebrae, intervertebral discs, nerves, blood vessels, and other tissues. The proposed network topologies are variants of the U-Net architecture. Several complementary blocks were used to define the variants: Three types of convolutional blocks, spatial attention models, deep supervision and multilevel feature extractor. This document describes the topologies and analyses the results of the neural network designs that obtained the most accurate segmentations. Several of the proposed designs outperform the standard U-Net used as baseline, especially when used in ensembles where the output of multiple neural networks is combined according to different strategies.

Rectified activation units (rectifiers) are essential for state-of-the-art neural networks. In this work, we study rectifier neural networks for image classification from two aspects. First, we propose a Parametric Rectified Linear Unit (PReLU) that generalizes the traditional rectified unit. PReLU improves model fitting with nearly zero extra computational cost and little overfitting risk. Second, we derive a robust initialization method that particularly considers the rectifier nonlinearities. This method enables us to train extremely deep rectified models directly from scratch and to investigate deeper or wider network architectures. Based on our PReLU networks (PReLU-nets), we achieve 4.94% top-5 test error on the ImageNet 2012 classification dataset. This is a 26% relative improvement over the ILSVRC 2014 winner (GoogLeNet, 6.66%). To our knowledge, our result is the first to surpass human-level performance (5.1%, Russakovsky et al.) on this visual recognition challenge.

The activation function plays a crucial role in model optimisation, yet the optimal choice remains unclear. For example, the Sigmoid activation is the de-facto activation in balanced classification tasks, however, in imbalanced classification, it proves inappropriate due to bias towards frequent classes. In this work, we delve deeper in this phenomenon by performing a comprehensive statistical analysis in the classification and intermediate layers of both balanced and imbalanced networks and we empirically show that aligning the activation function with the data distribution, enhances the performance in both balanced and imbalanced tasks. To this end, we propose the Adaptive Parametric Activation (APA) function, a novel and versatile activation function that unifies most common activation functions under a single formula. APA can be applied in both intermediate layers and attention layers, significantly outperforming the state-of-the-art on several imbalanced benchmarks such as ImageNet-LT, iNaturalist2018, Places-LT, CIFAR100-LT and LVIS and balanced benchmarks such as ImageNet1K, COCO and V3DET. The code is available at https://github.com/kostas1515/AGLU.

Meta learning have achieved promising performance in low-resource text classification which aims to identify target classes with knowledge transferred from source classes with sets of small tasks named episodes. However, due to the limited training data in the meta-learning scenario and the inherent properties of parameterized neural networks, poor generalization performance has become a pressing problem that needs to be addressed. To deal with this issue, we propose a meta-learning based method called Retrieval-Augmented Meta Learning(RAML). It not only uses parameterization for inference but also retrieves non-parametric knowledge from an external corpus to make inferences, which greatly alleviates the problem of poor generalization performance caused by the lack of diverse training data in meta-learning. This method differs from previous models that solely rely on parameters, as it explicitly emphasizes the importance of non-parametric knowledge, aiming to strike a balance between parameterized neural networks and non-parametric knowledge. The model is required to determine which knowledge to access and utilize during inference. Additionally, our multi-view passages fusion network module can effectively and efficiently integrate the retrieved information into low-resource classification task. The extensive experiments demonstrate that RAML significantly outperforms current SOTA low-resource text classification models.

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.

Chip-integrated nonlinear photonics holds the key for advanced optical information processing with superior performance and novel functionalities. Here, we present an optimally mode-matched, periodically poled lithium niobate nanowaveguide for efficient parametric frequency conversions on chip. Using a 4-mm nanowaveguide with subwavelength mode confinement, we demonstrate second harmonic generation with efficiency over 2200%~W^{-1}cm^{-2}, and broadband difference frequency generation with similar efficiency over a 4.5-THz spectral span. These allow us to generate correlated photon pairs over multiple frequency channels via spontaneous parametric down conversion, all in their fundamental spatial modes, with a coincidence to accidental ratio as high as 600. The high efficiency and dense integrability of the present chip devices may pave a viable route to scalable nonlinear applications in both classical and quantum domains.

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.

The behavior of Large Language Models (LLMs) when facing contextual information that conflicts with their internal parametric knowledge is inconsistent, with no generally accepted explanation for the expected outcome distribution. Recent work has identified in autoregressive transformer models a class of neurons -- called entropy neurons -- that produce a significant effect on the model output entropy while having an overall moderate impact on the ranking of the predicted tokens. In this paper, we investigate the preliminary claim that these neurons are involved in inhibiting context copying behavior in transformers by looking at their role in resolving conflicts between contextual and parametric information. We show that entropy neurons are responsible for suppressing context copying across a range of LLMs, and that ablating them leads to a significant change in the generation process. These results enhance our understanding of the internal dynamics of LLMs when handling conflicting information.

Assessing the quality of Large Language Model (LLM) outputs presents a critical challenge. Previous methods either rely on text-level information (e.g., reward models, majority voting), which can overfit to superficial cues, or on calibrated confidence from token probabilities, which would fail on less-calibrated models. Yet both of these signals are, in fact, partial projections of a richer source of information: the model's internal hidden states. Early layers, closer to token embeddings, preserve semantic and lexical features that underpin text-based judgments, while later layers increasingly align with output logits, embedding confidence-related information. This paper explores hidden states directly as a unified foundation for verification. We show that the correctness of a solution is encoded as a geometrically separable signature within the trajectory of hidden activations. To validate this, we present Clue (Clustering and Experience-based Verification), a deliberately minimalist, non-parametric verifier. With no trainable parameters, CLUE only summarizes each reasoning trace by an hidden state delta and classifies correctness via nearest-centroid distance to ``success'' and ``failure'' clusters formed from past experience. The simplicity of this method highlights the strength of the underlying signal. Empirically, CLUE consistently outperforms LLM-as-a-judge baselines and matches or exceeds modern confidence-based methods in reranking candidates, improving both top-1 and majority-vote accuracy across AIME 24/25 and GPQA. As a highlight, on AIME 24 with a 1.5B model, CLUE boosts accuracy from 56.7% (majority@64) to 70.0% (top-maj@16).

In recent years, the emergence of Transformers with self-attention mechanism has revolutionized the hyperspectral image (HSI) classification. However, these models face major challenges in computational efficiency, as their complexity increases quadratically with the sequence length. The Mamba architecture, leveraging a state space model (SSM), offers a more efficient alternative to Transformers. This paper introduces the Spatial-Spectral Morphological Mamba (MorpMamba) model in which, a token generation module first converts the HSI patch into spatial-spectral tokens. These tokens are then processed by morphological operations, which compute structural and shape information using depthwise separable convolutional operations. The extracted information is enhanced in a feature enhancement module that adjusts the spatial and spectral tokens based on the center region of the HSI sample, allowing for effective information fusion within each block. Subsequently, the tokens are refined through a multi-head self-attention which further improves the feature space. Finally, the combined information is fed into the state space block for classification and the creation of the ground truth map. Experiments on widely used HSI datasets demonstrate that the MorpMamba model outperforms (parametric efficiency) both CNN and Transformer models. The source code will be made publicly available at https://github.com/MHassaanButt/MorpMamba.

Tensorial neural networks (TNNs) combine the successes of multilinear algebra with those of deep learning to enable extremely efficient reduced-order models of high-dimensional problems. Here, I describe a deep neural network architecture that fuses multiple TNNs into a larger network, intended to solve a broader class of problems than a single TNN. I evaluate this architecture, referred to as a "stacked tensorial neural network" (STNN), on a parametric PDE with three independent variables and three parameters. The three parameters correspond to one PDE coefficient and two quantities describing the domain geometry. The STNN provides an accurate reduced-order description of the solution manifold over a wide range of parameters. There is also evidence of meaningful generalization to parameter values outside its training data. Finally, while the STNN architecture is relatively simple and problem agnostic, it can be regularized to incorporate problem-specific features like symmetries and physical modeling assumptions.

The output of Large Language Models (LLMs) are a function of the internal model's parameters and the input provided into the context window. The hypothesis presented here is that under a greedy sampling strategy the variance in the LLM's output is a function of the conceptual certainty embedded in the model's parametric knowledge, as well as the lexical variance in the input. Finetuning the model results in reducing the sensitivity of the model output to the lexical input variations. This is then applied to a classification problem and a probabilistic method is proposed for estimating the certainties of the predicted classes.

We introduce a new silhouette-based representation for modeling clothed human bodies using deep generative models. Our method can reconstruct a complete and textured 3D model of a person wearing clothes from a single input picture. Inspired by the visual hull algorithm, our implicit representation uses 2D silhouettes and 3D joints of a body pose to describe the immense shape complexity and variations of clothed people. Given a segmented 2D silhouette of a person and its inferred 3D joints from the input picture, we first synthesize consistent silhouettes from novel view points around the subject. The synthesized silhouettes which are the most consistent with the input segmentation are fed into a deep visual hull algorithm for robust 3D shape prediction. We then infer the texture of the subject's back view using the frontal image and segmentation mask as input to a conditional generative adversarial network. Our experiments demonstrate that our silhouette-based model is an effective representation and the appearance of the back view can be predicted reliably using an image-to-image translation network. While classic methods based on parametric models often fail for single-view images of subjects with challenging clothing, our approach can still produce successful results, which are comparable to those obtained from multi-view input.

Generating synthetic data that faithfully captures the statistical structure of real-world distributions is a fundamental challenge in data modeling. Classical approaches often depend on strong parametric assumptions or manual structural design and struggle in high-dimensional or heterogeneous domains. Recent progress in Large Language Models (LLMs) reveals their potential as flexible, high-dimensional priors over real-world distributions. However, when applied to data synthesis, standard LLM-based sampling is inefficient, constrained by fixed context limits, and fails to ensure statistical alignment. Given this, we introduce LLMSynthor, a general framework for data synthesis that transforms LLMs into structure-aware simulators guided by distributional feedback. LLMSynthor treats the LLM as a nonparametric copula simulator for modeling high-order dependencies and introduces LLM Proposal Sampling to generate grounded proposal distributions that improve sampling efficiency without requiring rejection. By minimizing discrepancies in the summary statistics space, the iterative synthesis loop aligns real and synthetic data while gradually uncovering and refining the latent generative structure. We evaluate LLMSynthor in both controlled and real-world settings using heterogeneous datasets in privacy-sensitive domains (e.g., e-commerce, population, and mobility) that encompass both structured and unstructured formats. The synthetic data produced by LLMSynthor shows high statistical fidelity, practical utility, and cross-data adaptability, positioning it as a valuable tool across economics, social science, urban studies, and beyond.

We study adaptive querying for learning user-dependent quantities of interest, such as responses to held-out items and psychometric indicators, within tight question budgets. Classical Bayesian design and computerized adaptive testing typically rely on restrictive parametric assumptions or expensive posterior approximations, limiting their use in heterogeneous, high-dimensional, and cold-start settings. We introduce a persona-induced latent variable model that represents a user's state through membership in a finite dictionary of AI personas, each offering response distributions produced by a large language model. This yields expressive priors with closed-form posterior updates and efficient finite-mixture predictions, enabling scalable Bayesian design for sequential item selection. Experiments on synthetic data and WorldValuesBench demonstrate that persona-based posteriors deliver accurate probabilistic predictions and an interpretable adaptive elicitation pipeline.

The task of perspective-aware classification introduces a bottleneck in terms of parametric efficiency that did not get enough recognition in existing studies. In this article, we aim to address this issue by applying an existing architecture, the hypernetwork+adapters combination, to perspectivist classification. Ultimately, we arrive at a solution that can compete with specialized models in adopting user perspectives on hate speech and toxicity detection, while also making use of considerably fewer parameters. Our solution is architecture-agnostic and can be applied to a wide range of base models out of the box.

In this paper, we introduce a framework for contextual distributionally robust optimization (DRO) that considers the causal and continuous structure of the underlying distribution by developing interpretable and tractable decision rules that prescribe decisions using covariates. We first introduce the causal Sinkhorn discrepancy (CSD), an entropy-regularized causal Wasserstein distance that encourages continuous transport plans while preserving the causal consistency. We then formulate a contextual DRO model with a CSD-based ambiguity set, termed Causal Sinkhorn DRO (Causal-SDRO), and derive its strong dual reformulation where the worst-case distribution is characterized as a mixture of Gibbs distributions. To solve the corresponding infinite-dimensional policy optimization, we propose the Soft Regression Forest (SRF) decision rule, which approximates optimal policies within arbitrary measurable function spaces. The SRF preserves the interpretability of classical decision trees while being fully parametric, differentiable, and Lipschitz smooth, enabling intrinsic interpretation from both global and local perspectives. To solve the Causal-SDRO with parametric decision rules, we develop an efficient stochastic compositional gradient algorithm that converges to an varepsilon-stationary point at a rate of O(varepsilon^{-4}), matching the convergence rate of standard stochastic gradient descent. Finally, we validate our method through numerical experiments on synthetic and real-world datasets, demonstrating its superior performance and interpretability.

Recurrent connectivity in the visual cortex is believed to aid object recognition for challenging conditions such as occlusion. Here we investigate if and how artificial neural networks also benefit from recurrence. We compare architectures composed of bottom-up, lateral and top-down connections and evaluate their performance using two novel stereoscopic occluded object datasets. We find that classification accuracy is significantly higher for recurrent models when compared to feedforward models of matched parametric complexity. Additionally we show that for challenging stimuli, the recurrent feedback is able to correctly revise the initial feedforward guess.

Face recognition from a single image per person is a challenging problem because the training sample is extremely small. We consider a variation of this problem. In our problem, we recognize only one person, and there are no labeled data for any other person. This setting naturally arises in authentication on personal computers and mobile devices, and poses additional challenges because it lacks negative examples. We formalize our problem as one-class classification, and propose and analyze an algorithm that learns a non-parametric model of the face from a single labeled image and a stream of unlabeled data. In many domains, for instance when a person interacts with a computer with a camera, unlabeled data are abundant and easy to utilize. This is the first paper that investigates how these data can help in learning better models in the single-image-per-person setting. Our method is evaluated on a dataset of 43 people and we show that these people can be recognized 90% of time at nearly zero false positives. This recall is 25+% higher than the recall of our best performing baseline. Finally, we conduct a comprehensive sensitivity analysis of our algorithm and provide a guideline for setting its parameters in practice.

Despite significant advances, the performance of state-of-the-art continual learning approaches hinges on the unrealistic scenario of fully labeled data. In this paper, we tackle this challenge and propose an approach for continual semi-supervised learning--a setting where not all the data samples are labeled. A primary issue in this scenario is the model forgetting representations of unlabeled data and overfitting the labeled samples. We leverage the power of nearest-neighbor classifiers to nonlinearly partition the feature space and flexibly model the underlying data distribution thanks to its non-parametric nature. This enables the model to learn a strong representation for the current task, and distill relevant information from previous tasks. We perform a thorough experimental evaluation and show that our method outperforms all the existing approaches by large margins, setting a solid state of the art on the continual semi-supervised learning paradigm. For example, on CIFAR-100 we surpass several others even when using at least 30 times less supervision (0.8% vs. 25% of annotations). Finally, our method works well on both low and high resolution images and scales seamlessly to more complex datasets such as ImageNet-100. The code is publicly available on https://github.com/kangzhiq/NNCSL

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this work, we argue that the cognitive mechanism of comparison, fundamental to human learning, is also vital for machines to recover true concepts underlying the data. This offers correctness guarantees for the field of concept learning, which, despite its impressive empirical successes, still lacks general theoretical support. Specifically, we aim to develop a theoretical framework for the identifiability of concepts with multiple classes of observations. We show that with sufficient diversity across classes, hidden concepts can be identified without assuming specific concept types, functional relations, or parametric generative models. Interestingly, even when conditions are not globally satisfied, we can still provide alternative guarantees for as many concepts as possible based on local comparisons, thereby extending the applicability of our theory to more flexible scenarios. Moreover, the hidden structure between classes and concepts can also be identified nonparametrically. We validate our theoretical results in both synthetic and real-world settings.

Wearable devices running Human Activity Recognition(HAR) on Inertial Measurement Units~(IMUs) waste energy by performing continuous classification for each window, even during long periods of unchanged activity. We address this with a lightweight change-detection gate: a non-parametric algorithm based on dynamic template matching that runs continuously at only approximately 16kFLOPs per step, requires no offline training, and does not need prior definition of target activity classes. The gate invokes the full HAR network only when it detects an activity change, reducing the computational load by over 67% in realistic monitoring settings. The algorithm is evaluated on smart glasses, smartwatch, and smartphone data, requiring only a brief device-specific calibration phase. The gate achieves 98% sensitivity on UCA-EHAR, ensuring no genuine activity transition is missed, while 75% specificity keeps unnecessary HAR invocations low. Results on WISDM are 97% sensitivity and 76% specificity, demonstrating robustness and flexibility to various settings.

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

Generative AI has matured to a point where large-scale models can generate text that seems indistinguishable from human-written text and remarkably photorealistic images. Automatically measuring how close the distribution of generated data is to the target real data distribution is a key step in diagnosing existing models and developing better models. We present MAUVE, a family of comparison measures between pairs of distributions such as those encountered in the generative modeling of text or images. These scores are statistical summaries of divergence frontiers capturing two types of errors in generative modeling. We explore four approaches to statistically estimate these scores: vector quantization, non-parametric estimation, classifier-based estimation, and parametric Gaussian approximations. We provide statistical bounds for the vector quantization approach. Empirically, we find that the proposed scores paired with a range of f-divergences and statistical estimation methods can quantify the gaps between the distributions of human-written text and those of modern neural language models by correlating with human judgments and identifying known properties of the generated texts. We conclude the paper by demonstrating its applications to other AI domains and discussing practical recommendations.

Predictive modeling over relational databases (RDBs) powers applications, yet remains challenging due to capturing both cross-table dependencies and complex feature interactions. Relational Deep Learning (RDL) methods automate feature engineering via message passing, while classical approaches like Deep Feature Synthesis (DFS) rely on predefined non-parametric aggregators. Despite performance gains, the comparative advantages of RDL over DFS and the design principles for selecting effective architectures remain poorly understood. We present a comprehensive study that unifies RDL and DFS in a shared design space and conducts architecture-centric searches across diverse RDB tasks. Our analysis yields three key findings: (1) RDL does not consistently outperform DFS, with performance being highly task-dependent; (2) no single architecture dominates across tasks, underscoring the need for task-aware model selection; and (3) validation accuracy is an unreliable guide for architecture choice. This search yields a model performance bank that links architecture configurations to their performance; leveraging this bank, we analyze the drivers of the RDL-DFS performance gap and introduce two task signals -- RDB task homophily and an affinity embedding that captures size, path, feature, and temporal structure -- whose correlation with the gap enables principled routing. Guided by these signals, we propose Relatron, a task embedding-based meta-selector that chooses between RDL and DFS and prunes the within-family search. Lightweight loss-landscape metrics further guard against brittle checkpoints by preferring flatter optima. In experiments, Relatron resolves the "more tuning, worse performance" effect and, in joint hyperparameter-architecture optimization, achieves up to 18.5% improvement over strong baselines with 10x lower cost than Fisher information-based alternatives.

At the core of the Transformer, the Softmax normalizes the attention matrix to be right stochastic. Previous research has shown that this often destabilizes training and that enforcing the attention matrix to be doubly stochastic (through Sinkhorn's algorithm) consistently improves performance across different tasks, domains and Transformer flavors. However, Sinkhorn's algorithm is iterative, approximative, non-parametric and thus inflexible w.r.t. the obtained doubly stochastic matrix (DSM). Recently, it has been proven that DSMs can be obtained with a parametric quantum circuit, yielding a novel quantum inductive bias for DSMs with no known classical analogue. Motivated by this, we demonstrate the feasibility of a hybrid classical-quantum doubly stochastic Transformer (QDSFormer) that replaces the Softmax in the self-attention layer with a variational quantum circuit. We study the expressive power of the circuit and find that it yields more diverse DSMs that better preserve information than classical operators. Across multiple small-scale object recognition tasks, we find that our QDSFormer consistently surpasses both a standard Vision Transformer and other doubly stochastic Transformers. Beyond the established Sinkformer, this comparison includes a novel quantum-inspired doubly stochastic Transformer (based on QR decomposition) that can be of independent interest. The QDSFormer also shows improved training stability and lower performance variation suggesting that it may mitigate the notoriously unstable training of ViTs on small-scale data.

We present DrivAerNet++, the largest and most comprehensive multimodal dataset for aerodynamic car design. DrivAerNet++ comprises 8,000 diverse car designs modeled with high-fidelity computational fluid dynamics (CFD) simulations. The dataset includes diverse car configurations such as fastback, notchback, and estateback, with different underbody and wheel designs to represent both internal combustion engines and electric vehicles. Each entry in the dataset features detailed 3D meshes, parametric models, aerodynamic coefficients, and extensive flow and surface field data, along with segmented parts for car classification and point cloud data. This dataset supports a wide array of machine learning applications including data-driven design optimization, generative modeling, surrogate model training, CFD simulation acceleration, and geometric classification. With more than 39 TB of publicly available engineering data, DrivAerNet++ fills a significant gap in available resources, providing high-quality, diverse data to enhance model training, promote generalization, and accelerate automotive design processes. Along with rigorous dataset validation, we also provide ML benchmarking results on the task of aerodynamic drag prediction, showcasing the breadth of applications supported by our dataset. This dataset is set to significantly impact automotive design and broader engineering disciplines by fostering innovation and improving the fidelity of aerodynamic evaluations.

We present Neural Spectral Methods, a technique to solve parametric Partial Differential Equations (PDEs), grounded in classical spectral methods. Our method uses orthogonal bases to learn PDE solutions as mappings between spectral coefficients. In contrast to current machine learning approaches which enforce PDE constraints by minimizing the numerical quadrature of the residuals in the spatiotemporal domain, we leverage Parseval's identity and introduce a new training strategy through a spectral loss. Our spectral loss enables more efficient differentiation through the neural network, and substantially reduces training complexity. At inference time, the computational cost of our method remains constant, regardless of the spatiotemporal resolution of the domain. Our experimental results demonstrate that our method significantly outperforms previous machine learning approaches in terms of speed and accuracy by one to two orders of magnitude on multiple different problems. When compared to numerical solvers of the same accuracy, our method demonstrates a 10times increase in performance speed.

Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policy by following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate the gradient, which tend to have high variance, requiring many samples and resulting in slow convergence. We first propose a Bayesian framework for policy gradient, based on modeling the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient and a measure of the uncertainty in the gradient estimates, namely, the gradient covariance, are provided at little extra cost. Since the proposed framework considers system trajectories as its basic observable unit, it does not require the dynamics within trajectories to be of any particular form, and can be extended to partially observable problems. On the downside, it cannot exploit the Markov property when the system is Markovian. To address this, we supplement our Bayesian policy gradient framework with a new actor-critic learning model in which a Bayesian class of non-parametric critics, based on Gaussian process temporal difference learning, is used. Such critics model the action-value function as a Gaussian process, allowing Bayes rule to be used to compute the posterior distribution over action-value functions, conditioned on the observed data. Appropriate choices of the policy parameterization and of the prior covariance (kernel) between action-values yield closed-form expressions for the posterior of the gradient of the expected return with respect to the policy parameters. We perform detailed experimental comparisons of the proposed Bayesian policy gradient and actor-critic algorithms with classic Monte-Carlo based policy gradient methods, on a number of reinforcement learning problems.

In recent years, unmanned aerial vehicles (UAVs) equipped with imaging sensors and automated processing algorithms have emerged as a promising tool to accelerate large-area surveys while reducing risk to human operators. Although hyperspectral imaging (HSI) enables material discrimination using spectral signatures, standardized benchmarks for UAV-based landmine detection remain scarce. In this work, we present a systematic benchmark of four classical statistical detection algorithms, including Spectral Angle Mapper (SAM), Matched Filter (MF), Adaptive Cosine Estimator (ACE), and Constrained Energy Minimization (CEM), alongside a proposed lightweight Spectral Neural Network utilizing Parametric Mish activations for PFM-1 landmine detection. We also release pixel-level binary ground truth masks (target/background) to enable standardized, reproducible evaluation. Evaluations were conducted on inert PFM-1 targets across multiple scene crops using a recently released VNIR hyperspectral dataset. Metrics such as receiver operating characteristic (ROC) curve, area under the curve (AUC), precision-recall (PR) curve, and average precision (AP) were used. While all methods achieve high ROC-AUC on an independent test set, the ACE method observes the highest AUC of 0.989. However, because target pixels are extremely sparse relative to background, ROC-AUC alone can be misleading; under precision-focused evaluation (PR and AP), the Spectral-NN outperforms classical detectors, achieving the highest AP. These results emphasize the need for precision-focused evaluation, scene-aware benchmarking, and learning-based spectral models for reliable UAV-based hyperspectral landmine detection. The code and pixel-level annotations will be released.

Social and collaborative platforms emit multivariate time-series traces in which early interactions-such as views, likes, or downloads-are followed, sometimes months or years later, by higher impact like citations, sales, or reviews. We formalize this setting as Lead-Lag Forecasting (LLF): given an early usage channel (the lead), predict a correlated but temporally shifted outcome channel (the lag). Despite the ubiquity of such patterns, LLF has not been treated as a unified forecasting problem within the time-series community, largely due to the absence of standardized datasets. To anchor research in LLF, here we present two high-volume benchmark datasets-arXiv (accesses -> citations of 2.3M papers) and GitHub (pushes/stars -> forks of 3M repositories)-and outline additional domains with analogous lead-lag dynamics, including Wikipedia (page views -> edits), Spotify (streams -> concert attendance), e-commerce (click-throughs -> purchases), and LinkedIn profile (views -> messages). Our datasets provide ideal testbeds for lead-lag forecasting, by capturing long-horizon dynamics across years, spanning the full spectrum of outcomes, and avoiding survivorship bias in sampling. We documented all technical details of data curation and cleaning, verified the presence of lead-lag dynamics through statistical and classification tests, and benchmarked parametric and non-parametric baselines for regression. Our study establishes LLF as a novel forecasting paradigm and lays an empirical foundation for its systematic exploration in social and usage data. Our data portal with downloads and documentation is available at https://lead-lag-forecasting.github.io/.

Transfer learning has become a central paradigm in modern machine learning, yet it suffers from the long-standing problem of negative transfer, where leveraging source representations can harm rather than help performance on the target task. Although empirical remedies have been proposed, there remains little theoretical understanding of how to reliably avoid negative transfer. In this paper, we investigate a simple yet remarkably effective strategy: augmenting frozen, pretrained source-side features with a trainable target-side encoder that adapts target features to capture residual signals overlooked by models pretrained on the source data. We show this residual feature integration strategy is sufficient to provably prevent negative transfer, by establishing theoretical guarantees that it has no worse convergence rate than training from scratch under the informative class of target distributions up to logarithmic factors, and that the convergence rate can transition seamlessly from nonparametric to near-parametric when source representations are informative. To our knowledge, this is the first theoretical work that ensures protection against negative transfer. We carry out extensive numerical experiments across image, text and tabular benchmarks, and empirically verify that the method consistently safeguards performance under distribution shift, label noise, semantic perturbation, and class imbalance. We additionally demonstrate that this residual integration mechanism uniquely supports adapt-time multimodality extension, enabling a pretrained single-cell foundation model to incorporate spatial signals for lymph-node anatomical classification despite the source model being trained without them. Our study thus advances the theory of safe transfer learning, and provides a principled approach that is simple, robust, architecture-agnostic, and broadly applicable.

A growing number of papers are published in the area of superconducting materials science. However, novel text and data mining (TDM) processes are still needed to efficiently access and exploit this accumulated knowledge, paving the way towards data-driven materials design. Herein, we present SuperMat (Superconductor Materials), an annotated corpus of linked data derived from scientific publications on superconductors, which comprises 142 articles, 16052 entities, and 1398 links that are characterised into six categories: the names, classes, and properties of materials; links to their respective superconducting critical temperature (Tc); and parametric conditions such as applied pressure or measurement methods. The construction of SuperMat resulted from a fruitful collaboration between computer scientists and material scientists, and its high quality is ensured through validation by domain experts. The quality of the annotation guidelines was ensured by satisfactory Inter Annotator Agreement (IAA) between the annotators and the domain experts. SuperMat includes the dataset, annotation guidelines, and annotation support tools that use automatic suggestions to help minimise human errors.

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.

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

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

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.

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.

Most applications of machine learning to classification assume a closed set of balanced classes. This is at odds with the real world, where class occurrence statistics often follow a long-tailed power-law distribution and it is unlikely that all classes are seen in a single sample. Nonparametric Bayesian models naturally capture this phenomenon, but have significant practical barriers to widespread adoption, namely implementation complexity and computational inefficiency. To address this, we present a method for extracting the inductive bias from a nonparametric Bayesian model and transferring it to an artificial neural network. By simulating data with a nonparametric Bayesian prior, we can metalearn a sequence model that performs inference over an unlimited set of classes. After training, this "neural circuit" has distilled the corresponding inductive bias and can successfully perform sequential inference over an open set of classes. Our experimental results show that the metalearned neural circuit achieves comparable or better performance than particle filter-based methods for inference in these models while being faster and simpler to use than methods that explicitly incorporate Bayesian nonparametric inference.

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.

The problem of Novel Class Discovery (NCD) consists in extracting knowledge from a labeled set of known classes to accurately partition an unlabeled set of novel classes. While NCD has recently received a lot of attention from the community, it is often solved on computer vision problems and under unrealistic conditions. In particular, the number of novel classes is usually assumed to be known in advance, and their labels are sometimes used to tune hyperparameters. Methods that rely on these assumptions are not applicable in real-world scenarios. In this work, we focus on solving NCD in tabular data when no prior knowledge of the novel classes is available. To this end, we propose to tune the hyperparameters of NCD methods by adapting the k-fold cross-validation process and hiding some of the known classes in each fold. Since we have found that methods with too many hyperparameters are likely to overfit these hidden classes, we define a simple deep NCD model. This method is composed of only the essential elements necessary for the NCD problem and performs impressively well under realistic conditions. Furthermore, we find that the latent space of this method can be used to reliably estimate the number of novel classes. Additionally, we adapt two unsupervised clustering algorithms (k-means and Spectral Clustering) to leverage the knowledge of the known classes. Extensive experiments are conducted on 7 tabular datasets and demonstrate the effectiveness of the proposed method and hyperparameter tuning process, and show that the NCD problem can be solved without relying on knowledge from the novel classes.

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.

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.

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.

Real-world datasets follow an imbalanced distribution, which poses significant challenges in rare-category object detection. Recent studies tackle this problem by developing re-weighting and re-sampling methods, that utilise the class frequencies of the dataset. However, these techniques focus solely on the frequency statistics and ignore the distribution of the classes in image space, missing important information. In contrast to them, we propose FRActal CALibration (FRACAL): a novel post-calibration method for long-tailed object detection. FRACAL devises a logit adjustment method that utilises the fractal dimension to estimate how uniformly classes are distributed in image space. During inference, it uses the fractal dimension to inversely downweight the probabilities of uniformly spaced class predictions achieving balance in two axes: between frequent and rare categories, and between uniformly spaced and sparsely spaced classes. FRACAL is a post-processing method and it does not require any training, also it can be combined with many off-the-shelf models such as one-stage sigmoid detectors and two-stage instance segmentation models. FRACAL boosts the rare class performance by up to 8.6% and surpasses all previous methods on LVIS dataset, while showing good generalisation to other datasets such as COCO, V3Det and OpenImages. We provide the code at https://github.com/kostas1515/FRACAL.

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

Optimization plays a costly and crucial role in developing machine learning systems. In learned optimizers, the few hyperparameters of commonly used hand-designed optimizers, e.g. Adam or SGD, are replaced with flexible parametric functions. The parameters of these functions are then optimized so that the resulting learned optimizer minimizes a target loss on a chosen class of models. Learned optimizers can both reduce the number of required training steps and improve the final test loss. However, they can be expensive to train, and once trained can be expensive to use due to computational and memory overhead for the optimizer itself. In this work, we identify and quantify the design features governing the memory, compute, and performance trade-offs for many learned and hand-designed optimizers. We further leverage our analysis to construct a learned optimizer that is both faster and more memory efficient than previous work. Our model and training code are open source.

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.

Parametric Computer-Aided Design (CAD) is central to contemporary mechanical design. However, it encounters challenges in achieving precise parametric sketch modeling and lacks practical evaluation metrics suitable for mechanical design. We harness the capabilities of pre-trained foundation models, renowned for their successes in natural language processing and computer vision, to develop generative models specifically for CAD. These models are adept at understanding complex geometries and design reasoning, a crucial advancement in CAD technology. In this paper, we propose CadVLM, an end-to-end vision language model for CAD generation. Our approach involves adapting pre-trained foundation models to manipulate engineering sketches effectively, integrating both sketch primitive sequences and sketch images. Extensive experiments demonstrate superior performance on multiple CAD sketch generation tasks such as CAD autocompletion, CAD autoconstraint, and image conditional generation. To our knowledge, this is the first instance of a multimodal Large Language Model (LLM) being successfully applied to parametric CAD generation, representing a pioneering step in the field of computer-aided mechanical design.

Large Language Models (LLMs) have demonstrated impressive capabilities in a wide range of code generation tasks. However, generating code for certain domains remains challenging. One such domain is Computer-Aided Design (CAD) program, where the goal is to produce scripted parametric models that define object geometry for precise design and manufacturing applications. A key challenge in LLM-based CAD program generation is the limited geometric complexity of generated shapes compared to those found in real-world industrial designs. This shortfall is in part due to the lack of diversity in the available CAD program training data. To address this, we propose a novel data augmentation paradigm that prompts an LLM to generate CAD programs conditioned on a reference surface program and a modeling procedure - an idea inspired by practices in industrial design. By varying the reference surface using a collection of organic shapes, our method enriches the geometric distribution of generated CAD models. In particular, it introduces edges and faces defined by spline-based curvature, which are typically missing or underrepresented in existing open-source CAD program datasets. Experiments show that our method produces CAD samples with significantly greater geometric diversity and a higher resemblance to industry-grade CAD designs in terms of the proportion of organic shape primitives. This enhancement makes our CAD data augmentation approach a useful tool for training LLMs and other deep learning models in CAD generation.

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.

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.

In order to properly train a machine learning model, data must be properly collected. To guarantee a proper data collection, verifying that the collected data set holds certain properties is a possible solution. For example, guaranteeing that the data set contains samples across the whole input space, or that the data set is balanced w.r.t. different classes. We present a formal approach for verifying a set of arbitrarily stated properties over a data set. The proposed approach relies on the transformation of the data set into a first order logic formula, which can be later verified w.r.t. the different properties also stated in the same logic. A prototype tool, which uses the z3 solver, has been developed; the prototype can take as an input a set of properties stated in a formal language and formally verify a given data set w.r.t. to the given set of properties. Preliminary experimental results show the feasibility and performance of the proposed approach, and furthermore the flexibility for expressing properties of interest.

Parametric human body models are foundational to human reconstruction, animation, and simulation, yet they remain mutually incompatible: SMPL, SMPL-X, MHR, Anny, and related models each diverge in mesh topology, skeletal structure, shape parameterization, and unit convention, making it impractical to exploit their complementary strengths within a single pipeline. We present SOMA, a unified body layer that bridges these heterogeneous representations through three abstraction layers. Mesh topology abstraction maps any source model's identity to a shared canonical mesh in constant time per vertex. Skeletal abstraction recovers a full set of identity-adapted joint transforms from any body shape, whether in rest pose or an arbitrary posed configuration, in a single closed-form pass, with no iterative optimization or per-model training. Pose abstraction inverts the skinning pipeline to recover unified skeleton rotations directly from posed vertices of any supported model, enabling heterogeneous motion datasets to be consumed without custom retargeting. Together, these layers reduce the O(M^2) per-pair adapter problem to O(M) single-backend connectors, letting practitioners freely mix identity sources and pose data at inference time. The entire pipeline is fully differentiable end-to-end and GPU-accelerated via NVIDIA-Warp.

Given the exponential growth of the volume of the ball w.r.t. its radius, the hyperbolic space is capable of embedding trees with arbitrarily small distortion and hence has received wide attention for representing hierarchical datasets. However, this exponential growth property comes at a price of numerical instability such that training hyperbolic learning models will sometimes lead to catastrophic NaN problems, encountering unrepresentable values in floating point arithmetic. In this work, we carefully analyze the limitation of two popular models for the hyperbolic space, namely, the Poincar\'e ball and the Lorentz model. We first show that, under the 64 bit arithmetic system, the Poincar\'e ball has a relatively larger capacity than the Lorentz model for correctly representing points. Then, we theoretically validate the superiority of the Lorentz model over the Poincar\'e ball from the perspective of optimization. Given the numerical limitations of both models, we identify one Euclidean parametrization of the hyperbolic space which can alleviate these limitations. We further extend this Euclidean parametrization to hyperbolic hyperplanes and exhibits its ability in improving the performance of hyperbolic SVM.

The complexity of learning a concept class under Gaussian marginals in the difficult agnostic model is closely related to its L_1-approximability by low-degree polynomials. For any concept class with Gaussian surface area at most Γ, Klivans et al. (2008) show that degree d = O(Γ^2 / varepsilon^4) suffices to achieve an varepsilon-approximation. This leads to the best-known bounds on the complexity of learning a variety of concept classes. In this note, we improve their analysis by showing that degree d = tilde O (Γ^2 / varepsilon^2) is enough. In light of lower bounds due to Diakonikolas et al. (2021), this yields (near) optimal bounds on the complexity of agnostically learning polynomial threshold functions in the statistical query model. Our proof relies on a direct analogue of a construction of Feldman et al. (2020), who considered L_1-approximation on the Boolean hypercube.

We study the problem of learning hierarchical polynomials over the standard Gaussian distribution with three-layer neural networks. We specifically consider target functions of the form h = g circ p where p : R^d rightarrow R is a degree k polynomial and g: R rightarrow R is a degree q polynomial. This function class generalizes the single-index model, which corresponds to k=1, and is a natural class of functions possessing an underlying hierarchical structure. Our main result shows that for a large subclass of degree k polynomials p, a three-layer neural network trained via layerwise gradient descent on the square loss learns the target h up to vanishing test error in mathcal{O}(d^k) samples and polynomial time. This is a strict improvement over kernel methods, which require widetilde Theta(d^{kq}) samples, as well as existing guarantees for two-layer networks, which require the target function to be low-rank. Our result also generalizes prior works on three-layer neural networks, which were restricted to the case of p being a quadratic. When p is indeed a quadratic, we achieve the information-theoretically optimal sample complexity mathcal{O}(d^2), which is an improvement over prior work~nichani2023provable requiring a sample size of widetildeTheta(d^4). Our proof proceeds by showing that during the initial stage of training the network performs feature learning to recover the feature p with mathcal{O}(d^k) samples. This work demonstrates the ability of three-layer neural networks to learn complex features and as a result, learn a broad class of hierarchical functions.

Creating Computer-Aided Design (CAD) models requires significant expertise and effort. Text-to-CAD, which converts textual descriptions into CAD parametric sequences, is crucial in streamlining this process. Recent studies have utilized ground-truth parametric sequences, known as sequential signals, as supervision to achieve this goal. However, CAD models are inherently multimodal, comprising parametric sequences and corresponding rendered visual objects. Besides,the rendering process from parametric sequences to visual objects is many-to-one. Therefore, both sequential and visual signals are critical for effective training. In this work, we introduce CADFusion, a framework that uses Large Language Models (LLMs) as the backbone and alternates between two training stages: the sequential learning (SL) stage and the visual feedback (VF) stage. In the SL stage, we train LLMs using ground-truth parametric sequences, enabling the generation of logically coherent parametric sequences. In the VF stage, we reward parametric sequences that render into visually preferred objects and penalize those that do not, allowing LLMs to learn how rendered visual objects are perceived and evaluated. These two stages alternate throughout the training, ensuring balanced learning and preserving benefits of both signals. Experiments demonstrate that CADFusion significantly improves performance, both qualitatively and quantitatively.

The study emphasizes the challenge of finding the optimal trade-off between bias and variance, especially as hyperparameter optimization increases in complexity. Through empirical analysis, three hyperparameter tuning algorithms Tree-structured Parzen Estimator (TPE), Genetic Search, and Random Search are evaluated across regression and classification tasks. The results show that nonlinear models, with properly tuned hyperparameters, significantly outperform linear models. Interestingly, Random Search excelled in regression tasks, while TPE was more effective for classification tasks. This suggests that there is no one-size-fits-all solution, as different algorithms perform better depending on the task and model type. The findings underscore the importance of selecting the appropriate tuning method and highlight the computational challenges involved in optimizing machine learning models, particularly as search spaces expand.

We introduce a new approach to nonlinear sufficient dimension reduction in cases where both the predictor and the response are distributional data, modeled as members of a metric space. Our key step is to build universal kernels (cc-universal) on the metric spaces, which results in reproducing kernel Hilbert spaces for the predictor and response that are rich enough to characterize the conditional independence that determines sufficient dimension reduction. For univariate distributions, we construct the universal kernel using the Wasserstein distance, while for multivariate distributions, we resort to the sliced Wasserstein distance. The sliced Wasserstein distance ensures that the metric space possesses similar topological properties to the Wasserstein space while also offering significant computation benefits. Numerical results based on synthetic data show that our method outperforms possible competing methods. The method is also applied to several data sets, including fertility and mortality data and Calgary temperature data.

In the realm of 3D computer vision, parametric models have emerged as a ground-breaking methodology for the creation of realistic and expressive 3D avatars. Traditionally, they rely on Principal Component Analysis (PCA), given its ability to decompose data to an orthonormal space that maximally captures shape variations. However, due to the orthogonality constraints and the global nature of PCA's decomposition, these models struggle to perform localized and disentangled editing of 3D shapes, which severely affects their use in applications requiring fine control such as face sculpting. In this paper, we leverage diffusion models to enable diverse and fully localized edits on 3D meshes, while completely preserving the un-edited regions. We propose an effective diffusion masking training strategy that, by design, facilitates localized manipulation of any shape region, without being limited to predefined regions or to sparse sets of predefined control vertices. Following our framework, a user can explicitly set their manipulation region of choice and define an arbitrary set of vertices as handles to edit a 3D mesh. Compared to the current state-of-the-art our method leads to more interpretable shape manipulations than methods relying on latent code state, greater localization and generation diversity while offering faster inference than optimization based approaches. Project page: https://rolpotamias.github.io/Shapefusion/

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.

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.

We consider the problem of how a teacher algorithm can enable an unknown Deep Reinforcement Learning (DRL) student to become good at a skill over a wide range of diverse environments. To do so, we study how a teacher algorithm can learn to generate a learning curriculum, whereby it sequentially samples parameters controlling a stochastic procedural generation of environments. Because it does not initially know the capacities of its student, a key challenge for the teacher is to discover which environments are easy, difficult or unlearnable, and in what order to propose them to maximize the efficiency of learning over the learnable ones. To achieve this, this problem is transformed into a surrogate continuous bandit problem where the teacher samples environments in order to maximize absolute learning progress of its student. We present a new algorithm modeling absolute learning progress with Gaussian mixture models (ALP-GMM). We also adapt existing algorithms and provide a complete study in the context of DRL. Using parameterized variants of the BipedalWalker environment, we study their efficiency to personalize a learning curriculum for different learners (embodiments), their robustness to the ratio of learnable/unlearnable environments, and their scalability to non-linear and high-dimensional parameter spaces. Videos and code are available at https://github.com/flowersteam/teachDeepRL.

Class-incremental learning (CIL) is a particularly challenging variant of continual learning, where the goal is to learn to discriminate between all classes presented in an incremental fashion. Existing approaches often suffer from excessive forgetting and imbalance of the scores assigned to classes that have not been seen together during training. In this study, we introduce a novel approach, Prediction Error-based Classification (PEC), which differs from traditional discriminative and generative classification paradigms. PEC computes a class score by measuring the prediction error of a model trained to replicate the outputs of a frozen random neural network on data from that class. The method can be interpreted as approximating a classification rule based on Gaussian Process posterior variance. PEC offers several practical advantages, including sample efficiency, ease of tuning, and effectiveness even when data are presented one class at a time. Our empirical results show that PEC performs strongly in single-pass-through-data CIL, outperforming other rehearsal-free baselines in all cases and rehearsal-based methods with moderate replay buffer size in most cases across multiple benchmarks.

The paper shows that the application of the fixed-effect multiple linear regression model to an overparameterized dataset is equivalent to fitting the data with a hyper-curve parameterized by a single scalar parameter. This equivalence allows for a predictor-focused approach, where each predictor is described by a function of the chosen parameter. It is proven that a linear model will produce exact predictions even in the presence of nonlinear dependencies that violate the model assumptions. Parameterization in terms of the dependent variable and the monomial basis in the predictor function space are applied here to both synthetic and experimental data. The hyper-curve approach is especially suited for the regularization of problems with noise in predictor variables and can be used to remove noisy and "improper" predictors from the model.

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.

A primary cost driver for training large models is wall-clock training time. We show that popular time estimates based on FLOPs are poor estimates, and construct a more accurate proxy based on memory copies. We show that with some simple accounting, we can estimate the training speed of a transformer model from its hyperparameters. Combined with a scaling law curve like Chinchilla, this lets us estimate the final loss of the model. We fit our estimate to real data with a linear regression, and apply the result to rewrite Chinchilla in terms of a model's estimated training time as opposed to the amount of training data. This gives an expression for the loss in terms of the model's hyperparameters alone. We show that this expression is accurate across a wide range of model hyperparameter values, enabling us to analytically make architectural decisions and train models more efficiently.

In "Backprop as functor", the authors show that the fundamental elements of deep learning -- gradient descent and backpropagation -- can be conceptualized as a strong monoidal functor Para(Euc)toLearn from the category of parameterized Euclidean spaces to that of learners, a category developed explicitly to capture parameter update and backpropagation. It was soon realized that there is an isomorphism LearncongPara(Slens), where Slens is the symmetric monoidal category of simple lenses as used in functional programming. In this note, we observe that Slens is a full subcategory of Poly, the category of polynomial functors in one variable, via the functor Amapsto Ay^A. Using the fact that (Poly,otimes) is monoidal closed, we show that a map Ato B in Para(Slens) has a natural interpretation in terms of dynamical systems (more precisely, generalized Moore machines) whose interface is the internal-hom type [Ay^A,By^B]. Finally, we review the fact that the category p-Coalg of dynamical systems on any p in Poly forms a topos, and consider the logical propositions that can be stated in its internal language. We give gradient descent as an example, and we conclude by discussing some directions for future work.

We study robustness to test-time adversarial attacks in the regression setting with ell_p losses and arbitrary perturbation sets. We address the question of which function classes are PAC learnable in this setting. We show that classes of finite fat-shattering dimension are learnable in both realizable and agnostic settings. Moreover, for convex function classes, they are even properly learnable. In contrast, some non-convex function classes provably require improper learning algorithms. Our main technique is based on a construction of an adversarially robust sample compression scheme of a size determined by the fat-shattering dimension. Along the way, we introduce a novel agnostic sample compression scheme for real-valued functions, which may be of independent interest.

Practitioners frequently aim to infer an unobserved population trajectory using sample snapshots at multiple time points. For instance, in single-cell sequencing, scientists would like to learn how gene expression evolves over time. But sequencing any cell destroys that cell. So we cannot access any cell's full trajectory, but we can access snapshot samples from many cells. Stochastic differential equations are commonly used to analyze systems with full individual-trajectory access; since here we have only sample snapshots, these methods are inapplicable. The deep learning community has recently explored using Schr\"odinger bridges (SBs) and their extensions to estimate these dynamics. However, these methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic within the SB, which is often just set to be Brownian motion. But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. In particular, we suggest an iterative projection method inspired by Schr\"odinger bridges; we alternate between learning a piecewise SB on the unobserved trajectories and using the learned SB to refine our best guess for the dynamics within the reference class. We demonstrate the advantages of our method via a well-known simulated parametric model from ecology, simulated and real data from systems biology, and real motion-capture data.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

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.

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.

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.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

Parametric body models offer expressive 3D representation of humans across a wide range of poses, shapes, and facial expressions, typically derived by learning a basis over registered 3D meshes. However, existing human mesh modeling approaches struggle to capture detailed variations across diverse body poses and shapes, largely due to limited training data diversity and restrictive modeling assumptions. Moreover, the common paradigm first optimizes the external body surface using a linear basis, then regresses internal skeletal joints from surface vertices. This approach introduces problematic dependencies between internal skeleton and outer soft tissue, limiting direct control over body height and bone lengths. To address these issues, we present ATLAS, a high-fidelity body model learned from 600k high-resolution scans captured using 240 synchronized cameras. Unlike previous methods, we explicitly decouple the shape and skeleton bases by grounding our mesh representation in the human skeleton. This decoupling enables enhanced shape expressivity, fine-grained customization of body attributes, and keypoint fitting independent of external soft-tissue characteristics. ATLAS outperforms existing methods by fitting unseen subjects in diverse poses more accurately, and quantitative evaluations show that our non-linear pose correctives more effectively capture complex poses compared to linear models.

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

Analysis of faces is one of the core applications of computer vision, with tasks ranging from landmark alignment, head pose estimation, expression recognition, and face recognition among others. However, building reliable methods requires time-consuming data collection and often even more time-consuming manual annotation, which can be unreliable. In our work we propose synthesizing such facial data, including ground truth annotations that would be almost impossible to acquire through manual annotation at the consistency and scale possible through use of synthetic data. We use a parametric face model together with hand crafted assets which enable us to generate training data with unprecedented quality and diversity (varying shape, texture, expression, pose, lighting, and hair).

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.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance varepsilon, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as varepsilon varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension, and under mild assumptions on the data distribution, we rigorously prove that one can use the initial value problem starting from varepsilon=0, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem for small values of varepsilon. In higher dimensions we provide a similar result, albeit conditional to the existence of regular solutions of the initial value problem. In the process of proving our main results we obtain a result of independent interest connecting the original adversarial problem with an optimal transport problem under no assumptions on whether classes are balanced or not. Numerical examples illustrating these ideas are also presented.

Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the over-parameterized regime, we examine a parallel direction: do similar scaling laws govern predictive uncertainties in deep learning? In identifiable parametric models, such scaling laws can be derived in a straightforward manner by treating model parameters in a Bayesian way. In this case, for example, we obtain O(1/N) contraction rates for epistemic uncertainty with respect to the number of data N. However, in over-parameterized models, these guarantees do not hold, leading to largely unexplored behaviors. In this work, we empirically show the existence of scaling laws associated with various measures of predictive uncertainty with respect to dataset and model sizes. Through experiments on vision and language tasks, we observe such scaling laws for in- and out-of-distribution predictive uncertainty estimated through popular approximate Bayesian inference and ensemble methods. Besides the elegance of scaling laws and the practical utility of extrapolating uncertainties to larger data or models, this work provides strong evidence to dispel recurring skepticism against Bayesian approaches: "In many applications of deep learning we have so much data available: what do we need Bayes for?". Our findings show that "so much data" is typically not enough to make epistemic uncertainty negligible.

Large Language Models (LLMs) have shown strong performance on programming tasks, but can they generate student-like code like real students - imperfect, iterative, and stylistically diverse? We present ParaStudent, a systematic study of LLM-based "student-like" code generation in an introductory programming course setting. Using a dataset of timestamped student submissions across multiple semesters, we design low- and high-resolution experiments to model student progress and evaluate code outputs along semantic, functional, and stylistic dimensions. Our results show that fine-tuning significantly improves alignment with real student trajectories and captures error patterns, incremental improvements, and stylistic variations more faithfully. This study shows that modeling realistic student code requires capturing learning dynamics through context-aware generation, temporal modeling, and multi-dimensional evaluation. Code for experiments and evaluation is available at https://github.com/mmiroyan/ParaStudent.

We study the problem of teaching multiple learners simultaneously in the nonparametric iterative teaching setting, where the teacher iteratively provides examples to the learner for accelerating the acquisition of a target concept. This problem is motivated by the gap between current single-learner teaching setting and the real-world scenario of human instruction where a teacher typically imparts knowledge to multiple students. Under the new problem formulation, we introduce a novel framework -- Multi-learner Nonparametric Teaching (MINT). In MINT, the teacher aims to instruct multiple learners, with each learner focusing on learning a scalar-valued target model. To achieve this, we frame the problem as teaching a vector-valued target model and extend the target model space from a scalar-valued reproducing kernel Hilbert space used in single-learner scenarios to a vector-valued space. Furthermore, we demonstrate that MINT offers significant teaching speed-up over repeated single-learner teaching, particularly when the multiple learners can communicate with each other. Lastly, we conduct extensive experiments to validate the practicality and efficiency of MINT.

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.

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 SuperClass, a super simple classification method for vision-language pre-training on image-text data. Unlike its contrastive counterpart CLIP who contrast with a text encoder, SuperClass directly utilizes tokenized raw text as supervised classification labels, without the need for additional text filtering or selection. Due to the absence of the text encoding as contrastive target, SuperClass does not require a text encoder and does not need to maintain a large batch size as CLIP does. SuperClass demonstrated superior performance on various downstream tasks, including classic computer vision benchmarks and vision language downstream tasks. We further explored the scaling behavior of SuperClass on model size, training length, or data size, and reported encouraging results and comparisons to CLIP. https://github.com/x-cls/superclass

We introduce BeepBank-500, a compact, fully synthetic earcon/alert dataset (300-500 clips) designed for rapid, rights-clean experimentation in human-computer interaction and audio machine learning. Each clip is generated from a parametric recipe controlling waveform family (sine, square, triangle, FM), fundamental frequency, duration, amplitude envelope, amplitude modulation (AM), and lightweight Schroeder-style reverberation. We use three reverberation settings: dry, and two synthetic rooms denoted 'rir small' ('small') and 'rir medium' ('medium') throughout the paper and in the metadata. We release mono 48 kHz WAV audio (16-bit), a rich metadata table (signal/spectral features), and tiny reproducible baselines for (i) waveform-family classification and (ii) f0 regression on single tones. The corpus targets tasks such as earcon classification, timbre analyses, and onset detection, with clearly stated licensing and limitations. Audio is dedicated to the public domain via CC0-1.0; code is under MIT. Data DOI: https://doi.org/10.5281/zenodo.17172015. Code: https://github.com/mandip42/earcons-mini-500.