Diffusion-based algorithms have emerged as promising techniques for weight generation, particularly in scenarios like multi-task learning that require frequent weight updates. However, existing solutions suffer from limited cross-task transferability. In addition, they only utilize optimal weights as training samples, ignoring the value of other weights in the optimization process. To address these issues, we propose Lt-Di, which integrates the diffusion algorithm with meta-learning to generate weights for unseen tasks. Furthermore, we extend the vanilla diffusion algorithm into a trajectory diffusion algorithm to utilize other weights along the optimization trajectory. Trajectory diffusion decomposes the entire diffusion chain into multiple shorter ones, improving training and inference efficiency. We analyze the convergence properties of the weight generation paradigm and improve convergence efficiency without additional time overhead. Our experiments demonstrate Lt-Di's higher accuracy while reducing computational overhead across various tasks, including zero-shot and few-shot learning, multi-domain generalization, and large-scale language model fine-tuning.Our code is released at https://github.com/tuantuange/Lt-Di.

Grokking, or delayed generalization, is an intriguing learning phenomenon where test set loss decreases sharply only after a model's training set loss has converged. This challenges conventional understanding of the training dynamics in deep learning networks. In this paper, we formalize and investigate grokking, highlighting that a key factor in its emergence is a distribution shift between training and test data. We introduce two synthetic datasets specifically designed to analyze grokking. One dataset examines the impact of limited sampling, and the other investigates transfer learning's role in grokking. By inducing distribution shifts through controlled imbalanced sampling of sub-categories, we systematically reproduce the phenomenon, demonstrating that while small-sampling is strongly associated with grokking, it is not its cause. Instead, small-sampling serves as a convenient mechanism for achieving the necessary distribution shift. We also show that when classes form an equivariant map, grokking can be explained by the model's ability to learn from similar classes or sub-categories. Unlike earlier work suggesting that grokking primarily arises from high regularization and sparse data, we demonstrate that it can also occur with dense data and minimal hyper-parameter tuning. Our findings deepen the understanding of grokking and pave the way for developing better stopping criteria in future training processes.

With climate change expected to exacerbate fire weather conditions, the accurate and timely anticipation of wildfires becomes increasingly crucial for disaster mitigation. In this study, we utilize SeasFire, a comprehensive global wildfire dataset with climate, vegetation, oceanic indices, and human-related variables, to enable seasonal wildfire forecasting with machine learning. For the predictive analysis, we present FireCastNet, a novel architecture which combines a 3D convolutional encoder with GraphCast, originally developed for global short-term weather forecasting using graph neural networks. FireCastNet is trained to capture the context leading to wildfires, at different spatial and temporal scales. Our investigation focuses on assessing the effectiveness of our model in predicting the presence of burned areas at varying forecasting time horizons globally, extending up to six months into the future, and on how different spatial or/and temporal context affects the performance. Our findings demonstrate the potential of deep learning models in seasonal fire forecasting; longer input time-series leads to more robust predictions, while integrating spatial information to capture wildfire spatio-temporal dynamics boosts performance. Finally, our results hint that in order to enhance performance at longer forecasting horizons, a larger receptive field spatially needs to be considered.

Multi-index models provide a popular framework to investigate the learnability of functions with low-dimensional structure and, also due to their connections with neural networks, they have been object of recent intensive study. In this paper, we focus on recovering the subspace spanned by the signals via spectral estimators -- a family of methods that are routinely used in practice, often as a warm-start for iterative algorithms. Our main technical contribution is a precise asymptotic characterization of the performance of spectral methods, when sample size and input dimension grow proportionally and the dimension $p$ of the space to recover is fixed. Specifically, we locate the top-$p$ eigenvalues of the spectral matrix and establish the overlaps between the corresponding eigenvectors (which give the spectral estimators) and a basis of the signal subspace. Our analysis unveils a phase transition phenomenon in which, as the sample complexity grows, eigenvalues escape from the bulk of the spectrum and, when that happens, eigenvectors recover directions of the desired subspace. The precise characterization we put forward enables the optimization of the data preprocessing, thus allowing to identify the spectral estimator that requires the minimal sample size for weak recovery.

Gradient Boosting Decision Tree (GBDT) is one of the most popular machine learning models in various applications. However, in the traditional settings, all data should be simultaneously accessed in the training procedure: it does not allow to add or delete any data instances after training. In this paper, we propose an efficient online learning framework for GBDT supporting both incremental and decremental learning. To the best of our knowledge, this is the first work that considers an in-place unified incremental and decremental learning on GBDT. To reduce the learning cost, we present a collection of optimizations for our framework, so that it can add or delete a small fraction of data on the fly. We theoretically show the relationship between the hyper-parameters of the proposed optimizations, which enables trading off accuracy and cost on incremental and decremental learning. The backdoor attack results show that our framework can successfully inject and remove backdoor in a well-trained model using incremental and decremental learning, and the empirical results on public datasets confirm the effectiveness and efficiency of our proposed online learning framework and optimizations.

Layer-wise preconditioning methods are a family of memory-efficient optimization algorithms that introduce preconditioners per axis of each layer's weight tensors. These methods have seen a recent resurgence, demonstrating impressive performance relative to entry-wise ("diagonal") preconditioning methods such as Adam(W) on a wide range of neural network optimization tasks. Complementary to their practical performance, we demonstrate that layer-wise preconditioning methods are provably necessary from a statistical perspective. To showcase this, we consider two prototypical models, linear representation learning and single-index learning, which are widely used to study how typical algorithms efficiently learn useful features to enable generalization. In these problems, we show SGD is a suboptimal feature learner when extending beyond ideal isotropic inputs $\mathbf{x} \sim \mathsf{N}(\mathbf{0}, \mathbf{I})$ and well-conditioned settings typically assumed in prior work. We demonstrate theoretically and numerically that this suboptimality is fundamental, and that layer-wise preconditioning emerges naturally as the solution. We further show that standard tools like Adam preconditioning and batch-norm only mildly mitigate these issues, supporting the unique benefits of layer-wise preconditioning.

In experimental settings with network interference, a unit's treatment can influence outcomes of other units, challenging both causal effect estimation and its validation. Classic validation approaches fail as outcomes are only observable under one treatment scenario and exhibit complex correlation patterns due to interference. To address these challenges, we introduce a new framework enabling cross-validation for counterfactual estimation. At its core is our distribution-preserving network bootstrap method -- a theoretically-grounded approach inspired by approximate message passing. This method creates multiple subpopulations while preserving the underlying distribution of network effects. We extend recent causal message-passing developments by incorporating heterogeneous unit-level characteristics and varying local interactions, ensuring reliable finite-sample performance through non-asymptotic analysis. We also develop and publicly release a comprehensive benchmark toolbox with diverse experimental environments, from networks of interacting AI agents to opinion formation in real-world communities and ride-sharing applications. These environments provide known ground truth values while maintaining realistic complexities, enabling systematic examination of causal inference methods. Extensive evaluation across these environments demonstrates our method's robustness to diverse forms of network interference. Our work provides researchers with both a practical estimation framework and a standardized platform for testing future methodological developments.

This paper presents a methodology combining multimodal semantic analysis with an eye-tracking experimental protocol to investigate the cognitive effort involved in understanding the communication of future scenarios. To demonstrate the methodology, we conduct a pilot study examining how visual fixation patterns vary during the evaluation of valence and counterfactuality in fictional ad pieces describing futuristic scenarios, using a portable eye tracker. Participants eye movements are recorded while evaluating the stimuli and describing them to a conversation partner. Gaze patterns are analyzed alongside semantic representations of the stimuli and participants descriptions, constructed from a frame semantic annotation of both linguistic and visual modalities. Preliminary results show that far-future and pessimistic scenarios are associated with longer fixations and more erratic saccades, supporting the hypothesis that fractures in the base spaces underlying the interpretation of future scenarios increase cognitive load for comprehenders.

Neural network based Optimal Transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing approaches to OT, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural networks). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for more general OT formulations, paving the promising direction for future research.

Thanks to their compliance and adaptability, soft robots can be deployed to perform tasks in constrained or complex environments. In these scenarios, spatial awareness of the surroundings and the ability to localize the robot within the environment represent key aspects. While state-of-the-art localization techniques are well-explored in autonomous vehicles and walking robots, they rely on data retrieved with lidar or depth sensors which are bulky and thus difficult to integrate into small soft robots. Recent developments in miniaturized Time of Flight (ToF) sensors show promise as a small and lightweight alternative to bulky sensors. These sensors can be potentially distributed on the soft robot body, providing multi-point depth data of the surroundings. However, the small spatial resolution and the noisy measurements pose a challenge to the success of state-of-the-art localization algorithms, which are generally applied to much denser and more reliable measurements. In this paper, we enforce distributed VL53L5CX ToF sensors, mount them on the tip of a soft robot, and investigate their usage for self-localization tasks. Experimental results show that the soft robot can effectively be localized with respect to a known map, with an error comparable to the uncertainty on the measures provided by the miniaturized ToF sensors.