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Time Series

Shivam Grover, Amin Jalali, Ali Etemad

Existing approaches for learning representations of time-series keep the temporal arrangement of the time-steps intact with the presumption that the original order is the most optimal for learning. However, non-adjacent sections of real-world time-series may have strong dependencies. Accordingly, we raise the question: Is there an alternative arrangement for time-series which could enable more effective representation learning? To address this, we propose a simple plug-and-play neural network layer called Segment, Shuffle, and Stitch (S3) designed to improve representation learning in time-series models. S3 works by creating non-overlapping segments from the original sequence and shuffling them in a learned manner that is optimal for the task at hand. It then re-attaches the shuffled segments back together and performs a learned weighted sum with the original input to capture both the newly shuffled sequence along with the original sequence. S3 is modular and can be stacked to achieve different levels of granularity, and can be added to many forms of neural architectures including CNNs or Transformers with negligible computation overhead. Through extensive experiments on several datasets and state-of-the-art baselines, we show that incorporating S3 results in significant improvements for the tasks of time-series classification, forecasting, and anomaly detection, improving performance on certain datasets by up to 68\%. We also show that S3 makes the learning more stable with a smoother training loss curve and loss landscape compared to the original baseline. The code is available at https://github.com/shivam-grover/S3-TimeSeries.

Reinforcement Learning · Deep RL

Wesley Chung, Lynn Cherif, Doina Precup, David Meger

Plasticity loss, trainability loss, and primacy bias have been identified as issues arising when training deep neural networks on sequences of tasks---referring to the increased difficulty in training on new tasks.We propose to use Parseval regularization, which maintains orthogonality of weight matrices, to preserve useful optimization properties and improve training in a continual reinforcement learning setting.We show that it provides significant benefits to RL agents on a suite of gridworld, CARL and MetaWorld tasks.We conduct comprehensive ablations to identify the source of its benefits and investigate the effect of certain metrics associated to network trainability including weight matrix rank, weight norms and policy entropy.

Trustworthy Machine Learning

Frederik Hoppe, Claudio Mayrink Verdun, Hannah Laus, Felix Krahmer, Holger Rauhut

Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that applies both to classical optimization approaches such as the LASSO as well as to neural networks. One of the most notable UQ techniques is the debiased LASSO, which modifies the LASSO to allow for the construction of asymptotic confidence intervals by decomposing the estimation error into a Gaussian and an asymptotically vanishing bias component. However, in real-world problems with finite-dimensional data, the bias term is often too significant to disregard, resulting in overly narrow confidence intervals. Our work rigorously addresses this issue and derives a data-driven adjustment that corrects the confidence intervals for a large class of predictors by estimating the means and variances of the bias terms from training data, exploiting high-dimensional concentration phenomena. This gives rise to non-asymptotic confidence intervals, which can help avoid overestimating certainty in critical applications such as MRI diagnosis. Importantly, our analysis extends beyond sparse regression to data-driven predictors like neural networks, enhancing the reliability of model-based deep learning. Our findings bridge the gap between established theory and the practical applicability of such methods.

Generative Models · New Approaches

Peter Sorrenson, Felix Draxler, Armand Rousselot, Sander Hummerich, Ullrich Köthe

We propose Manifold Free-Form Flows (M-FFF), a simple new generative model for data on manifolds. The existing approaches to learning a distribution on arbitrary manifolds are expensive at inference time, since sampling requires solving a differential equation. Our method overcomes this limitation by sampling in a single function evaluation. The key innovation is to optimize a neural network via maximum likelihood on the manifold, possible by adapting the free-form flow framework to Riemannian manifolds. M-FFF is straightforwardly adapted to any manifold with a known projection. It consistently matches or outperforms previous single-step methods specialized to specific manifolds. It is typically two orders of magnitude faster than multi-step methods based on diffusion or flow matching, achieving better likelihoods in several experiments. We provide our code at https://github.com/vislearn/FFF.

Graph Neural Networks

Shijin Duan, Ruyi Ding, Jiaxing He, Aidong Ding, Yunsi Fei, Xiaolin Xu

Graph-structured data is integral to many applications, prompting the development of various graph representation methods. Graph autoencoders (GAEs), in particular, reconstruct graph structures from node embeddings. Current GAE models primarily utilize self-correlation to represent graph structures and focus on node-level tasks, often overlooking multi-graph scenarios. Our theoretical analysis indicates that self-correlation generally falls short in accurately representing specific graph features such as islands, symmetrical structures, and directional edges, particularly in smaller or multiple graph contexts.To address these limitations, we introduce a cross-correlation mechanism that significantly enhances the GAE representational capabilities. Additionally, we propose the GraphCroc, a new GAE that supports flexible encoder architectures tailored for various downstream tasks and ensures robust structural reconstruction, through a mirrored encoding-decoding process. This model also tackles the challenge of representation bias during optimization by implementing a loss-balancing strategy. Both theoretical analysis and numerical evaluations demonstrate that our methodology significantly outperforms existing self-correlation-based GAEs in graph structure reconstruction.

Deep Learning · Theory

Evan Markou, Thalaiyasingam Ajanthan, Stephen Gould

Neural Collapse (NC) is a recently observed phenomenon in neural networks that characterises the solution space of the final classifier layer when trained until zero training loss. Specifically, NC suggests that the final classifier layer converges to a Simplex Equiangular Tight Frame (ETF), which maximally separates the weights corresponding to each class. By duality, the penultimate layer feature means also converge to the same simplex ETF. Since this simple symmetric structure is optimal, our idea is to utilise this property to improve convergence speed. Specifically, we introduce the notion of \textit{nearest simplex ETF geometry} for the penultimate layer features at any given training iteration, by formulating it as a Riemannian optimisation. Then, at each iteration, the classifier weights are implicitly set to the nearest simplex ETF by solving this inner-optimisation, which is encapsulated within a declarative node to allow backpropagation. Our experiments on synthetic and real-world architectures on classification tasks demonstrate that our approach accelerates convergence and enhances training stability.

Neuroscience, Cognitive Science

Klara Kaleb, Barbara Feulner, Juan Gallego, Claudia Clopath

How do brain circuits learn to generate behaviour? While significant strides have been made in understanding learning in artificial neural networks, applying this knowledge to biological networks remains challenging. For instance, while backpropagation is known to perform accurate credit assignment of error in artificial neural networks, how a similarly powerful process can be realized within the constraints of biological circuits remains largely unclear. One of the major challenges is that the brain's extensive recurrent connectivity requires the propagation of error through both space and time, a problem that is notoriously difficult to solve in vanilla recurrent neural networks. Moreover, the extensive feedback connections in the brain are known to influence forward network activity, but the interaction between feedback-driven activity changes and local, synaptic plasticity-based learning is not fully understood. Building on our previous work modelling motor learning, this work investigates the mechanistic properties of pre-trained networks with feedback control on a standard motor task. We show that feedback control of the ongoing recurrent network dynamics approximates the optimal first-order gradient with respect to the network activities, allowing for rapid, ongoing movement correction. Moreover, we show that trial-by-trial adaptation to a persistent perturbation using a local, biologically plausible learning rule that integrates recent activity and error feedback is both more accurate and more efficient with feedback control during learning, due to the decoupling of the recurrent network dynamics and the injection of an adaptive, second-order gradient into the network dynamics. Thus, our results suggest that feedback control may guide credit assignment in biological recurrent neural networks, enabling both rapid and efficient learning in the brain.

Haixu Wu, Huakun Luo, Yuezhou Ma, Jianmin Wang, Mingsheng Long

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation, PINNs are conventionally optimized on finite selected points. However, since PDEs are usually defined on continuous domains, solely optimizing models on scattered points may be insufficient to obtain an accurate solution for the whole domain. To mitigate this inherent deficiency of the default scatter-point optimization, this paper proposes and theoretically studies a new training paradigm as region optimization. Concretely, we propose to extend the optimization process of PINNs from isolated points to their continuous neighborhood regions, which can theoretically decrease the generalization error, especially for hidden high-order constraints of PDEs. A practical training algorithm, Region Optimized PINN (RoPINN), is seamlessly derived from this new paradigm, which is implemented by a straightforward but effective Monte Carlo sampling method. By calibrating the sampling process into trust regions, RoPINN finely balances optimization and generalization error. Experimentally, RoPINN consistently boosts the performance of diverse PINNs on a wide range of PDEs without extra backpropagation or gradient calculation. Code is available at this repository: https://github.com/thuml/RoPINN.

Computer Vision · Stereo

Liqiang Lin, Wenpeng Wu, Chi-Wing Fu, Hao Zhang, Hui Huang

We introduce camera ray matching (CRAYM) into the joint optimization of camera poses and neural fields from multi-view images. The optimized field, referred to as a feature volume, can be “probed” by the camera rays for novel view synthesis (NVS) and 3D geometry reconstruction. One key reason for matching camera rays, instead of pixels as in prior works, is that the camera rays can be parameterized by the feature volume to carry both geometric and photometric information. Multi-view consistencies involving the camera rays and scene rendering can be naturally integrated into the joint optimization and network training, to impose physically meaningful constraints to improve the final quality of both the geometric reconstruction and photorealistic rendering. We formulate our per-ray optimization and matched ray coherence by focusing on camera rays passing through keypoints in the input images to elevate both the efficiency and accuracy of scene correspondences. Accumulated ray features along the feature volume provide a means to discount the coherence constraint amid erroneous ray matching. We demonstrate the effectiveness of CRAYM for both NVS and geometry reconstruction, over dense- or sparse-view settings, with qualitative and quantitative comparisons to state-of-the-art alternatives.

Learning Theory

Hongyu Cheng, Sammy Khalife, Barbara Fiedorowicz, Amitabh Basu

Data-driven algorithm design is a paradigm that uses statistical and machine learning techniques to select from a class of algorithms for a computational problem an algorithm that has the best expected performance with respect to some (unknown) distribution on the instances of the problem. We build upon recent work in this line of research by considering the setup where, instead of selecting a single algorithm that has the best performance, we allow the possibility of selecting an algorithm based on the instance to be solved, using neural networks. In particular, given a representative sample of instances, we learn a neural network that maps an instance of the problem to the most appropriate algorithm *for that instance*. We formalize this idea and derive rigorous sample complexity bounds for this learning problem, in the spirit of recent work in data-driven algorithm design. We then apply this approach to the problem of making good decisions in the branch-and-cut framework for mixed-integer optimization (e.g., which cut to add?). In other words, the neural network will take as input a mixed-integer optimization instance and output a decision that will result in a small branch-and-cut tree for that instance. Our computational results provide evidence that our particular way of using neural networks for cut selection can make a significant impact in reducing branch-and-cut tree sizes, compared to previous data-driven approaches.

Graph Neural Networks

Jinsong Chen, Hanpeng Liu, John Hopcroft, Kun He

While tokenized graph Transformers have demonstrated strong performance in node classification tasks, their reliance on a limited subset of nodes with high similarity scores for constructing token sequences overlooks valuable information from other nodes, hindering their ability to fully harness graph information for learning optimal node representations. To address this limitation, we propose a novel graph Transformer called GCFormer. Unlike previous approaches, GCFormer develops a hybrid token generator to create two types of token sequences, positive and negative, to capture diverse graph information. And a tailored Transformer-based backbone is adopted to learn meaningful node representations from these generated token sequences. Additionally, GCFormer introduces contrastive learning to extract valuable information from both positive and negative token sequences, enhancing the quality of learned node representations. Extensive experimental results across various datasets, including homophily and heterophily graphs, demonstrate the superiority of GCFormer in node classification, when compared to representative graph neural networks (GNNs) and graph Transformers.

Theory · Active Learning and Interactive Learning

Jonas Hübotter, Bhavya, Lenart Treven, Yarden As, Andreas Krause

We study a generalization of classical active learning to real-world settings with concrete prediction targets where sampling is restricted to an accessible region of the domain, while prediction targets may lie outside this region.We analyze a family of decision rules that sample adaptively to minimize uncertainty about prediction targets.We are the first to show, under general regularity assumptions, that such decision rules converge uniformly to the smallest possible uncertainty obtainable from the accessible data.We demonstrate their strong sample efficiency in two key applications: active fine-tuning of large neural networks and safe Bayesian optimization, where they achieve state-of-the-art performance.

Trustworthy Machine Learning

Zhehao Huang, Xinwen Cheng, JingHao Zheng, Haoran Wang, Zhengbao He, Tao Li, Xiaolin Huang

Machine unlearning (MU) has emerged to enhance the privacy and trustworthiness of deep neural networks. Approximate MU is a practical method for large-scale models. Our investigation into approximate MU starts with identifying the steepest descent direction, minimizing the output Kullback-Leibler divergence to exact MU inside a parameters' neighborhood. This probed direction decomposes into three components: weighted forgetting gradient ascent, fine-tuning retaining gradient descent, and a weight saliency matrix. Such decomposition derived from Euclidean metric encompasses most existing gradient-based MU methods. Nevertheless, adhering to Euclidean space may result in sub-optimal iterative trajectories due to the overlooked geometric structure of the output probability space. We suggest embedding the unlearning update into a manifold rendered by the remaining geometry, incorporating second-order Hessian from the remaining data. It helps prevent effective unlearning from interfering with the retained performance. However, computing the second-order Hessian for large-scale models is intractable. To efficiently leverage the benefits of Hessian modulation, we propose a fast-slow parameter update strategy to implicitly approximate the up-to-date salient unlearning direction.Free from specific modal constraints, our approach is adaptable across computer vision unlearning tasks, including classification and generation. Extensive experiments validate our efficacy and efficiency. Notably, our method successfully performs class-forgetting on ImageNet using DiT and forgets a class on CIFAR-10 using DDPM in just 50 steps, compared to thousands of steps required by previous methods. Code is available at [Unified-Unlearning-w-Remain-Geometry](https://github.com/K1nght/Unified-Unlearning-w-Remain-Geometry).

Deep Learning · Theory

yoonsoo nam, Nayara Fonseca, Seok Hyeong Lee, Chris Mingard, Ard Louis

Deep learning models can exhibit what appears to be a sudden ability to solve a new problem as training time, training data, or model size increases, a phenomenon known as emergence. In this paper, we present a framework where each new ability (a skill) is represented as a basis function. We solve a simple multi-linear model in this skill-basis, finding analytic expressions for the emergence of new skills, as well as for scaling laws of the loss with training time, data size, model size, and optimal compute. We compare our detailed calculations to direct simulations of a two-layer neural network trained on multitask sparse parity, where the tasks in the dataset are distributed according to a power-law. Our simple model captures, using a single fit parameter, the sigmoidal emergence of multiple new skills as training time, data size or model size increases in the neural network.

Optimization · Zero-order and Black-box Optimization

Shogo Iwazaki, Shinya Suzumura

We propose a novel stochastic bandit algorithm that employs reward estimates using a tree ensemble model. Specifically, our focus is on a soft tree model, a variant of the conventional decision tree that has undergone both practical and theoretical scrutiny in recent years. By deriving several non-trivial properties of soft trees, we extend the existing analytical techniques used for neural bandit algorithms to our soft tree-based algorithm. We demonstrate that our algorithm achieves a smaller cumulative regret compared to the existing ReLU-based neural bandit algorithms. We also show that this advantage comes with a trade-off: the hypothesis space of the soft tree ensemble model is more constrained than that of a ReLU-based neural network.

Deep Learning · Algorithms

Lorenzo Orecchia, Jiawei Hu, Xue He, Wang Mark, Xulei Yang, Min Wu, Xue Geng

Current methods for training Binarized Neural Networks (BNNs) heavily rely on the heuristic straight-through estimator (STE), which crucially enables the application of SGD-based optimizers to the combinatorial training problem. Although the STE heuristics and their variants have led to significant improvements in BNN performance, their theoretical underpinnings remain unclear and relatively understudied. In this paper, we propose a theoretically motivated optimization framework for BNN training based on Gaussian variational inference. In its simplest form, our approach yields a non-convex linear programming formulation whose variables and associated gradients motivate the use of latent weights and STE gradients. More importantly, our framework allows us to formulate semidefinite programming (SDP) relaxations to the BNN training task. Such formulations are able to explicitly models pairwise correlations between weights during training, leading to a more accurate optimization characterization of the training problem. As the size of such formulations grows quadratically in the number of weights, quickly becoming intractable for large networks, we apply the Burer-Monteiro approach and only optimize over linear-size low-rank SDP solutions. Our empirical evaluation on CIFAR-10, CIFAR-100, Tiny-ImageNet and ImageNet datasets shows our method consistently outperforming all state-of-the-art algorithms for training BNNs.

Zhiwen Fan, Jian Zhang, Wenyan Cong, Peihao Wang, Renjie Li, Kairun Wen, Shijie Zhou, Achuta Kadambi, Zhangyang "Atlas" Wang, Danfei Xu 等

Reconstructing and understanding 3D structures from a limited number of images is a classical problem in computer vision. Traditional approaches typically decompose this task into multiple subtasks, involving several stages of complex mappings between different data representations. For example, dense reconstruction using Structure-from-Motion (SfM) requires transforming images into key points, optimizing camera parameters, and estimating structures. Following this, accurate sparse reconstructions are necessary for further dense modeling, which is then input into task-specific neural networks. This multi-stage paradigm leads to significant processing times and engineering complexity.In this work, we introduce the Large Spatial Model (LSM), which directly processes unposed RGB images into semantic radiance fields. LSM simultaneously estimates geometry, appearance, and semantics in a single feed-forward pass and can synthesize versatile label maps by interacting through language at novel views. Built on a general Transformer-based framework, LSM predicts global geometry via pixel-aligned point maps. To improve spatial attribute regression, we adopt local context aggregation with multi-scale fusion, enhancing the accuracy of fine local details. To address the scarcity of labeled 3D semantic data and enable natural language-driven scene manipulation, we incorporate a pre-trained 2D language-based segmentation model into a 3D-consistent semantic feature field. An efficient decoder parameterizes a set of semantic anisotropic Gaussians, allowing supervised end-to-end learning. Comprehensive experiments on various tasks demonstrate that LSM unifies multiple 3D vision tasks directly from unposed images, achieving real-time semantic 3D reconstruction for the first time.

Optimization · Learning for Optimization

Andrea Corsini, Angelo Porrello, SIMONE CALDERARA, Mauro Dell'Amico

This work proposes a self-supervised training strategy designed for combinatorial problems. An obstacle in applying supervised paradigms to such problems is the need for costly target solutions often produced with exact solvers. Inspired by semi- and self-supervised learning, we show that generative models can be trained by sampling multiple solutions and using the best one according to the problem objective as a pseudo-label. In this way, we iteratively improve the model generation capability by relying only on its self-supervision, eliminating the need for optimality information. We validate this Self-Labeling Improvement Method (SLIM) on the Job Shop Scheduling (JSP), a complex combinatorial problem that is receiving much attention from the neural combinatorial community. We propose a generative model based on the well-known Pointer Network and train it with SLIM. Experiments on popular benchmarks demonstrate the potential of this approach as the resulting models outperform constructive heuristics and state-of-the-art learning proposals for the JSP. Lastly, we prove the robustness of SLIM to various parameters and its generality by applying it to the Traveling Salesman Problem.

Graph Neural Networks

Fedor Velikonivtsev, Mikhail Mironov, Liudmila Prokhorenkova

For many graph-related problems, it can be essential to have a set of structurally diverse graphs. For instance, such graphs can be used for testing graph algorithms or their neural approximations. However, to the best of our knowledge, the problem of generating structurally diverse graphs has not been explored in the literature. In this paper, we fill this gap. First, we discuss how to define diversity for a set of graphs, why this task is non-trivial, and how one can choose a proper diversity measure. Then, for a given diversity measure, we propose and compare several algorithms optimizing it: we consider approaches based on standard random graph models, local graph optimization, genetic algorithms, and neural generative models. We show that it is possible to significantly improve diversity over basic random graph generators. Additionally, our analysis of generated graphs allows us to better understand the properties of graph distances: depending on which diversity measure is used for optimization, the obtained graphs may possess very different structural properties which gives a better understanding of the graph distance underlying the diversity measure.

Physical Models · Physics

Timothy Nest, Maxence Ernoult

Power efficiency is plateauing in the standard digital electronics realm such that new hardware, models, and algorithms are needed to reduce the costs of AI training. The combination of energy-based analog circuits and the Equilibrium Propagation (EP) algorithm constitutes a compelling alternative compute paradigm for gradient-based optimization of neural nets. Existing analog hardware accelerators, however, typically incorporate digital circuitry to sustain auxiliary non-weight-stationary operations, mitigate analog device imperfections, and leverage existing digital platforms. Such heterogeneous hardware lacks a supporting theoretical framework. In this work, we introduce \emph{Feedforward-tied Energy-based Models} (ff-EBMs), a hybrid model comprised of feedforward and energy-based blocks housed on digital and analog circuits. We derive a novel algorithm to compute gradients end-to-end in ff-EBMs by backpropagating and ``eq-propagating'' through feedforward and energy-based parts respectively, enabling EP to be applied flexibly on realistic architectures. We experimentally demonstrate the effectiveness of this approach on ff-EBMs using Deep Hopfield Networks (DHNs) as energy-based blocks, and show that a standard DHN can be arbitrarily split into any uniform size while maintaining or improving performance with increases in simulation speed of up to four times. We then train ff-EBMs on ImageNet32 where we establish a new state-of-the-art performance for the EP literature (46 top-1 \%). Our approach offers a principled, scalable, and incremental roadmap for the gradual integration of self-trainable analog computational primitives into existing digital accelerators.