NeurIPS 2024 论文列表

Conference on Neural Information Processing Systems

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    3828.4%
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    4,06489.1%
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Evidence of Learned Look-Ahead in a Chess-Playing Neural Network

Erik Jenner, Shreyas Kapur, Vasil Georgiev, Cameron Allen, Scott Emmons, Stuart Russell

展开摘要

Do neural networks learn to implement algorithms such as look-ahead or search "in the wild"? Or do they rely purely on collections of simple heuristics? We present evidence of *learned look-ahead* in the policy and value network of Leela Chess Zero, the currently strongest deep neural chess engine. We find that Leela internally represents future optimal moves and that these representations are crucial for its final output in certain board states. Concretely, we exploit the fact that Leela is a transformer that treats every chessboard square like a token in language models, and give three lines of evidence: (1) activations on certain squares of future moves are unusually important causally; (2) we find attention heads that move important information "forward and backward in time," e.g., from squares of future moves to squares of earlier ones; and (3) we train a simple probe that can predict the optimal move 2 turns ahead with 92% accuracy (in board states where Leela finds a single best line). These findings are clear evidence of learned look-ahead in neural networks and might be a step towards a better understanding of their capabilities.

Poster
CV-VAE: A Compatible Video VAE for Latent Generative Video Models

Sijie Zhao, Yong Zhang, Xiaodong Cun, Shaoshu Yang, Muyao Niu, Xiaoyu Li, Wenbo Hu, Ying Shan

展开摘要

Spatio-temporal compression of videos, utilizing networks such as Variational Autoencoders (VAE), plays a crucial role in OpenAI's SORA and numerous other video generative models. For instance, many LLM-like video models learn the distribution of discrete tokens derived from 3D VAEs within the VQVAE framework, while most diffusion-based video models capture the distribution of continuous latent extracted by 2D VAEs without quantization. The temporal compression is simply realized by uniform frame sampling which results in unsmooth motion between consecutive frames. Currently, there lacks of a commonly used continuous video (3D) VAE for latent diffusion-based video models in the research community. Moreover, since current diffusion-based approaches are often implemented using pre-trained text-to-image (T2I) models, directly training a video VAE without considering the compatibility with existing T2I models will result in a latent space gap between them, which will take huge computational resources for training to bridge the gap even with the T2I models as initialization. To address this issue, we propose a method for training a video VAE of latent video models, namely CV-VAE, whose latent space is compatible with that of a given image VAE, e.g., image VAE of Stable Diffusion (SD). The compatibility is achieved by the proposed novel latent space regularization, which involves formulating a regularization loss using the image VAE. Benefiting from the latent space compatibility, video models can be trained seamlessly from pre-trained T2I or video models in a truly spatio-temporally compressed latent space, rather than simply sampling video frames at equal intervals. To improve the training efficiency, we also design a novel architecture for the video VAE. With our CV-VAE, existing video models can generate four times more frames with minimal finetuning. Extensive experiments are conducted to demonstrate the effectiveness of the proposed video VAE.

Poster
Globally Convergent Variational Inference

Declan McNamara, Jackson Loper, Jeffrey Regier

展开摘要

In variational inference (VI), an approximation of the posterior distribution is selected from a family of distributions through numerical optimization. With the most common variational objective function, known as the evidence lower bound (ELBO), only convergence to a *local* optimum can be guaranteed. In this work, we instead establish the *global* convergence of a particular VI method. This VI method, which may be considered an instance of neural posterior estimation (NPE), minimizes an expectation of the inclusive (forward) KL divergence to fit a variational distribution that is parameterized by a neural network. Our convergence result relies on the neural tangent kernel (NTK) to characterize the gradient dynamics that arise from considering the variational objective in function space. In the asymptotic regime of a fixed, positive-definite neural tangent kernel, we establish conditions under which the variational objective admits a unique solution in a reproducing kernel Hilbert space (RKHS). Then, we show that the gradient descent dynamics in function space converge to this unique function. In ablation studies and practical problems, we demonstrate that our results explain the behavior of NPE in non-asymptotic finite-neuron settings, and show that NPE outperforms ELBO-based optimization, which often converges to shallow local optima.

Poster
Conformalized Multiple Testing after Data-dependent Selection

Xiaoning Wang, Yuyang Huo, Liuhua Peng, Changliang Zou

展开摘要

The task of distinguishing individuals of interest from a vast pool of candidates using predictive models has garnered significant attention in recent years. This task can be framed as a *conformalized multiple testing* procedure, which aims at quantifying prediction uncertainty by controlling the false discovery rate (FDR) via conformal inference. In this paper, we tackle the challenge of conformalized multiple testing after data-dependent selection procedures. To guarantee the construction of valid test statistics that accurately capture the distorted distribution resulting from the selection process, we leverage a holdout labeled set to closely emulate the selective distribution. Our approach involves adaptively picking labeled data to create a calibration set based on the stability of the selection rule. This strategy ensures that the calibration data and the selected test unit are exchangeable, allowing us to develop valid conformal p-values. Implementing with the famous Benjamini-Hochberg (BH) procedure, it effectively controls the FDR over the selected subset. To handle the randomness of the selected subset and the dependence among the constructed p-values, we establish a unified theoretical framework. This framework extends the application of conformalized multiple testing to complex selective settings. Furthermore, we conduct numerical studies to showcase the effectiveness and validity of our procedures across various scenarios.

Poster
GO4Align: Group Optimization for Multi-Task Alignment

Jiayi Shen, Cheems Wang, Zehao Xiao, Nanne Van Noord, Marcel Worring

展开摘要

This paper proposes **GO4Align**, a multi-task optimization approach that tackles task imbalance by explicitly aligning the optimization across tasks. To achieve this, we design an adaptive group risk minimization strategy, comprising two techniques in implementation: (i) dynamical group assignment, which clusters similar tasks based on task interactions; (ii) risk-guided group indicators, which exploit consistent task correlations with risk information from previous iterations. Comprehensive experimental results on diverse benchmarks demonstrate our method's performance superiority with even lower computational costs.

Poster
Private Algorithms for Stochastic Saddle Points and Variational Inequalities: Beyond Euclidean Geometry

Raef Bassily, Cristóbal A Guzmán, Michael Menart

展开摘要

In this work, we conduct a systematic study of stochastic saddle point problems (SSP) and stochastic variational inequalities (SVI) under the constraint of $(\epsilon,\delta)$-differential privacy (DP) in both Euclidean and non-Euclidean setups. We first consider Lipschitz convex-concave SSPs in the $\ell_p/\ell_q$ setup, $p,q\in[1,2]$. That is, we consider the case where the primal problem has an $\ell_p$-setup (i.e., the primal parameter is constrained to an $\ell_p$ bounded domain and the loss is $\ell_p$-Lipschitz with respect to the primal parameter) and the dual problem has an $\ell_q$ setup. Here, we obtain a bound of $\tilde{O}\big(\frac{1}{\sqrt{n}} + \frac{\sqrt{d}}{n\epsilon}\big)$ on the strong SP-gap, where $n$ is the number of samples and $d$ is the dimension. This rate is nearly optimal for any $p,q\in[1,2]$. Without additional assumptions, such as smoothness or linearity requirements, prior work under DP has only obtained this rate when $p=q=2$ (i.e., only in the Euclidean setup). Further, existing algorithms have each only been shown to work for specific settings of $p$ and $q$ and under certain assumptions on the loss and the feasible set, whereas we provide a general algorithm for DP SSPs whenever $p,q\in[1,2]$. Our result is obtained via a novel analysis of the recursive regularization algorithm. In particular, we develop new tools for analyzing generalization, which may be of independent interest. Next, we turn our attention towards SVIs with a monotone, bounded and Lipschitz operator and consider $\ell_p$-setups, $p\in[1,2]$. Here, we provide the first analysis which obtains a bound on the strong VI-gap of $\tilde{O}\big(\frac{1}{\sqrt{n}} + \frac{\sqrt{d}}{n\epsilon}\big)$. For $p-1=\Omega(1)$, this rate is near optimal due to existing lower bounds. To obtain this result, we develop a modified version of recursive regularization. Our analysis builds on the techniques we develop for SSPs as well as employing additional novel components which handle difficulties arising from adapting the recursive regularization framework to SVIs.

Poster
BoostAdapter: Improving Vision-Language Test-Time Adaptation via Regional Bootstrapping

Taolin Zhang, Jinpeng Wang, Hang Guo, Tao Dai, Bin CHEN, Shu-Tao Xia

展开摘要

Adaptation of pretrained vision-language models such as CLIP to various downstream tasks have raised great interest in recent researches. Previous works have proposed a variety of test-time adaptation (TTA) methods to achieve strong generalization without any knowledge of the target domain. However, existing training-required TTA approaches like TPT necessitate entropy minimization that involves large computational overhead, while training-free methods like TDA overlook the potential for information mining from the test samples themselves. In this paper, we break down the design of existing popular training-required and training-free TTA methods and bridge the gap between them within our framework. Specifically, we maintain a light-weight key-value memory for feature retrieval from instance-agnostic historical samples and instance-aware boosting samples. The historical samples are filtered from the testing data stream and serve to extract useful information from the target distribution, while the boosting samples are drawn from regional bootstrapping and capture the knowledge of the test sample itself. We theoretically justify the rationality behind our method and empirically verify its effectiveness on both the out-of-distribution and the cross-domain datasets, showcasing its applicability in real-world situations.

Poster
ReST-MCTS*: LLM Self-Training via Process Reward Guided Tree Search

Dan Zhang, Sining Zhoubian, Ziniu Hu, Yisong Yue, Yuxiao Dong, Jie Tang

展开摘要

Recent methodologies in LLM self-training mostly rely on LLM generating responses and filtering those with correct output answers as training data. This approach often yields a low-quality fine-tuning training set (e.g., incorrect plans or intermediate reasoning). In this paper, we develop a reinforced self-training approach, called ReST-MCTS*, based on integrating process reward guidance with tree search MCTS* for collecting higher-quality reasoning traces as well as per-step value to train policy and reward models. ReST-MCTS* circumvents the per-step manual annotation typically used to train process rewards by tree-search-based reinforcement learning: Given oracle final correct answers, ReST-MCTS* is able to infer the correct process rewards by estimating the probability this step can help lead to the correct answer. These inferred rewards serve dual purposes: they act as value targets for further refining the process reward model and also facilitate the selection of high-quality traces for policy model self-training. We first show that the tree-search policy in ReST-MCTS* achieves higher accuracy compared with prior LLM reasoning baselines such as Best-of-N and Tree-of-Thought, within the same search budget. We then show that by using traces searched by this tree-search policy as training data, we can continuously enhance the three language models for multiple iterations, and outperform other self-training algorithms such as ReST$^\text{EM}$ and Self-Rewarding LM.

Poster
NeuroClips: Towards High-fidelity and Smooth fMRI-to-Video Reconstruction

Zixuan Gong, Guangyin Bao, Qi Zhang, Zhongwei Wan, Duoqian Miao, Shoujin Wang, Lei Zhu, Changwei Wang, Rongtao Xu, LIANG HU, Ke Liu, Yu Zhang

展开摘要

Reconstruction of static visual stimuli from non-invasion brain activity fMRI achieves great success, owning to advanced deep learning models such as CLIP and Stable Diffusion. However, the research on fMRI-to-video reconstruction remains limited since decoding the spatiotemporal perception of continuous visual experiences is formidably challenging. We contend that the key to addressing these challenges lies in accurately decoding both high-level semantics and low-level perception flows, as perceived by the brain in response to video stimuli. To the end, we propose NeuroClips, an innovative framework to decode high-fidelity and smooth video from fMRI. NeuroClips utilizes a semantics reconstructor to reconstruct video keyframes, guiding semantic accuracy and consistency, and employs a perception reconstructor to capture low-level perceptual details, ensuring video smoothness. During inference, it adopts a pre-trained T2V diffusion model injected with both keyframes and low-level perception flows for video reconstruction. Evaluated on a publicly available fMRI-video dataset, NeuroClips achieves smooth high-fidelity video reconstruction of up to 6s at 8FPS, gaining significant improvements over state-of-the-art models in various metrics, e.g., a 128% improvement in SSIM and an 81% improvement in spatiotemporal metrics. Our project is available at https://github.com/gongzix/NeuroClips.

Oral
Off-policy estimation with adaptively collected data: the power of online learning

Jeonghwan Lee, Cong Ma

展开摘要

We consider estimation of a linear functional of the treatment effect from adaptively collected data. This problem finds a variety of applications including off-policy evaluation in contextual bandits, and estimation of the average treatment effect in causal inference. While a certain class of augmented inverse propensity weighting (AIPW) estimators enjoys desirable asymptotic properties including the semi-parametric efficiency, much less is known about their non-asymptotic theory with adaptively collected data. To fill in the gap, we first present generic upper bounds on the mean-squared error of the class of AIPW estimators that crucially depends on a sequentially weighted error between the treatment effect and its estimates. Motivated by this, we propose a general reduction scheme that allows one to produce a sequence of estimates for the treatment effect via online learning to minimize the sequentially weighted estimation error. To illustrate this, we provide three concrete instantiations in (1) the tabular case; (2) the case of linear function approximation; and (3) the case of general function approximation for the outcome model. We then provide a local minimax lower bound to show the instance-dependent optimality of the AIPW estimator using no-regret online learning algorithms.

Poster
Beyond the Doors of Perception: Vision Transformers Represent Relations Between Objects

Michael A. Lepori, Alexa R. Tartaglini, Wai Keen Vong, Thomas Serre, Brenden Lake, Ellie Pavlick

展开摘要

Though vision transformers (ViTs) have achieved state-of-the-art performance in a variety of settings, they exhibit surprising failures when performing tasks involving visual relations. This begs the question: how do ViTs attempt to perform tasks that require computing visual relations between objects? Prior efforts to interpret ViTs tend to focus on characterizing relevant low-level visual features. In contrast, we adopt methods from mechanistic interpretability to study the higher-level visual algorithms that ViTs use to perform abstract visual reasoning. We present a case study of a fundamental, yet surprisingly difficult, relational reasoning task: judging whether two visual entities are the same or different. We find that pretrained ViTs fine-tuned on this task often exhibit two qualitatively different stages of processing despite having no obvious inductive biases to do so: 1) a perceptual stage wherein local object features are extracted and stored in a disentangled representation, and 2) a relational stage wherein object representations are compared. In the second stage, we find evidence that ViTs can learn to represent somewhat abstract visual relations, a capability that has long been considered out of reach for artificial neural networks. Finally, we demonstrate that failures at either stage can prevent a model from learning a generalizable solution to our fairly simple tasks. By understanding ViTs in terms of discrete processing stages, one can more precisely diagnose and rectify shortcomings of existing and future models.

Poster
Visual Prompt Tuning in Null Space for Continual Learning

Yue Lu, Shizhou Zhang, De Cheng, Yinghui Xing, Nannan Wang, Peng Wang, Yanning Zhang

展开摘要

Existing prompt-tuning methods have demonstrated impressive performances in continual learning (CL), by selecting and updating relevant prompts in the vision-transformer models. On the contrary, this paper aims to learn each task by tuning the prompts in the direction orthogonal to the subspace spanned by previous tasks' features, so as to ensure no interference on tasks that have been learned to overcome catastrophic forgetting in CL. However, different from the orthogonal projection in the traditional CNN architecture, the prompt gradient orthogonal projection in the ViT architecture shows completely different and greater challenges, i.e., 1) the high-order and non-linear self-attention operation; 2) the drift of prompt distribution brought by the LayerNorm in the transformer block. Theoretically, we have finally deduced two consistency conditions to achieve the prompt gradient orthogonal projection, which provide a theoretical guarantee of eliminating interference on previously learned knowledge via the self-attention mechanism in visual prompt tuning. In practice, an effective null-space-based approximation solution has been proposed to implement the prompt gradient orthogonal projection. Extensive experimental results demonstrate the effectiveness of anti-forgetting on four class-incremental benchmarks with diverse pre-trained baseline models, and our approach achieves superior performances to state-of-the-art methods. Our code is available at https://github.com/zugexiaodui/VPTinNSforCL

Poster
Provable Benefit of Cutout and CutMix for Feature Learning

Junsoo Oh, Chulhee Yun

展开摘要

Patch-level data augmentation techniques such as Cutout and CutMix have demonstrated significant efficacy in enhancing the performance of vision tasks. However, a comprehensive theoretical understanding of these methods remains elusive. In this paper, we study two-layer neural networks trained using three distinct methods: vanilla training without augmentation, Cutout training, and CutMix training. Our analysis focuses on a feature-noise data model, which consists of several label-dependent features of varying rarity and label-independent noises of differing strengths. Our theorems demonstrate that Cutout training can learn low-frequency features that vanilla training cannot, while CutMix training can learn even rarer features that Cutout cannot capture. From this, we establish that CutMix yields the highest test accuracy among the three. Our novel analysis reveals that CutMix training makes the network learn all features and noise vectors "evenly" regardless of the rarity and strength, which provides an interesting insight into understanding patch-level augmentation.

Spotlight
Graph Diffusion Policy Optimization

Yijing Liu, Chao Du, Tianyu Pang, Chongxuan Li, Min Lin, Wei Chen

展开摘要

Recent research has made significant progress in optimizing diffusion models for downstream objectives, which is an important pursuit in fields such as graph generation for drug design. However, directly applying these models to graph presents challenges, resulting in suboptimal performance. This paper introduces graph diffusion policy optimization (GDPO), a novel approach to optimize graph diffusion models for arbitrary (e.g., non-differentiable) objectives using reinforcement learning. GDPO is based on an eager policy gradient tailored for graph diffusion models, developed through meticulous analysis and promising improved performance. Experimental results show that GDPO achieves state-of-the-art performance in various graph generation tasks with complex and diverse objectives. Code is available at https://github.com/sail-sg/GDPO.

Poster
Finding Transformer Circuits With Edge Pruning

Adithya Bhaskar, Alexander Wettig, Dan Friedman, Danqi Chen

展开摘要

The path to interpreting a language model often proceeds via analysis of circuits---sparse computational subgraphs of the model that capture specific aspects of its behavior. Recent work has automated the task of discovering circuits. Yet, these methods have practical limitations, as they either rely on inefficient search algorithms or inaccurate approximations. In this paper, we frame circuit discovery as an optimization problem and propose _Edge Pruning_ as an effective and scalable solution. Edge Pruning leverages gradient-based pruning techniques, but instead of removing neurons or components, prunes the _edges_ between components. Our method finds circuits in GPT-2 that use less than half the number of edges than circuits found by previous methods while being equally faithful to the full model predictions on standard circuit-finding tasks. Edge Pruning is efficient on tasks involving up to 100,000 examples, outperforming previous methods in speed and producing substantially better circuits. It also perfectly recovers the ground-truth circuits in two models compiled with Tracr. Thanks to its efficiency, we scale Edge Pruning to CodeLlama-13B, a model over 100x the size of GPT-2. We use this setting for a case study, where we compare the mechanisms behind instruction prompting and in-context learning. We find two circuits with more than 99.96% sparsity that match the performance of the full model. Further analysis reveals that the mechanisms in the two settings overlap substantially. This shows that Edge Pruning is a practical and scalable tool for interpretability, which can shed light on behaviors that only emerge in large models.

Spotlight
Temporal-Difference Learning Using Distributed Error Signals

Jonas Guan, Shon Eduard Verch, Claas A Voelcker, Ethan C Jackson, Nicolas Papernot, William A Cunningham

展开摘要

A computational problem in biological reward-based learning is how credit assignment is performed in the nucleus accumbens (NAc). Much research suggests that NAc dopamine encodes temporal-difference (TD) errors for learning value predictions. However, dopamine is synchronously distributed in regionally homogeneous concentrations, which does not support explicit credit assignment (like used by backpropagation). It is unclear whether distributed errors alone are sufficient for synapses to make coordinated updates to learn complex, nonlinear reward-based learning tasks. We design a new deep Q-learning algorithm, Artificial Dopamine, to computationally demonstrate that synchronously distributed, per-layer TD errors may be sufficient to learn surprisingly complex RL tasks. We empirically evaluate our algorithm on MinAtar, the DeepMind Control Suite, and classic control tasks, and show it often achieves comparable performance to deep RL algorithms that use backpropagation.

Poster
Learning Cut Generating Functions for Integer Programming

Hongyu Cheng, Amitabh Basu

展开摘要

The branch-and-cut algorithm is the method of choice to solve large scale integer programming problems in practice. A key ingredient of branch-and-cut is the use of *cutting planes* which are derived constraints that reduce the search space for an optimal solution. Selecting effective cutting planes to produce small branch-and-cut trees is a critical challenge in the branch-and-cut algorithm. Recent advances have employed a data-driven approach to select good cutting planes from a parameterized family, aimed at reducing the branch-and-bound tree size (in expectation) for a given distribution of integer programming instances. We extend this idea to the selection of the best cut generating function (CGF), which is a tool in the integer programming literature for generating a wide variety of cutting planes that generalize the well-known Gomory Mixed-Integer (GMI) cutting planes. We provide rigorous sample complexity bounds for the selection of an effective CGF from certain parameterized families that provably performs well for any specified distribution on the problem instances. Our empirical results show that the selected CGF can outperform the GMI cuts for certain distributions. Additionally, we explore the sample complexity of using neural networks for instance-dependent CGF selection.

Poster
Image2Struct: Benchmarking Structure Extraction for Vision-Language Models

Josselin Somerville Roberts, Tony Lee, Chi Heem Wong, Michihiro Yasunaga, Yifan Mai, Percy Liang

展开摘要

We introduce Image2Struct, a benchmark to evaluate vision-language models (VLMs) on extracting structure from images. Our benchmark 1) captures real-world use cases, 2) is fully automatic and does not require human judgment, and 3) is based on a renewable stream of fresh data. In Image2Struct, VLMs are prompted to generate the underlying structure (e.g., LaTeX code or HTML) from an input image (e.g., webpage screenshot). The structure is then rendered to produce an output image (e.g., rendered webpage), which is compared against the input image to produce a similarity score. This round-trip evaluation allows us to quantitatively evaluate VLMs on tasks with multiple valid structures. We create a pipeline that downloads fresh data from active online communities upon execution and evaluates the VLMs without human intervention. We introduce three domains (Webpages, LaTeX, and Musical Scores) and use five image metrics (pixel similarity, cosine similarity between the Inception vectors, learned perceptual image patch similarity, structural similarity index measure, and earth mover similarity) that allow efficient and automatic comparison between pairs of images. We evaluate Image2Struct on 14 prominent VLMs and find that scores vary widely, indicating that Image2Struct can differentiate between the performances of different VLMs. Additionally, the best score varies considerably across domains (e.g., 0.402 on sheet music vs. 0.830 on LaTeX equations), indicating that Image2Struct contains tasks of varying difficulty. For transparency, we release the full results at https://crfm.stanford.edu/helm/image2struct/v1.0.1/.

Poster
Any2Policy: Learning Visuomotor Policy with Any-Modality

Yichen Zhu, Zhicai Ou, Feifei Feng, Jian Tang

展开摘要

Humans can communicate and observe media with different modalities, such as texts, sounds, and images. For robots to be more generalizable embodied agents, they should be capable of following instructions and perceiving the world with adaptation to diverse modalities. Current robotic learning methodologies often focus on single-modal task specification and observation, thereby limiting their ability to process rich multi-modal information. Addressing this limitation, we present an end-to-end general-purpose multi-modal system named Any-to-Policy Embodied Agents. This system empowers robots to handle tasks using various modalities, whether in combinations like text-image, audio-image, text-point cloud, or in isolation. Our innovative approach involves training a versatile modality network that adapts to various inputs and connects with policy networks for effective control. Because of the lack of existing multi-modal robotics datasets for evaluation, we assembled a comprehensive real-world dataset encompassing 30 robotic tasks. Each task in this dataset is richly annotated across multiple modalities, providing a robust foundation for assessment. We conducted extensive validation of our proposed unified modality embodied agent using several simulation benchmarks, including Franka Kitchen, Meta-World, and Maniskill2, as well as in our real-world settings. Our experiments showcase the promising capability of building embodied agents that can adapt to diverse multi-modal in a unified framework.

Poster
Improving Neural Network Surface Processing with Principal Curvatures

Josquin Harrison, James Benn, Maxime Sermesant

展开摘要

The modern study and use of surfaces is a research topic grounded in centuries of mathematical and empirical inquiry. From a mathematical point of view, curvature is an invariant that characterises the intrinsic geometry and the extrinsic shape of a surface. Yet, in modern applications the focus has shifted away from finding expressive representations of surfaces, and towards the design of efficient neural network architectures to process them. The literature suggests a tendency to either overlook the representation of the processed surface, or use overcomplicated representations whose ability to capture the essential features of a surface is opaque. We propose using curvature as the input of neural network architectures for surface processing, and explore this proposition through experiments making use of the shape operator. Our results show that using curvature as input leads to significant a increase in performance on segmentation and classification tasks, while allowing far less computational overhead than current methods.

Poster