Daily Papers

WordArt (artistic text) features highly customized fonts, textures, and layouts, making WordArt-oriented scene TExt Recognition (WATER) substantially more challenging than general Scene Text Recognition (STR). Existing STR datasets and methods, typically built around regular scene text and fixed-template inputs, struggle to scale to WATER. Thus, we aim to advance this task from both data and model perspectives. On the data side, we construct a 2M synthetic dataset, WATER-S, with the scale improved by hundreds of times compared to existing artistic text data. WATER-S consists of two complementary subsets. One rendered by an upgraded rendering pipeline (SynthWordArt), which provides highly accurate and controllable synthetic WordArt data. The other is generated by combining Qwen3-VL for prompt mining and Z-Image for image synthesis, which improves the coverage of realistic and diverse data. On the model side, we propose WATERec. It adopts an visual encoder supporting arbitrary-shaped inputs and an autoregressive decoder to model complex layouts, structurally breaking the bottleneck of fixed-template STR on WordArt. Experiments show that this architecture outperforms prior STR methods, achieving state-of-the-art performance on irregular texts such as WordArt. Together with WATER-R, carefully reorganized from existing real STR data, our strong baseline with the new synthetic data and model design reaches 90.40% accuracy on WordArt-Bench, surpassing both general-purpose and OCR-specialized vision-language models by a large margin. Code and data are available at https://github.com/YesianRohn/WATER.

We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We show that these data-driven features are more interpretable, and have better predictive performance on a variety of tasks.

We present CSWin Transformer, an efficient and effective Transformer-based backbone for general-purpose vision tasks. A challenging issue in Transformer design is that global self-attention is very expensive to compute whereas local self-attention often limits the field of interactions of each token. To address this issue, we develop the Cross-Shaped Window self-attention mechanism for computing self-attention in the horizontal and vertical stripes in parallel that form a cross-shaped window, with each stripe obtained by splitting the input feature into stripes of equal width. We provide a mathematical analysis of the effect of the stripe width and vary the stripe width for different layers of the Transformer network which achieves strong modeling capability while limiting the computation cost. We also introduce Locally-enhanced Positional Encoding (LePE), which handles the local positional information better than existing encoding schemes. LePE naturally supports arbitrary input resolutions, and is thus especially effective and friendly for downstream tasks. Incorporated with these designs and a hierarchical structure, CSWin Transformer demonstrates competitive performance on common vision tasks. Specifically, it achieves 85.4\% Top-1 accuracy on ImageNet-1K without any extra training data or label, 53.9 box AP and 46.4 mask AP on the COCO detection task, and 52.2 mIOU on the ADE20K semantic segmentation task, surpassing previous state-of-the-art Swin Transformer backbone by +1.2, +2.0, +1.4, and +2.0 respectively under the similar FLOPs setting. By further pretraining on the larger dataset ImageNet-21K, we achieve 87.5% Top-1 accuracy on ImageNet-1K and high segmentation performance on ADE20K with 55.7 mIoU. The code and models are available at https://github.com/microsoft/CSWin-Transformer.

We develop a method to generate predictive regions that cover a multivariate response variable with a user-specified probability. Our work is composed of two components. First, we use a deep generative model to learn a representation of the response that has a unimodal distribution. Existing multiple-output quantile regression approaches are effective in such cases, so we apply them on the learned representation, and then transform the solution to the original space of the response. This process results in a flexible and informative region that can have an arbitrary shape, a property that existing methods lack. Second, we propose an extension of conformal prediction to the multivariate response setting that modifies any method to return sets with a pre-specified coverage level. The desired coverage is theoretically guaranteed in the finite-sample case for any distribution. Experiments conducted on both real and synthetic data show that our method constructs regions that are significantly smaller compared to existing techniques.

Programs are an increasingly popular representation for visual data, exposing compact, interpretable structure that supports manipulation. Visual programs are usually written in domain-specific languages (DSLs). Finding "good" programs, that only expose meaningful degrees of freedom, requires access to a DSL with a "good" library of functions, both of which are typically authored by domain experts. We present ShapeCoder, the first system capable of taking a dataset of shapes, represented with unstructured primitives, and jointly discovering (i) useful abstraction functions and (ii) programs that use these abstractions to explain the input shapes. The discovered abstractions capture common patterns (both structural and parametric) across the dataset, so that programs rewritten with these abstractions are more compact, and expose fewer degrees of freedom. ShapeCoder improves upon previous abstraction discovery methods, finding better abstractions, for more complex inputs, under less stringent input assumptions. This is principally made possible by two methodological advancements: (a) a shape to program recognition network that learns to solve sub-problems and (b) the use of e-graphs, augmented with a conditional rewrite scheme, to determine when abstractions with complex parametric expressions can be applied, in a tractable manner. We evaluate ShapeCoder on multiple datasets of 3D shapes, where primitive decompositions are either parsed from manual annotations or produced by an unsupervised cuboid abstraction method. In all domains, ShapeCoder discovers a library of abstractions that capture high-level relationships, remove extraneous degrees of freedom, and achieve better dataset compression compared with alternative approaches. Finally, we investigate how programs rewritten to use discovered abstractions prove useful for downstream tasks.

Recent text detection frameworks require several handcrafted components such as anchor generation, non-maximum suppression (NMS), or multiple processing stages (e.g. label generation) to detect arbitrarily shaped text images. In contrast, we propose an end-to-end trainable architecture based on Detection using Transformers (DETR), that outperforms previous state-of-the-art methods in arbitrary-shaped text detection. At its core, our proposed method leverages a bounding box loss function that accurately measures the arbitrary detected text regions' changes in scale and aspect ratio. This is possible due to a hybrid shape representation made from Bezier curves, that are further split into piece-wise polygons. The proposed loss function is then a combination of a generalized-split-intersection-over-union loss defined over the piece-wise polygons and regularized by a Smooth-ln regression over the Bezier curve's control points. We evaluate our proposed model using Total-Text and CTW-1500 datasets for curved text, and MSRA-TD500 and ICDAR15 datasets for multi-oriented text, and show that the proposed method outperforms the previous state-of-the-art methods in arbitrary-shape text detection tasks.

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.

We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data read/writes. We demonstrate that a constant number of encoder layers can emulate basic computing blocks, including embedding edit operations, non-linear functions, function calls, program counters, and conditional branches. Using these building blocks, we emulate a small instruction-set computer. This allows us to map iterative algorithms to programs that can be executed by a looped, 13-layer transformer. We show how this transformer, instructed by its input, can emulate a basic calculator, a basic linear algebra library, and in-context learning algorithms that employ backpropagation. Our work highlights the versatility of the attention mechanism, and demonstrates that even shallow transformers can execute full-fledged, general-purpose programs.

We present a neural architecture that takes as input a 2D or 3D shape and outputs a program that generates the shape. The instructions in our program are based on constructive solid geometry principles, i.e., a set of boolean operations on shape primitives defined recursively. Bottom-up techniques for this shape parsing task rely on primitive detection and are inherently slow since the search space over possible primitive combinations is large. In contrast, our model uses a recurrent neural network that parses the input shape in a top-down manner, which is significantly faster and yields a compact and easy-to-interpret sequence of modeling instructions. Our model is also more effective as a shape detector compared to existing state-of-the-art detection techniques. We finally demonstrate that our network can be trained on novel datasets without ground-truth program annotations through policy gradient techniques.

Neural networks adapt very well to distributed and continuous representations, but struggle to generalize from small amounts of data. Symbolic systems commonly achieve data efficient generalization by exploiting modularity to benefit from local and discrete features of a representation. These features allow symbolic programs to be improved one module at a time and to experience combinatorial growth in the values they can successfully process. However, it is difficult to design a component that can be used to form symbolic abstractions and which is adequately overparametrized to learn arbitrary high-dimensional transformations. I present Graph-based Symbolically Synthesized Neural Networks (G-SSNNs), a class of neural modules that operate on representations modified with synthesized symbolic programs to include a fixed set of local and discrete features. I demonstrate that the choice of injected features within a G-SSNN module modulates the data efficiency and generalization of baseline neural models, creating predictable patterns of both heightened and curtailed generalization. By training G-SSNNs, we also derive information about desirable semantics of symbolic programs without manual engineering. This information is compact and amenable to abstraction, but can also be flexibly recontextualized for other high-dimensional settings. In future work, I will investigate data efficient generalization and the transferability of learned symbolic representations in more complex G-SSNN designs based on more complex classes of symbolic programs. Experimental code and data are available at https://github.com/shlomenu/symbolically_synthesized_networks .

Humans have the ability to adapt the type of information they use, the procedure they employ, and the amount of time they spend when solving problems. However, most standard neural networks have a fixed function type and computation budget regardless of the sample's nature or difficulty. Adaptivity is a powerful paradigm as it not only imbues practitioners with flexibility pertaining to the downstream usage of these models but can also serve as a powerful inductive bias for solving certain challenging classes of problems. In this work, we introduce a new approach called AdaTape, which allows for dynamic computation in neural networks through adaptive tape tokens. AdaTape utilizes an elastic input sequence by equipping an architecture with a dynamic read-and-write tape. Specifically, we adaptively generate input sequences using tape tokens obtained from a tape bank which can be either trainable or derived from input data. We examine the challenges and requirements to obtain dynamic sequence content and length, and propose the Adaptive Tape Reading (ATR) algorithm to achieve both goals. Through extensive experiments on image recognition tasks, we show that AdaTape can achieve better performance while maintaining the computational cost. To facilitate further research, we have released code at https://github.com/google-research/scenic.

In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate for a given task. Here, we explore the possibility that one can uncover useful geometric inductive biases by studying how training molds the Riemannian geometry induced by unconstrained neural network feature maps. We first show that at infinite width, neural networks with random parameters induce highly symmetric metrics on input space. This symmetry is broken by feature learning: networks trained to perform classification tasks learn to magnify local areas along decision boundaries. This holds in deep networks trained on high-dimensional image classification tasks, and even in self-supervised representation learning. These results begin to elucidate how training shapes the geometry induced by unconstrained neural network feature maps, laying the groundwork for an understanding of this richly nonlinear form of feature learning.

Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural representations. This mismatch leaves no suitable method to solve surface PDEs directly within the neural domain, forcing explicit mesh extraction or per-instance residual training, preventing end-to-end workflows. We present a novel, mesh-free formulation that learns a local update operator conditioned on neural (local) shape attributes, enabling surface PDEs to be solved directly where the (neural) data lives. The operator integrates naturally with prevalent neural surface representations, is trained once on a single representative shape, and generalizes across shape and topology variations, enabling accurate, fast inference without explicit meshing or per-instance optimization while preserving differentiability. Across analytic benchmarks (heat equation and Poisson solve on sphere) and real neural assets across different representations, our method slightly outperforms CPM while remaining reasonably close to FEM, and, to our knowledge, delivers the first end-to-end pipeline that solves surface PDEs on both neural and classical surface representations. Code will be released on acceptance.

Understanding what generative models retain from training data remains challenging, with implications for copyright and privacy. Beyond verbatim reproduction, models can encode subtler traces of their training data that never surface in their outputs yet remain exploitable. We study this regime for Rectified Flows, which are increasingly used in deployed generative systems. We analyse the interpolation path X_λ= (1-λ)X_0 + λX_1 that defines the Rectified Flow training. We show that a gap exists between the reconstruction of train and test data that follows a bell-shaped curve over λ, wich accumulates during training, while the validation metrics remain stable. The signal has a maximum whose location we derive in closed form under Gaussian assumptions. We validate these predictions on both audio and images and show that the bell-shaped structure is universal, while the peak prediction holds when our assumptions are satisfied. As a proof of concept, we exploit this specific λ-resolved structure to perform a Membership Inference Attack, distinguishing members of the training set from non-members.

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

Significant progress has been made in training large generative models for natural language and images. Yet, the advancement of 3D generative models is hindered by their substantial resource demands for training, along with inefficient, non-compact, and less expressive representations. This paper introduces Make-A-Shape, a new 3D generative model designed for efficient training on a vast scale, capable of utilizing 10 millions publicly-available shapes. Technical-wise, we first innovate a wavelet-tree representation to compactly encode shapes by formulating the subband coefficient filtering scheme to efficiently exploit coefficient relations. We then make the representation generatable by a diffusion model by devising the subband coefficients packing scheme to layout the representation in a low-resolution grid. Further, we derive the subband adaptive training strategy to train our model to effectively learn to generate coarse and detail wavelet coefficients. Last, we extend our framework to be controlled by additional input conditions to enable it to generate shapes from assorted modalities, e.g., single/multi-view images, point clouds, and low-resolution voxels. In our extensive set of experiments, we demonstrate various applications, such as unconditional generation, shape completion, and conditional generation on a wide range of modalities. Our approach not only surpasses the state of the art in delivering high-quality results but also efficiently generates shapes within a few seconds, often achieving this in just 2 seconds for most conditions.

We propose LGGPT, an LLM-based model tailored for unified layout generation. First, we propose Arbitrary Layout Instruction (ALI) and Universal Layout Response (ULR) as the uniform I/O template. ALI accommodates arbitrary layout generation task inputs across multiple layout domains, enabling LGGPT to unify both task-generic and domain-generic layout generation hitherto unexplored. Collectively, ALI and ULR boast a succinct structure that forgoes superfluous tokens typically found in existing HTML-based formats, facilitating efficient instruction tuning and boosting unified generation performance. In addition, we propose an Interval Quantization Encoding (IQE) strategy that compresses ALI into a more condensed structure. IQE precisely preserves valid layout clues while eliminating the less informative placeholders, facilitating LGGPT to capture complex and variable layout generation conditions during the unified training process. Experimental results demonstrate that LGGPT achieves superior or on par performance compared to existing methods. Notably, LGGPT strikes a prominent balance between proficiency and efficiency with a compact 1.5B parameter LLM, which beats prior 7B or 175B models even in the most extensive and challenging unified scenario. Furthermore, we underscore the necessity of employing LLMs for unified layout generation and suggest that 1.5B could be an optimal parameter size by comparing LLMs of varying scales. Code is available at https://github.com/NiceRingNode/LGGPT.

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

One of the main challenges for arbitrary-shaped text detection is to design a good text instance representation that allows networks to learn diverse text geometry variances. Most of existing methods model text instances in image spatial domain via masks or contour point sequences in the Cartesian or the polar coordinate system. However, the mask representation might lead to expensive post-processing, while the point sequence one may have limited capability to model texts with highly-curved shapes. To tackle these problems, we model text instances in the Fourier domain and propose one novel Fourier Contour Embedding (FCE) method to represent arbitrary shaped text contours as compact signatures. We further construct FCENet with a backbone, feature pyramid networks (FPN) and a simple post-processing with the Inverse Fourier Transformation (IFT) and Non-Maximum Suppression (NMS). Different from previous methods, FCENet first predicts compact Fourier signatures of text instances, and then reconstructs text contours via IFT and NMS during test. Extensive experiments demonstrate that FCE is accurate and robust to fit contours of scene texts even with highly-curved shapes, and also validate the effectiveness and the good generalization of FCENet for arbitrary-shaped text detection. Furthermore, experimental results show that our FCENet is superior to the state-of-the-art (SOTA) methods on CTW1500 and Total-Text, especially on challenging highly-curved text subset.

This paper introduces GenCorres, a novel unsupervised joint shape matching (JSM) approach. Our key idea is to learn a mesh generator to fit an unorganized deformable shape collection while constraining deformations between adjacent synthetic shapes to preserve geometric structures such as local rigidity and local conformality. GenCorres presents three appealing advantages over existing JSM techniques. First, GenCorres performs JSM among a synthetic shape collection whose size is much bigger than the input shapes and fully leverages the datadriven power of JSM. Second, GenCorres unifies consistent shape matching and pairwise matching (i.e., by enforcing deformation priors between adjacent synthetic shapes). Third, the generator provides a concise encoding of consistent shape correspondences. However, learning a mesh generator from an unorganized shape collection is challenging, requiring a good initialization. GenCorres addresses this issue by learning an implicit generator from the input shapes, which provides intermediate shapes between two arbitrary shapes. We introduce a novel approach for computing correspondences between adjacent implicit surfaces, which we use to regularize the implicit generator. Synthetic shapes of the implicit generator then guide initial fittings (i.e., via template-based deformation) for learning the mesh generator. Experimental results show that GenCorres considerably outperforms state-of-the-art JSM techniques. The synthetic shapes of GenCorres also achieve salient performance gains against state-of-the-art deformable shape generators.

In the artificial neuron, I replace the dot product with the weighted Lehmer mean, which may emulate different cases of a generalized mean. The single neuron instance is replaced by a multiplet of neurons which have the same averaging weights. A group of outputs feed forward, in lieu of the single scalar. The generalization parameter is typically set to a different value for each neuron in the multiplet. I further extend the concept to a multiplet taken from the Gini mean. Derivatives with respect to the weight parameters and with respect to the two generalization parameters are given. Some properties of the network are investigated, showing the capacity to emulate the classical exclusive-or problem organically in two layers and perform some multiplication and division. The network can instantiate truncated power series and variants, which can be used to approximate different functions, provided that parameters are constrained. Moreover, a mean case slope score is derived that can facilitate a learning-rate novelty based on homogeneity of the selected elements. The multiplet neuron equation provides a way to segment regularization timeframes and approaches.

In this work we target a learnable output representation that allows continuous, high resolution outputs of arbitrary shape. Recent works represent 3D surfaces implicitly with a Neural Network, thereby breaking previous barriers in resolution, and ability to represent diverse topologies. However, neural implicit representations are limited to closed surfaces, which divide the space into inside and outside. Many real world objects such as walls of a scene scanned by a sensor, clothing, or a car with inner structures are not closed. This constitutes a significant barrier, in terms of data pre-processing (objects need to be artificially closed creating artifacts), and the ability to output open surfaces. In this work, we propose Neural Distance Fields (NDF), a neural network based model which predicts the unsigned distance field for arbitrary 3D shapes given sparse point clouds. NDF represent surfaces at high resolutions as prior implicit models, but do not require closed surface data, and significantly broaden the class of representable shapes in the output. NDF allow to extract the surface as very dense point clouds and as meshes. We also show that NDF allow for surface normal calculation and can be rendered using a slight modification of sphere tracing. We find NDF can be used for multi-target regression (multiple outputs for one input) with techniques that have been exclusively used for rendering in graphics. Experiments on ShapeNet show that NDF, while simple, is the state-of-the art, and allows to reconstruct shapes with inner structures, such as the chairs inside a bus. Notably, we show that NDF are not restricted to 3D shapes, and can approximate more general open surfaces such as curves, manifolds, and functions. Code is available for research at https://virtualhumans.mpi-inf.mpg.de/ndf/.

We show that transformer-based large language models are computationally universal when augmented with an external memory. Any deterministic language model that conditions on strings of bounded length is equivalent to a finite automaton, hence computationally limited. However, augmenting such models with a read-write memory creates the possibility of processing arbitrarily large inputs and, potentially, simulating any algorithm. We establish that an existing large language model, Flan-U-PaLM 540B, can be combined with an associative read-write memory to exactly simulate the execution of a universal Turing machine, U_{15,2}. A key aspect of the finding is that it does not require any modification of the language model weights. Instead, the construction relies solely on designing a form of stored instruction computer that can subsequently be programmed with a specific set of prompts.

Mapping high-fidelity 3D geometry to a representation that allows for intuitive edits remains an elusive goal in computer vision and graphics. The key challenge is the need to model both continuous and discrete shape variations. Current approaches, such as implicit shape representation, lack straightforward interpretable encoding, while others that employ procedural methods output coarse geometry. We present GeoCode, a technique for 3D shape synthesis using an intuitively editable parameter space. We build a novel program that enforces a complex set of rules and enables users to perform intuitive and controlled high-level edits that procedurally propagate at a low level to the entire shape. Our program produces high-quality mesh outputs by construction. We use a neural network to map a given point cloud or sketch to our interpretable parameter space. Once produced by our procedural program, shapes can be easily modified. Empirically, we show that GeoCode can infer and recover 3D shapes more accurately compared to existing techniques and we demonstrate its ability to perform controlled local and global shape manipulations.

With the goal of understanding the visual concepts that CLIP associates with text prompts, we show that the latent space of CLIP can be visualized solely in terms of linear transformations on simple geometric primitives like circles and straight lines. Although existing approaches achieve this by sketch-synthesis-through-optimization, they do so on the space of B\'ezier curves, which exhibit a wastefully large set of structures that they can evolve into, as most of them are non-essential for generating meaningful sketches. We present CLIPDrawX, an algorithm that provides significantly better visualizations for CLIP text embeddings, using only simple primitive shapes like straight lines and circles. This constrains the set of possible outputs to linear transformations on these primitives, thereby exhibiting an inherently simpler mathematical form. The synthesis process of CLIPDrawX can be tracked end-to-end, with each visual concept being explained exclusively in terms of primitives. Implementation will be released upon acceptance. Project Page: https://clipdrawx.github.io/{https://clipdrawx.github.io/}.

In the past few years, neural networks have evolved from simple Feedforward Neural Networks to more complex neural networks, such as Convolutional Neural Networks and Recurrent Neural Networks. Where CNNs are a perfect fit for tasks where the sequence is not important such as image recognition, RNNs are useful when order is important such as machine translation. An increasing number of layers in a neural network is one way to improve its performance, but it also increases its complexity making it much more time and power-consuming to train. One way to tackle this problem is to introduce sparsity in the architecture of the neural network. Pruning is one of the many methods to make a neural network architecture sparse by clipping out weights below a certain threshold while keeping the performance near to the original. Another way is to generate arbitrary structures using random graphs and embed them between an input and output layer of an Artificial Neural Network. Many researchers in past years have focused on pruning mainly CNNs, while hardly any research is done for the same in RNNs. The same also holds in creating sparse architectures for RNNs by generating and embedding arbitrary structures. Therefore, this thesis focuses on investigating the effects of the before-mentioned two techniques on the performance of RNNs. We first describe the pruning of RNNs, its impact on the performance of RNNs, and the number of training epochs required to regain accuracy after the pruning is performed. Next, we continue with the creation and training of Sparse Recurrent Neural Networks and identify the relation between the performance and the graph properties of its underlying arbitrary structure. We perform these experiments on RNN with Tanh nonlinearity (RNN-Tanh), RNN with ReLU nonlinearity (RNN-ReLU), GRU, and LSTM. Finally, we analyze and discuss the results achieved from both the experiments.

We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural fields. The concept of neural fields has previously been combined with a global latent vector, a regular grid of latent vectors, or an irregular grid of latent vectors. Our new representation encodes neural fields on top of a set of vectors. We draw from multiple concepts, such as the radial basis function representation and the cross attention and self-attention function, to design a learnable representation that is especially suitable for processing with transformers. Our results show improved performance in 3D shape encoding and 3D shape generative modeling tasks. We demonstrate a wide variety of generative applications: unconditioned generation, category-conditioned generation, text-conditioned generation, point-cloud completion, and image-conditioned generation.

The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer vision, playing Go, or protein folding -- are in fact feasible with appropriate computational scale. Remarkably, the essence of deep learning is built from two simple algorithmic principles: first, the notion of representation or feature learning, whereby adapted, often hierarchical, features capture the appropriate notion of regularity for each task, and second, learning by local gradient-descent type methods, typically implemented as backpropagation. While learning generic functions in high dimensions is a cursed estimation problem, most tasks of interest are not generic, and come with essential pre-defined regularities arising from the underlying low-dimensionality and structure of the physical world. This text is concerned with exposing these regularities through unified geometric principles that can be applied throughout a wide spectrum of applications. Such a 'geometric unification' endeavour, in the spirit of Felix Klein's Erlangen Program, serves a dual purpose: on one hand, it provides a common mathematical framework to study the most successful neural network architectures, such as CNNs, RNNs, GNNs, and Transformers. On the other hand, it gives a constructive procedure to incorporate prior physical knowledge into neural architectures and provide principled way to build future architectures yet to be invented.

Generating editable 3D CAD models from natural language remains challenging, as existing text-to-CAD systems either produce meshes or rely on scarce design-history data. We present NURBGen, the first framework to generate high-fidelity 3D CAD models directly from text using Non-Uniform Rational B-Splines (NURBS). To achieve this, we fine-tune a large language model (LLM) to translate free-form texts into JSON representations containing NURBS surface parameters (i.e, control points, knot vectors, degrees, and rational weights) which can be directly converted into BRep format using Python. We further propose a hybrid representation that combines untrimmed NURBS with analytic primitives to handle trimmed surfaces and degenerate regions more robustly, while reducing token complexity. Additionally, we introduce partABC, a curated subset of the ABC dataset consisting of individual CAD components, annotated with detailed captions using an automated annotation pipeline. NURBGen demonstrates strong performance on diverse prompts, surpassing prior methods in geometric fidelity and dimensional accuracy, as confirmed by expert evaluations. Code and dataset will be released publicly.

As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK parametrization). However, we show that the standard and NTK parametrizations of a neural network do not admit infinite-width limits that can learn features, which is crucial for pretraining and transfer learning such as with BERT. We propose simple modifications to the standard parametrization to allow for feature learning in the limit. Using the *Tensor Programs* technique, we derive explicit formulas for such limits. On Word2Vec and few-shot learning on Omniglot via MAML, two canonical tasks that rely crucially on feature learning, we compute these limits exactly. We find that they outperform both NTK baselines and finite-width networks, with the latter approaching the infinite-width feature learning performance as width increases. More generally, we classify a natural space of neural network parametrizations that generalizes standard, NTK, and Mean Field parametrizations. We show 1) any parametrization in this space either admits feature learning or has an infinite-width training dynamics given by kernel gradient descent, but not both; 2) any such infinite-width limit can be computed using the Tensor Programs technique. Code for our experiments can be found at github.com/edwardjhu/TP4.

Arbitrary-shaped text detection is a challenging task since curved texts in the wild are of the complex geometric layouts. Existing mainstream methods follow the instance segmentation pipeline to obtain the text regions. However, arbitraryshaped texts are difficult to be depicted through one single segmentation network because of the varying scales. In this paper, we propose a two-stage segmentation-based detector, termed as NASK (Need A Second looK), for arbitrary-shaped text detection. Compared to the traditional single-stage segmentation network, our NASK conducts the detection in a coarse-to-fine manner with the first stage segmentation spotting the rectangle text proposals and the second one retrieving compact representations. Specifically, NASK is composed of a Text Instance Segmentation (TIS) network (1st stage), a Geometry-aware Text RoI Alignment (GeoAlign) module, and a Fiducial pOint eXpression (FOX) module (2nd stage). Firstly, TIS extracts the augmented features with a novel Group Spatial and Channel Attention (GSCA) module and conducts instance segmentation to obtain rectangle proposals. Then, GeoAlign converts these rectangles into the fixed size and encodes RoI-wise feature representation. Finally, FOX disintegrates the text instance into serval pivotal geometrical attributes to refine the detection results. Extensive experimental results on three public benchmarks including Total-Text, SCUTCTW1500, and ICDAR 2015 verify that our NASK outperforms recent state-of-the-art methods.

In this work, we present a novel framework built to simplify 3D asset generation for amateur users. To enable interactive generation, our method supports a variety of input modalities that can be easily provided by a human, including images, text, partially observed shapes and combinations of these, further allowing to adjust the strength of each input. At the core of our approach is an encoder-decoder, compressing 3D shapes into a compact latent representation, upon which a diffusion model is learned. To enable a variety of multi-modal inputs, we employ task-specific encoders with dropout followed by a cross-attention mechanism. Due to its flexibility, our model naturally supports a variety of tasks, outperforming prior works on shape completion, image-based 3D reconstruction, and text-to-3D. Most interestingly, our model can combine all these tasks into one swiss-army-knife tool, enabling the user to perform shape generation using incomplete shapes, images, and textual descriptions at the same time, providing the relative weights for each input and facilitating interactivity. Despite our approach being shape-only, we further show an efficient method to texture the generated shape using large-scale text-to-image models.

We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to 1/2 everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.

Text-driven inversion of generative models is a core paradigm for manipulating 2D or 3D content, unlocking numerous applications such as text-based editing, style transfer, or inverse problems. However, it relies on the assumption that generative models remain sensitive to natural language prompts. We demonstrate that for state-of-the-art native text-to-3D generative models, this assumption often collapses. We identify a critical failure mode where generation trajectories are drawn into latent ``sink traps'': regions where the model becomes insensitive to prompt modifications. In these regimes, changes to the input text fail to alter internal representations in a way that alters the output geometry. Crucially, we observe that this is not a limitation of the model's geometric expressivity; the same generative models possess the ability to produce a vast diversity of shapes but, as we demonstrate, become insensitive to out-of-distribution text guidance. We investigate this behavior by analyzing the sampling trajectories of the generative model, and find that complex geometries can still be represented and produced by leveraging the model's unconditional generative prior. This leads to a more robust framework for text-based 3D shape editing that bypasses latent sinks by decoupling a model's geometric representation power from its linguistic sensitivity. Our approach addresses the limitations of current 3D pipelines and enables high-fidelity semantic manipulation of out-of-distribution 3D shapes. Project webpage: https://daidedou.sorpi.fr/publication/beyondprompts

We present an open-vocabulary and zero-shot method for arbitrary referring expression segmentation (RES), targeting input expressions that are more general than what prior works were designed to handle. Specifically, our inputs encompass both object- and part-level labels as well as implicit references pointing to properties or qualities of object/part function, design, style, material, etc. Our model, coined RESAnything, leverages Chain-of-Thoughts (CoT) reasoning, where the key idea is attribute prompting. We generate detailed descriptions of object/part attributes including shape, color, and location for potential segment proposals through systematic prompting of a large language model (LLM), where the proposals are produced by a foundational image segmentation model. Our approach encourages deep reasoning about object or part attributes related to function, style, design, etc., enabling the system to handle implicit queries without any part annotations for training or fine-tuning. As the first zero-shot and LLM-based RES method, RESAnything achieves clearly superior performance among zero-shot methods on traditional RES benchmarks and significantly outperforms existing methods on challenging scenarios involving implicit queries and complex part-level relations. Finally, we contribute a new benchmark dataset to offer ~3K carefully curated RES instances to assess part-level, arbitrary RES solutions.

Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate dimension reduction, typically achieved via basis expansions. Currently, these bases are chosen a priori without the information for the task at hand and thus may not be effective for the designated task. We instead propose to adaptively learn these bases in an end-to-end fashion. We introduce neural networks that employ a new Basis Layer whose hidden units are each basis functions themselves implemented as a micro neural network. Our architecture learns to apply parsimonious dimension reduction to functional inputs that focuses only on information relevant to the target rather than irrelevant variation in the input function. Across numerous classification/regression tasks with functional data, our method empirically outperforms other types of neural networks, and we prove that our approach is statistically consistent with low generalization error. Code is available at: https://github.com/jwyyy/AdaFNN.

Modern continuous-time generative models typically induce V-shaped flows: each sample travels independently along a nearly straight trajectory from the prior to the data. Although effective, this independent movement overlooks the hierarchical structures that exist in real-world data. To address this, we introduce Y-shaped generative flows, a framework in which samples travel together along shared pathways before branching off to target-specific endpoints. Our formulation is theoretically justified, yet remains practical, requiring only minimal modifications to standard velocity-driven models. We implement this through a scalable, neural network-based training objective. Experiments on synthetic, image, and biological datasets demonstrate that our method recovers hierarchy-aware structures, improves distributional metrics over strong flow-based baselines, and reaches targets in fewer steps.

Can Transformers predict new syllogisms by composing established ones? More generally, what type of targets can be learned by such models from scratch? Recent works show that Transformers can be Turing-complete in terms of expressivity, but this does not address the learnability objective. This paper puts forward the notion of 'globality degree' of a target distribution to capture when weak learning is efficiently achievable by regular Transformers, where the latter measures the least number of tokens required in addition to the tokens histogram to correlate nontrivially with the target. As shown experimentally and theoretically under additional assumptions, distributions with high globality cannot be learned efficiently. In particular, syllogisms cannot be composed on long chains. Furthermore, we show that (i) an agnostic scratchpad cannot help to break the globality barrier, (ii) an educated scratchpad can help if it breaks the globality at each step, however not all such scratchpads can generalize to out-of-distribution (OOD) samples, (iii) a notion of 'inductive scratchpad', that composes the prior information more efficiently, can both break the globality barrier and improve the OOD generalization. In particular, some inductive scratchpads can achieve length generalizations of up to 6x for some arithmetic tasks depending on the input formatting.

Foundation models are a strong trend in deep learning and computer vision. These models serve as a base for applications as they require minor or no further fine-tuning by developers to integrate into their applications. Foundation models for zero-shot object segmentation such as Segment Anything (SAM) output segmentation masks from images without any further object information. When they are followed in a pipeline by an object identification model, they can perform object detection without training. Here, we focus on training such an object identification model. A crucial practical aspect for an object identification model is to be flexible in input size. As object identification is an image retrieval problem, a suitable method should handle multi-query multi-gallery situations without constraining the number of input images (e.g. by having fixed-size aggregation layers). The key solution to train such a model is the centroid triplet loss (CTL), which aggregates image features to their centroids. CTL yields high accuracy, avoids misleading training signals and keeps the model input size flexible. In our experiments, we establish a new state of the art on the ArmBench object identification task, which shows general applicability of our model. We furthermore demonstrate an integrated unseen object detection pipeline on the challenging HOPE dataset, which requires fine-grained detection. There, our pipeline matches and surpasses related methods which have been trained on dataset-specific data.

While learning models are typically studied for inputs in the form of a fixed dimensional feature vector, real world data is rarely found in this form. In order to meet the basic requirement of traditional learning models, structural data generally have to be converted into fix-length vectors in a handcrafted manner, which is tedious and may even incur information loss. A common form of structured data is what we term "semantic tree-structures", corresponding to data where rich semantic information is encoded in a compositional manner, such as those expressed in JavaScript Object Notation (JSON) and eXtensible Markup Language (XML). For tree-structured data, several learning models have been studied to allow for working directly on raw tree-structure data, However such learning models are limited to either a specific tree-topology or a specific tree-structured data format, e.g., synthetic parse trees. In this paper, we propose a novel framework for end-to-end learning on generic semantic tree-structured data of arbitrary topology and heterogeneous data types, such as data expressed in JSON, XML and so on. Motivated by the works in recursive and recurrent neural networks, we develop exemplar neural implementations of our framework for the JSON format. We evaluate our approach on several UCI benchmark datasets, including ablation and data-efficiency studies, and on a toy reinforcement learning task. Experimental results suggest that our framework yields comparable performance to use of standard models with dedicated feature-vectors in general, and even exceeds baseline performance in cases where compositional nature of the data is particularly important. The source code for a JSON-based implementation of our framework along with experiments can be downloaded at https://github.com/EndingCredits/json2vec.

We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate geometric properties, such as the metric and curvatures, (ii) to approximate Partial Differential Equations (PDEs) on manifolds, (iii) learn solution maps for Laplace-Beltrami (LB) operators, and (iv) to solve Bayesian inverse problems for identifying manifold shapes. The methods allow for handling geometries of general shape including point-cloud representations. The developed GNPs provide approaches for incorporating the roles of geometry in data-driven learning of operators.

Recent advances in deep generative models have led to immense progress in 3D shape synthesis. While existing models are able to synthesize shapes represented as voxels, point-clouds, or implicit functions, these methods only indirectly enforce the plausibility of the final 3D shape surface. Here we present a 3D shape synthesis framework (SurfGen) that directly applies adversarial training to the object surface. Our approach uses a differentiable spherical projection layer to capture and represent the explicit zero isosurface of an implicit 3D generator as functions defined on the unit sphere. By processing the spherical representation of 3D object surfaces with a spherical CNN in an adversarial setting, our generator can better learn the statistics of natural shape surfaces. We evaluate our model on large-scale shape datasets, and demonstrate that the end-to-end trained model is capable of generating high fidelity 3D shapes with diverse topology.

Assessing the complexity of functions computed by a neural network helps us understand how the network will learn and generalize. One natural measure of complexity is how the network distorts length - if the network takes a unit-length curve as input, what is the length of the resulting curve of outputs? It has been widely believed that this length grows exponentially in network depth. We prove that in fact this is not the case: the expected length distortion does not grow with depth, and indeed shrinks slightly, for ReLU networks with standard random initialization. We also generalize this result by proving upper bounds both for higher moments of the length distortion and for the distortion of higher-dimensional volumes. These theoretical results are corroborated by our experiments.

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a variety of PDEs, such as fluid flows. However, the FNO uses the Fast Fourier transform (FFT), which is limited to rectangular domains with uniform grids. In this work, we propose a new framework, viz., geo-FNO, to solve PDEs on arbitrary geometries. Geo-FNO learns to deform the input (physical) domain, which may be irregular, into a latent space with a uniform grid. The FNO model with the FFT is applied in the latent space. The resulting geo-FNO model has both the computation efficiency of FFT and the flexibility of handling arbitrary geometries. Our geo-FNO is also flexible in terms of its input formats, viz., point clouds, meshes, and design parameters are all valid inputs. We consider a variety of PDEs such as the Elasticity, Plasticity, Euler's, and Navier-Stokes equations, and both forward modeling and inverse design problems. Geo-FNO is 10^5 times faster than the standard numerical solvers and twice more accurate compared to direct interpolation on existing ML-based PDE solvers such as the standard FNO.

We introduce STRING: Separable Translationally Invariant Position Encodings. STRING extends Rotary Position Encodings, a recently proposed and widely used algorithm in large language models, via a unifying theoretical framework. Importantly, STRING still provides exact translation invariance, including token coordinates of arbitrary dimensionality, whilst maintaining a low computational footprint. These properties are especially important in robotics, where efficient 3D token representation is key. We integrate STRING into Vision Transformers with RGB(-D) inputs (color plus optional depth), showing substantial gains, e.g. in open-vocabulary object detection and for robotics controllers. We complement our experiments with a rigorous mathematical analysis, proving the universality of our methods.

We propose a novel interpretation technique to explain the behavior of structured output models, which learn mappings between an input vector to a set of output variables simultaneously. Because of the complex relationship between the computational path of output variables in structured models, a feature can affect the value of output through other ones. We focus on one of the outputs as the target and try to find the most important features utilized by the structured model to decide on the target in each locality of the input space. In this paper, we assume an arbitrary structured output model is available as a black box and argue how considering the correlations between output variables can improve the explanation performance. The goal is to train a function as an interpreter for the target output variable over the input space. We introduce an energy-based training process for the interpreter function, which effectively considers the structural information incorporated into the model to be explained. The effectiveness of the proposed method is confirmed using a variety of simulated and real data sets.

In this work, we demonstrate that a simple two-layer neural network with standard activation functions can learn an arbitrary word operation in any finite group, provided sufficient width is available and exhibits grokking while doing so. To explain the mechanism by which this is achieved, we reframe the problem as that of learning a particular 3-tensor, which we show is typically of low rank. A key insight is that low-rank implementations of this tensor can be obtained by decomposing it along triplets of basic self-conjugate representations of the group and leveraging the fusion structure to rule out many components. Focusing on a phenomenologically similar but more tractable surrogate model, we show that the network is able to find such low-rank implementations (or approximations thereof), thereby using limited width to approximate the word-tensor in a generalizable way. In the case of the simple multiplication word, we further elucidate the form of these low-rank implementations, showing that the network effectively implements efficient matrix multiplication in the sense of Strassen. Our work also sheds light on the mechanism by which a network reaches such a solution under gradient descent.

We prove that any Turing machine running on inputs of arbitrary length can be simulated by a constant bit-size transformer, as long as the context window is sufficiently long. This improves previous works, which require scaling up either the model's precision or the number of parameters on longer inputs. Furthermore, we prove that the complexity class SPACE[s(n)] exactly characterizes the expressive power of a constant bit-size transformer with a context window of length s(n). Our approach relies on simulating Post machines, a Turing-complete computational model. Post machines can be modeled as automata equipped with a queue, exhibiting computational behaviors naturally aligned with those of transformers. The behavioral similarity between transformers and Post machines may offer new insights into the mechanisms underlying the reasoning abilities of transformers.

We introduce an algorithm where the individual bits representing the weights of a neural network are learned. This method allows training weights with integer values on arbitrary bit-depths and naturally uncovers sparse networks, without additional constraints or regularization techniques. We show better results than the standard training technique with fully connected networks and similar performance as compared to standard training for convolutional and residual networks. By training bits in a selective manner we found that the biggest contribution to achieving high accuracy is given by the first three most significant bits, while the rest provide an intrinsic regularization. As a consequence more than 90\% of a network can be used to store arbitrary codes without affecting its accuracy. These codes may be random noise, binary files or even the weights of previously trained networks.

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.

Scene text detection and recognition has received increasing research attention. Existing methods can be roughly categorized into two groups: character-based and segmentation-based. These methods either are costly for character annotation or need to maintain a complex pipeline, which is often not suitable for real-time applications. Here we address the problem by proposing the Adaptive Bezier-Curve Network (ABCNet). Our contributions are three-fold: 1) For the first time, we adaptively fit arbitrarily-shaped text by a parameterized Bezier curve. 2) We design a novel BezierAlign layer for extracting accurate convolution features of a text instance with arbitrary shapes, significantly improving the precision compared with previous methods. 3) Compared with standard bounding box detection, our Bezier curve detection introduces negligible computation overhead, resulting in superiority of our method in both efficiency and accuracy. Experiments on arbitrarily-shaped benchmark datasets, namely Total-Text and CTW1500, demonstrate that ABCNet achieves state-of-the-art accuracy, meanwhile significantly improving the speed. In particular, on Total-Text, our realtime version is over 10 times faster than recent state-of-the-art methods with a competitive recognition accuracy. Code is available at https://tinyurl.com/AdelaiDet

Since its inception in "Attention Is All You Need", transformer architecture has led to revolutionary advancements in NLP. The attention layer within the transformer admits a sequence of input tokens X and makes them interact through pairwise similarities computed as softmax(XQK^top X^top), where (K,Q) are the trainable key-query parameters. In this work, we establish a formal equivalence between the optimization geometry of self-attention and a hard-margin SVM problem that separates optimal input tokens from non-optimal tokens using linear constraints on the outer-products of token pairs. This formalism allows us to characterize the implicit bias of 1-layer transformers optimized with gradient descent: (1) Optimizing the attention layer with vanishing regularization, parameterized by (K,Q), converges in direction to an SVM solution minimizing the nuclear norm of the combined parameter W=KQ^top. Instead, directly parameterizing by W minimizes a Frobenius norm objective. We characterize this convergence, highlighting that it can occur toward locally-optimal directions rather than global ones. (2) Complementing this, we prove the local/global directional convergence of gradient descent under suitable geometric conditions. Importantly, we show that over-parameterization catalyzes global convergence by ensuring the feasibility of the SVM problem and by guaranteeing a benign optimization landscape devoid of stationary points. (3) While our theory applies primarily to linear prediction heads, we propose a more general SVM equivalence that predicts the implicit bias with nonlinear heads. Our findings are applicable to arbitrary datasets and their validity is verified via experiments. We also introduce several open problems and research directions. We believe these findings inspire the interpretation of transformers as a hierarchy of SVMs that separates and selects optimal tokens.

Length generalization refers to the ability to extrapolate from short training sequences to long test sequences and is a challenge for current large language models. While prior work has proposed some architecture or data format changes to achieve length generalization, these proposals typically apply to a limited set of tasks. Building on prior scratchpad and Chain-of-Thought (CoT) techniques, we propose Turing Programs, a novel CoT strategy that decomposes an algorithmic task into steps mimicking the computation of a Turing Machine. This framework is both universal, as it can accommodate any algorithmic task, and simple, requiring only copying text from the context with small modifications. We show that by using Turing Programs, we obtain robust length generalization on a range of algorithmic tasks: addition, multiplication and in-context SGD. We then demonstrate that transformers achieve length generalization on random Turing Programs, suggesting that length generalization is possible for any algorithmic task. Finally, we theoretically prove that transformers can implement Turing Programs, constructing a simple RASP (Weiss et al.) program that simulates an arbitrary Turing machine.

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.

In this paper, we develop a new method to automatically convert 2D line drawings from three orthographic views into 3D CAD models. Existing methods for this problem reconstruct 3D models by back-projecting the 2D observations into 3D space while maintaining explicit correspondence between the input and output. Such methods are sensitive to errors and noises in the input, thus often fail in practice where the input drawings created by human designers are imperfect. To overcome this difficulty, we leverage the attention mechanism in a Transformer-based sequence generation model to learn flexible mappings between the input and output. Further, we design shape programs which are suitable for generating the objects of interest to boost the reconstruction accuracy and facilitate CAD modeling applications. Experiments on a new benchmark dataset show that our method significantly outperforms existing ones when the inputs are noisy or incomplete.

A single two-input gate suffices for all of Boolean logic in digital hardware. No comparable primitive has been known for continuous mathematics: computing elementary functions such as sin, cos, sqrt, and log has always required multiple distinct operations. Here I show that a single binary operator, eml(x,y)=exp(x)-ln(y), together with the constant 1, generates the standard repertoire of a scientific calculator. This includes constants such as e, pi, and i; arithmetic operations including addition, subtraction, multiplication, division, and exponentiation as well as the usual transcendental and algebraic functions. For example, exp(x)=eml(x,1), ln(x)=eml(1,eml(eml(1,x),1)), and likewise for all other operations. That such an operator exists was not anticipated; I found it by systematic exhaustive search and established constructively that it suffices for the concrete scientific-calculator basis. In EML (Exp-Minus-Log) form, every such expression becomes a binary tree of identical nodes, yielding a grammar as simple as S -> 1 | eml(S,S). This uniform structure also enables gradient-based symbolic regression: using EML trees as trainable circuits with standard optimizers (Adam), I demonstrate the feasibility of exact recovery of closed-form elementary functions from numerical data at shallow tree depths up to 4. The same architecture can fit arbitrary data, but when the generating law is elementary, it may recover the exact formula.

Since the success of GPT, large language models (LLMs) have been revolutionizing machine learning and have initiated the so-called LLM prompting paradigm. In the era of LLMs, people train a single general-purpose LLM and provide the LLM with different prompts to perform different tasks. However, such empirical success largely lacks theoretical understanding. Here, we present the first theoretical study on the LLM prompting paradigm to the best of our knowledge. In this work, we show that prompting is in fact Turing-complete: there exists a finite-size Transformer such that for any computable function, there exists a corresponding prompt following which the Transformer computes the function. Furthermore, we show that even though we use only a single finite-size Transformer, it can still achieve nearly the same complexity bounds as that of the class of all unbounded-size Transformers. Overall, our result reveals that prompting can enable a single finite-size Transformer to be efficiently universal, which establishes a theoretical underpinning for prompt engineering in practice.

Human perception of 3D shapes goes beyond reconstructing them as a set of points or a composition of geometric primitives: we also effortlessly understand higher-level shape structure such as the repetition and reflective symmetry of object parts. In contrast, recent advances in 3D shape sensing focus more on low-level geometry but less on these higher-level relationships. In this paper, we propose 3D shape programs, integrating bottom-up recognition systems with top-down, symbolic program structure to capture both low-level geometry and high-level structural priors for 3D shapes. Because there are no annotations of shape programs for real shapes, we develop neural modules that not only learn to infer 3D shape programs from raw, unannotated shapes, but also to execute these programs for shape reconstruction. After initial bootstrapping, our end-to-end differentiable model learns 3D shape programs by reconstructing shapes in a self-supervised manner. Experiments demonstrate that our model accurately infers and executes 3D shape programs for highly complex shapes from various categories. It can also be integrated with an image-to-shape module to infer 3D shape programs directly from an RGB image, leading to 3D shape reconstructions that are both more accurate and more physically plausible.

We investigate the learning of implicit neural representation (INR) using an overparameterized multilayer perceptron (MLP) via a novel nonparametric teaching perspective. The latter offers an efficient example selection framework for teaching nonparametrically defined (viz. non-closed-form) target functions, such as image functions defined by 2D grids of pixels. To address the costly training of INRs, we propose a paradigm called Implicit Neural Teaching (INT) that treats INR learning as a nonparametric teaching problem, where the given signal being fitted serves as the target function. The teacher then selects signal fragments for iterative training of the MLP to achieve fast convergence. By establishing a connection between MLP evolution through parameter-based gradient descent and that of function evolution through functional gradient descent in nonparametric teaching, we show for the first time that teaching an overparameterized MLP is consistent with teaching a nonparametric learner. This new discovery readily permits a convenient drop-in of nonparametric teaching algorithms to broadly enhance INR training efficiency, demonstrating 30%+ training time savings across various input modalities.

Current foundation models exhibit impressive capabilities when prompted either with text only or with both image and text inputs. But do their capabilities change depending on the input modality? In this work, we propose IsoBench, a benchmark dataset containing problems from four major areas: math, science, algorithms, and games. Each example is presented with multiple isomorphic representations of inputs, such as visual, textual, and mathematical presentations. IsoBench provides fine-grained feedback to diagnose performance gaps caused by the form of the representation. Across various foundation models, we observe that on the same problem, models have a consistent preference towards textual representations. Most prominently, when evaluated on all IsoBench problems, Claude-3 Opus performs 28.7 points worse when provided with images instead of text; similarly, GPT-4 Turbo is 18.7 points worse and Gemini Pro is 14.9 points worse. Finally, we present two prompting techniques, IsoCombination and IsoScratchPad, which improve model performance by considering combinations of, and translations between, different input representations.

We introduce a new neural architecture to learn the conditional probability of an output sequence with elements that are discrete tokens corresponding to positions in an input sequence. Such problems cannot be trivially addressed by existent approaches such as sequence-to-sequence and Neural Turing Machines, because the number of target classes in each step of the output depends on the length of the input, which is variable. Problems such as sorting variable sized sequences, and various combinatorial optimization problems belong to this class. Our model solves the problem of variable size output dictionaries using a recently proposed mechanism of neural attention. It differs from the previous attention attempts in that, instead of using attention to blend hidden units of an encoder to a context vector at each decoder step, it uses attention as a pointer to select a member of the input sequence as the output. We call this architecture a Pointer Net (Ptr-Net). We show Ptr-Nets can be used to learn approximate solutions to three challenging geometric problems -- finding planar convex hulls, computing Delaunay triangulations, and the planar Travelling Salesman Problem -- using training examples alone. Ptr-Nets not only improve over sequence-to-sequence with input attention, but also allow us to generalize to variable size output dictionaries. We show that the learnt models generalize beyond the maximum lengths they were trained on. We hope our results on these tasks will encourage a broader exploration of neural learning for discrete problems.

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

In this work, we propose a concise neural operator architecture for operator learning. Drawing an analogy with a conventional fully connected neural network, we define the neural operator as follows: the output of the i-th neuron in a nonlinear operator layer is defined by mathcal O_i(u) = sigmaleft( sum_j mathcal W_{ij} u + mathcal B_{ij}right). Here, mathcal W_{ij} denotes the bounded linear operator connecting j-th input neuron to i-th output neuron, and the bias mathcal B_{ij} takes the form of a function rather than a scalar. Given its new universal approximation property, the efficient parameterization of the bounded linear operators between two neurons (Banach spaces) plays a critical role. As a result, we introduce MgNO, utilizing multigrid structures to parameterize these linear operators between neurons. This approach offers both mathematical rigor and practical expressivity. Additionally, MgNO obviates the need for conventional lifting and projecting operators typically required in previous neural operators. Moreover, it seamlessly accommodates diverse boundary conditions. Our empirical observations reveal that MgNO exhibits superior ease of training compared to other CNN-based models, while also displaying a reduced susceptibility to overfitting when contrasted with spectral-type neural operators. We demonstrate the efficiency and accuracy of our method with consistently state-of-the-art performance on different types of partial differential equations (PDEs).

Neural networks require a careful design in order to perform properly on a given task. In particular, selecting a good activation function (possibly in a data-dependent fashion) is a crucial step, which remains an open problem in the research community. Despite a large amount of investigations, most current implementations simply select one fixed function from a small set of candidates, which is not adapted during training, and is shared among all neurons throughout the different layers. However, neither two of these assumptions can be supposed optimal in practice. In this paper, we present a principled way to have data-dependent adaptation of the activation functions, which is performed independently for each neuron. This is achieved by leveraging over past and present advances on cubic spline interpolation, allowing for local adaptation of the functions around their regions of use. The resulting algorithm is relatively cheap to implement, and overfitting is counterbalanced by the inclusion of a novel damping criterion, which penalizes unwanted oscillations from a predefined shape. Experimental results validate the proposal over two well-known benchmarks.

We present Diff3F as a simple, robust, and class-agnostic feature descriptor that can be computed for untextured input shapes (meshes or point clouds). Our method distills diffusion features from image foundational models onto input shapes. Specifically, we use the input shapes to produce depth and normal maps as guidance for conditional image synthesis. In the process, we produce (diffusion) features in 2D that we subsequently lift and aggregate on the original surface. Our key observation is that even if the conditional image generations obtained from multi-view rendering of the input shapes are inconsistent, the associated image features are robust and, hence, can be directly aggregated across views. This produces semantic features on the input shapes, without requiring additional data or training. We perform extensive experiments on multiple benchmarks (SHREC'19, SHREC'20, FAUST, and TOSCA) and demonstrate that our features, being semantic instead of geometric, produce reliable correspondence across both isometric and non-isometrically related shape families. Code is available via the project page at https://diff3f.github.io/

With the emergence of powerful representations of continuous data in the form of neural fields, there is a need for discretization invariant learning: an approach for learning maps between functions on continuous domains without being sensitive to how the function is sampled. We present a new framework for understanding and designing discretization invariant neural networks (DI-Nets), which generalizes many discrete networks such as convolutional neural networks as well as continuous networks such as neural operators. Our analysis establishes upper bounds on the deviation in model outputs under different finite discretizations, and highlights the central role of point set discrepancy in characterizing such bounds. This insight leads to the design of a family of neural networks driven by numerical integration via quasi-Monte Carlo sampling with discretizations of low discrepancy. We prove by construction that DI-Nets universally approximate a large class of maps between integrable function spaces, and show that discretization invariance also describes backpropagation through such models. Applied to neural fields, convolutional DI-Nets can learn to classify and segment visual data under various discretizations, and sometimes generalize to new types of discretizations at test time. Code: https://github.com/clintonjwang/DI-net.

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integral operators and nonlinear activation functions. We prove a universal approximation theorem for our proposed neural operator, showing that it can approximate any given nonlinear continuous operator. The proposed neural operators are also discretization-invariant, i.e., they share the same model parameters among different discretization of the underlying function spaces. Furthermore, we introduce four classes of efficient parameterization, viz., graph neural operators, multi-pole graph neural operators, low-rank neural operators, and Fourier neural operators. An important application for neural operators is learning surrogate maps for the solution operators of partial differential equations (PDEs). We consider standard PDEs such as the Burgers, Darcy subsurface flow, and the Navier-Stokes equations, and show that the proposed neural operators have superior performance compared to existing machine learning based methodologies, while being several orders of magnitude faster than conventional PDE solvers.

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.

The ability to automatically generate music that appropriately matches an arbitrary input track is a challenging task. We present a novel controllable system for generating single stems to accompany musical mixes of arbitrary length. At the core of our method are audio autoencoders that efficiently compress audio waveform samples into invertible latent representations, and a conditional latent diffusion model that takes as input the latent encoding of a mix and generates the latent encoding of a corresponding stem. To provide control over the timbre of generated samples, we introduce a technique to ground the latent space to a user-provided reference style during diffusion sampling. For further improving audio quality, we adapt classifier-free guidance to avoid distortions at high guidance strengths when generating an unbounded latent space. We train our model on a dataset of pairs of mixes and matching bass stems. Quantitative experiments demonstrate that, given an input mix, the proposed system can generate basslines with user-specified timbres. Our controllable conditional audio generation framework represents a significant step forward in creating generative AI tools to assist musicians in music production.

Image segmentation is usually addressed by training a model for a fixed set of object classes. Incorporating additional classes or more complex queries later is expensive as it requires re-training the model on a dataset that encompasses these expressions. Here we propose a system that can generate image segmentations based on arbitrary prompts at test time. A prompt can be either a text or an image. This approach enables us to create a unified model (trained once) for three common segmentation tasks, which come with distinct challenges: referring expression segmentation, zero-shot segmentation and one-shot segmentation. We build upon the CLIP model as a backbone which we extend with a transformer-based decoder that enables dense prediction. After training on an extended version of the PhraseCut dataset, our system generates a binary segmentation map for an image based on a free-text prompt or on an additional image expressing the query. We analyze different variants of the latter image-based prompts in detail. This novel hybrid input allows for dynamic adaptation not only to the three segmentation tasks mentioned above, but to any binary segmentation task where a text or image query can be formulated. Finally, we find our system to adapt well to generalized queries involving affordances or properties. Code is available at https://eckerlab.org/code/clipseg.

In this work, we develop intuitive controls for editing the style of 3D objects. Our framework, Text2Mesh, stylizes a 3D mesh by predicting color and local geometric details which conform to a target text prompt. We consider a disentangled representation of a 3D object using a fixed mesh input (content) coupled with a learned neural network, which we term neural style field network. In order to modify style, we obtain a similarity score between a text prompt (describing style) and a stylized mesh by harnessing the representational power of CLIP. Text2Mesh requires neither a pre-trained generative model nor a specialized 3D mesh dataset. It can handle low-quality meshes (non-manifold, boundaries, etc.) with arbitrary genus, and does not require UV parameterization. We demonstrate the ability of our technique to synthesize a myriad of styles over a wide variety of 3D meshes.

Neural operators have become increasingly popular in solving partial differential equations (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the data-hungry nature of operator learning inevitably poses a bottleneck for their widespread applications. At the core of the challenge lies the absence of transferability of neural operators to new geometries. To tackle this issue, we propose operator learning with domain decomposition, a local-to-global framework to solve PDEs on arbitrary geometries. Under this framework, we devise an iterative scheme Schwarz Neural Inference (SNI). This scheme allows for partitioning of the problem domain into smaller subdomains, on which local problems can be solved with neural operators, and stitching local solutions to construct a global solution. Additionally, we provide a theoretical analysis of the convergence rate and error bound. We conduct extensive experiments on several representative PDEs with diverse boundary conditions and achieve remarkable geometry generalization compared to alternative methods. These analysis and experiments demonstrate the proposed framework's potential in addressing challenges related to geometry generalization and data efficiency.

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks and numerical methods. We show how our GNPs can be trained to learn robust latent representations for the differential geometry of point-clouds to provide estimates of metric, curvature, and other shape-related features. We demonstrate how our pre-trained GNPs can be used (i) to estimate the geometric properties of surfaces of arbitrary shape and topologies with robustness in the presence of noise, (ii) to approximate solutions of geometric partial differential equations (PDEs) on manifolds, and (iii) to solve equations for shape deformations such as curvature driven flows. We release codes and weights for using GNPs in the package geo_neural_op. This allows for incorporating our pre-trained GNPs as components for reuse within existing and new data processing pipelines. The GNPs also can be used as part of numerical solvers involving geometry or as part of methods for performing inference and other geometric tasks.

Shape abstraction is an important task for simplifying complex geometric structures while retaining essential features. Sweep surfaces, commonly found in human-made objects, aid in this process by effectively capturing and representing object geometry, thereby facilitating abstraction. In this paper, we introduce \papername, a novel approach to shape abstraction through sweep surfaces. We propose an effective parameterization for sweep surfaces, utilizing superellipses for profile representation and B-spline curves for the axis. This compact representation, requiring as few as 14 float numbers, facilitates intuitive and interactive editing while preserving shape details effectively. Additionally, by introducing a differentiable neural sweeper and an encoder-decoder architecture, we demonstrate the ability to predict sweep surface representations without supervision. We show the superiority of our model through several quantitative and qualitative experiments throughout the paper. Our code is available at https://mingrui-zhao.github.io/SweepNet/

Industrial CAD workflows require robust, generalizable 3D geometric representations supporting accuracy and explainability. We introduce Shape, a self-supervised foundation model converting surface meshes into dense per-token embeddings. Shape combines a structured 3D latent grid, a multi-scale geometry-aware tokenizer (MAGNO) with cross-attention, and a transformer processor using grouped-query attention and RMSNorm. A learned reconstruction prior enables per-region attribution for explainable predictions. Pretraining uses masked-token reconstruction of normalized geometry statistics and multi-resolution contrastive consistency. The 10.9M-parameter backbone is pretrained on 61,052 CAD meshes from Thingi10K, MFCAD, and Fusion360. On a held-out split of 2,983 meshes, Shape achieves reconstruction R2 = 0.729 and 98.1% top-1 retrieval under the Wang-Isola protocol, with near-zero reconstruction train/val gap (contrastive scores use a larger evaluation pool). A 2x2 ablation on loss type and target-space normalization shows per-dimension normalization is critical: without it, performance collapses (R2 < 0.14, top-1 < 88%); with it, both losses succeed (R2 > 0.70, top-1 > 96%). Smooth-L1 offers secondary stability. Code, embeddings, and an interactive demo are released at https://github.com/simd-ai/shape.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

We present a unified representation of the most popular neural network activation functions. Adopting Mittag-Leffler functions of fractional calculus, we propose a flexible and compact functional form that is able to interpolate between various activation functions and mitigate common problems in training neural networks such as vanishing and exploding gradients. The presented gated representation extends the scope of fixed-shape activation functions to their adaptive counterparts whose shape can be learnt from the training data. The derivatives of the proposed functional form can also be expressed in terms of Mittag-Leffler functions making it a suitable candidate for gradient-based backpropagation algorithms. By training multiple neural networks of different complexities on various datasets with different sizes, we demonstrate that adopting a unified gated representation of activation functions offers a promising and affordable alternative to individual built-in implementations of activation functions in conventional machine learning frameworks.

This paper introduces a new learning paradigm termed Neural Metamorphosis (NeuMeta), which aims to build self-morphable neural networks. Contrary to crafting separate models for different architectures or sizes, NeuMeta directly learns the continuous weight manifold of neural networks. Once trained, we can sample weights for any-sized network directly from the manifold, even for previously unseen configurations, without retraining. To achieve this ambitious goal, NeuMeta trains neural implicit functions as hypernetworks. They accept coordinates within the model space as input, and generate corresponding weight values on the manifold. In other words, the implicit function is learned in a way, that the predicted weights is well-performed across various models sizes. In training those models, we notice that, the final performance closely relates on smoothness of the learned manifold. In pursuit of enhancing this smoothness, we employ two strategies. First, we permute weight matrices to achieve intra-model smoothness, by solving the Shortest Hamiltonian Path problem. Besides, we add a noise on the input coordinates when training the implicit function, ensuring models with various sizes shows consistent outputs. As such, NeuMeta shows promising results in synthesizing parameters for various network configurations. Our extensive tests in image classification, semantic segmentation, and image generation reveal that NeuMeta sustains full-size performance even at a 75% compression rate.

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time R^3times R, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions. The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually R^3 times {0}. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

Trainable input embedding tables are a standard component of modern language models. We ask whether they are actually necessary at the input interface. For a vocabulary of size V, exact token identity requires only K=lceil log_2 Vrceil bits. We replace the usual trainable Vtimes d_{model} input embedding matrix with fixed minimal binary token codes and a zero-parameter lift to model width. In our main setting, V=65{,}536, so K=16, and tokens are represented by fixed 16-dimensional binary codes tiled to d_{model}=1024. We also evaluate a fully table-free variant in which codes are generated from token IDs on the fly and randomly recoded by an invertible affine transform over F_2^K. Across matched 32-layer decoder-only models trained on approximately 17B tokens and evaluated over three independent training seeds, fixed minimal codes achieve comparable held-out validation perplexity to a standard learned-input baseline while removing 67.1M trainable input parameters. The fixed-code runs have a lower mean validation perplexity in our experiments, 2.36 versus 2.44, but the observed gap is within the measured seed-to-seed variation of 4.8\%; we therefore interpret the result as evidence that the trainable input table is not necessary, rather than as a statistically resolved superiority claim. The table-free affine-recoded variant remains close at 2.39 despite a slightly shorter training run. These results show that, in this regime, a trainable input embedding table is not necessary for useful language modeling. The output projection remains standard and trainable.

A Transformer-based deep direct sampling method is proposed for electrical impedance tomography, a well-known severely ill-posed nonlinear boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and the reconstructed images. An effort is made to give a specific example to a fundamental question: whether and how one can benefit from the theoretical structure of a mathematical problem to develop task-oriented and structure-conforming deep neural networks? Specifically, inspired by direct sampling methods for inverse problems, the 1D boundary data in different frequencies are preprocessed by a partial differential equation-based feature map to yield 2D harmonic extensions as different input channels. Then, by introducing learnable non-local kernels, the direct sampling is recast to a modified attention mechanism. The new method achieves superior accuracy over its predecessors and contemporary operator learners and shows robustness to noises in benchmarks. This research shall strengthen the insights that, despite being invented for natural language processing tasks, the attention mechanism offers great flexibility to be modified in conformity with the a priori mathematical knowledge, which ultimately leads to the design of more physics-compatible neural architectures.

Neural networks are trained to learn an approximate mapping from an input domain to a target domain. Incorporating prior knowledge about true mappings is critical to learning a useful approximation. With current architectures, it is challenging to enforce structure on the derivatives of the input-output mapping. We propose to use a neural network to directly learn the Jacobian of the input-output function, which allows easy control of the derivative. We focus on structuring the derivative to allow invertibility and also demonstrate that other useful priors, such as k-Lipschitz, can be enforced. Using this approach, we can learn approximations to simple functions that are guaranteed to be invertible and easily compute the inverse. We also show similar results for 1-Lipschitz functions.

We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on neural fields are grid-based representations with latents defined on a regular grid. In contrast, we define latents on irregular grids, enabling our representation to be sparse and adaptive. In the context of shape reconstruction from point clouds, our shape representation built on irregular grids improves upon grid-based methods in terms of reconstruction accuracy. For shape generation, our representation promotes high-quality shape generation using auto-regressive probabilistic models. We show different applications that improve over the current state of the art. First, we show results for probabilistic shape reconstruction from a single higher resolution image. Second, we train a probabilistic model conditioned on very low resolution images. Third, we apply our model to category-conditioned generation. All probabilistic experiments confirm that we are able to generate detailed and high quality shapes to yield the new state of the art in generative 3D shape modeling.

We propose TR0N, a highly general framework to turn pre-trained unconditional generative models, such as GANs and VAEs, into conditional models. The conditioning can be highly arbitrary, and requires only a pre-trained auxiliary model. For example, we show how to turn unconditional models into class-conditional ones with the help of a classifier, and also into text-to-image models by leveraging CLIP. TR0N learns a lightweight stochastic mapping which "translates" between the space of conditions and the latent space of the generative model, in such a way that the generated latent corresponds to a data sample satisfying the desired condition. The translated latent samples are then further improved upon through Langevin dynamics, enabling us to obtain higher-quality data samples. TR0N requires no training data nor fine-tuning, yet can achieve a zero-shot FID of 10.9 on MS-COCO, outperforming competing alternatives not only on this metric, but also in sampling speed -- all while retaining a much higher level of generality. Our code is available at https://github.com/layer6ai-labs/tr0n.

Neural networks are famously nonlinear. However, linearity is defined relative to a pair of vector spaces, f:XtoY. Is it possible to identify a pair of non-standard vector spaces for which a conventionally nonlinear function is, in fact, linear? This paper introduces a method that makes such vector spaces explicit by construction. We find that if we sandwich a linear operator A between two invertible neural networks, f(x)=g_y^{-1}(A g_x(x)), then the corresponding vector spaces X and Y are induced by newly defined addition and scaling actions derived from g_x and g_y. We term this kind of architecture a Linearizer. This framework makes the entire arsenal of linear algebra, including SVD, pseudo-inverse, orthogonal projection and more, applicable to nonlinear mappings. Furthermore, we show that the composition of two Linearizers that share a neural network is also a Linearizer. We leverage this property and demonstrate that training diffusion models using our architecture makes the hundreds of sampling steps collapse into a single step. We further utilize our framework to enforce idempotency (i.e. f(f(x))=f(x)) on networks leading to a globally projective generative model and to demonstrate modular style transfer.

Accurate 3D shape abstraction from a single 2D image is a long-standing problem in computer vision and graphics. By leveraging a set of primitives to represent the target shape, recent methods have achieved promising results. However, these methods either use a relatively large number of primitives or lack geometric flexibility due to the limited expressibility of the primitives. In this paper, we propose a novel bi-channel Transformer architecture, integrated with parameterized deformable models, termed DeFormer, to simultaneously estimate the global and local deformations of primitives. In this way, DeFormer can abstract complex object shapes while using a small number of primitives which offer a broader geometry coverage and finer details. Then, we introduce a force-driven dynamic fitting and a cycle-consistent re-projection loss to optimize the primitive parameters. Extensive experiments on ShapeNet across various settings show that DeFormer achieves better reconstruction accuracy over the state-of-the-art, and visualizes with consistent semantic correspondences for improved interpretability.

Deep-learning models can extract a rich assortment of features from data. Which features a model uses depends not only on predictivity-how reliably a feature indicates train-set labels-but also on availability-how easily the feature can be extracted, or leveraged, from inputs. The literature on shortcut learning has noted examples in which models privilege one feature over another, for example texture over shape and image backgrounds over foreground objects. Here, we test hypotheses about which input properties are more available to a model, and systematically study how predictivity and availability interact to shape models' feature use. We construct a minimal, explicit generative framework for synthesizing classification datasets with two latent features that vary in predictivity and in factors we hypothesize to relate to availability, and quantify a model's shortcut bias-its over-reliance on the shortcut (more available, less predictive) feature at the expense of the core (less available, more predictive) feature. We find that linear models are relatively unbiased, but introducing a single hidden layer with ReLU or Tanh units yields a bias. Our empirical findings are consistent with a theoretical account based on Neural Tangent Kernels. Finally, we study how models used in practice trade off predictivity and availability in naturalistic datasets, discovering availability manipulations which increase models' degree of shortcut bias. Taken together, these findings suggest that the propensity to learn shortcut features is a fundamental characteristic of deep nonlinear architectures warranting systematic study given its role in shaping how models solve tasks.

Symbolic equations are at the core of scientific discovery. The task of discovering the underlying equation from a set of input-output pairs is called symbolic regression. Traditionally, symbolic regression methods use hand-designed strategies that do not improve with experience. In this paper, we introduce the first symbolic regression method that leverages large scale pre-training. We procedurally generate an unbounded set of equations, and simultaneously pre-train a Transformer to predict the symbolic equation from a corresponding set of input-output-pairs. At test time, we query the model on a new set of points and use its output to guide the search for the equation. We show empirically that this approach can re-discover a set of well-known physical equations, and that it improves over time with more data and compute.

Effective data-driven PDE forecasting methods often rely on fixed spatial and / or temporal discretizations. This raises limitations in real-world applications like weather prediction where flexible extrapolation at arbitrary spatiotemporal locations is required. We address this problem by introducing a new data-driven approach, DINo, that models a PDE's flow with continuous-time dynamics of spatially continuous functions. This is achieved by embedding spatial observations independently of their discretization via Implicit Neural Representations in a small latent space temporally driven by a learned ODE. This separate and flexible treatment of time and space makes DINo the first data-driven model to combine the following advantages. It extrapolates at arbitrary spatial and temporal locations; it can learn from sparse irregular grids or manifolds; at test time, it generalizes to new grids or resolutions. DINo outperforms alternative neural PDE forecasters in a variety of challenging generalization scenarios on representative PDE systems.

Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems. Although modern models are trained on massive datasets, they still cover only a tiny fraction of the combinatorial space of possible inputs, raising the question of what structure representations must have to support generalization to unseen combinations. We formalize three desiderata for compositional generalization under standard training (divisibility, transferability, stability) and show they impose necessary geometric constraints: representations must decompose linearly into per-concept components, and these components must be orthogonal across concepts. This provides theoretical grounding for the Linear Representation Hypothesis: the linear structure widely observed in neural representations is a necessary consequence of compositional generalization. We further derive dimension bounds linking the number of composable concepts to the embedding geometry. Empirically, we evaluate these predictions across modern vision models (CLIP, SigLIP, DINO) and find that representations exhibit partial linear factorization with low-rank, near-orthogonal per-concept factors, and that the degree of this structure correlates with compositional generalization on unseen combinations. As models continue to scale, these conditions predict the representational geometry they may converge to. Code is available at https://github.com/oshapio/necessary-compositionality.

We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of elementary programming instructions which are additive outer products of self-invented activation patterns (today called keys and values). Such Fast Weight Programmers (FWPs) learn to manipulate the contents of a finite memory and dynamically interact with it. We infer a memory capacity limitation of recent linearised softmax attention variants, and replace the purely additive outer products by a delta rule-like programming instruction, such that the FWP can more easily learn to correct the current mapping from keys to values. The FWP also learns to compute dynamically changing learning rates. We also propose a new kernel function to linearise attention which balances simplicity and effectiveness. We conduct experiments on synthetic retrieval problems as well as standard machine translation and language modelling tasks which demonstrate the benefits of our methods.

We present ShapeNet: a richly-annotated, large-scale repository of shapes represented by 3D CAD models of objects. ShapeNet contains 3D models from a multitude of semantic categories and organizes them under the WordNet taxonomy. It is a collection of datasets providing many semantic annotations for each 3D model such as consistent rigid alignments, parts and bilateral symmetry planes, physical sizes, keywords, as well as other planned annotations. Annotations are made available through a public web-based interface to enable data visualization of object attributes, promote data-driven geometric analysis, and provide a large-scale quantitative benchmark for research in computer graphics and vision. At the time of this technical report, ShapeNet has indexed more than 3,000,000 models, 220,000 models out of which are classified into 3,135 categories (WordNet synsets). In this report we describe the ShapeNet effort as a whole, provide details for all currently available datasets, and summarize future plans.

The rise of capabilities expressed by large language models has been quickly followed by the integration of the same complex systems into application level logic. Algorithms, programs, systems, and companies are built around structured prompting to black box models where the majority of the design and implementation lies in capturing and quantifying the `agent mode'. The standard way to shape a closed language model is to prime it for a specific task with a tailored prompt, often initially handwritten by a human. The textual prompts co-evolve with the codebase, taking shape over the course of project life as artifacts which must be reviewed and maintained, just as the traditional code files might be. Unlike traditional code, we find that prompts do not receive effective static testing and linting to prevent runtime issues. In this work, we present a novel dataset called PromptSet, with more than 61,000 unique developer prompts used in open source Python programs. We perform analysis on this dataset and introduce the notion of a static linter for prompts. Released with this publication is a HuggingFace dataset and a Github repository to recreate collection and processing efforts, both under the name pisterlabs/promptset.

Arbitrary image style transfer is a challenging task which aims to stylize a content image conditioned on arbitrary style images. In this task the feature-level content-style transformation plays a vital role for proper fusion of features. Existing feature transformation algorithms often suffer from loss of content or style details, non-natural stroke patterns, and unstable training. To mitigate these issues, this paper proposes a new feature-level style transformation technique, named Style Projection, for parameter-free, fast, and effective content-style transformation. This paper further presents a real-time feed-forward model to leverage Style Projection for arbitrary image style transfer, which includes a regularization term for matching the semantics between input contents and stylized outputs. Extensive qualitative analysis, quantitative evaluation, and user study have demonstrated the effectiveness and efficiency of the proposed methods.

Recent work found that LLMs are sensitive to a wide range of arbitrary prompt dimensions, including the type of delimiters, answer enumerators, instruction wording, and more. This throws into question popular single-prompt evaluation practices. We present DOVE (Dataset Of Variation Evaluation) a large-scale dataset containing prompt perturbations of various evaluation benchmarks. In contrast to previous work, we examine LLM sensitivity from an holistic perspective, and assess the joint effects of perturbations along various dimensions, resulting in thousands of perturbations per instance. We evaluate several model families against DOVE, leading to several findings, including efficient methods for choosing well-performing prompts, observing that few-shot examples reduce sensitivity, and identifying instances which are inherently hard across all perturbations. DOVE consists of more than 250M prompt perturbations and model outputs, which we make publicly available to spur a community-wide effort toward meaningful, robust, and efficient evaluation. Browse the data, contribute, and more: https://slab-nlp.github.io/DOVE/

This paper considers the learning of logical (Boolean) functions with focus on the generalization on the unseen (GOTU) setting, a strong case of out-of-distribution generalization. This is motivated by the fact that the rich combinatorial nature of data in certain reasoning tasks (e.g., arithmetic/logic) makes representative data sampling challenging, and learning successfully under GOTU gives a first vignette of an 'extrapolating' or 'reasoning' learner. We then study how different network architectures trained by (S)GD perform under GOTU and provide both theoretical and experimental evidence that for a class of network models including instances of Transformers, random features models, and diagonal linear networks, a min-degree-interpolator (MDI) is learned on the unseen. We also provide evidence that other instances with larger learning rates or mean-field networks reach leaky MDIs. These findings lead to two implications: (1) we provide an explanation to the length generalization problem (e.g., Anil et al. 2022); (2) we introduce a curriculum learning algorithm called Degree-Curriculum that learns monomials more efficiently by incrementing supports.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods.

Large Language Models exhibit paradoxical fragility in fundamental arithmetic, implying a disconnect between internal computation and discrete output. By analyzing the residual stream geometry during multi-operand addition, we identify the Iso-Raw-Sum Trajectory (IRST), a geometric structure where representations are anchored by semantic digits and modulated by continuous carry fibers. We propose the Noisy Quantization Model to explain this geometry, framing arithmetic errors as Geometric Slippages caused by internal neural noise pushing a continuous, latent Carry Potential across quantization thresholds. This geometric framework further elucidates Probe Versatility, explaining how lightweight probes can disentangle coexisting latent signals (such as ground truth versus hallucination) from a single activation vector. Finally, we validate these insights through a geometric consistency check method that effectively detects and corrects these quantization failures during inference. Our code is available at https://github.com/RL-MIND/Shape-of-Addition.

The advent of large language models, enabling flexibility through instruction-driven approaches, has revolutionized many traditional generative tasks, but large models for 3D data, particularly in comprehensively handling 3D shapes with other modalities, are still under-explored. By achieving instruction-based shape generations, versatile multimodal generative shape models can significantly benefit various fields like 3D virtual construction and network-aided design. In this work, we present ShapeGPT, a shape-included multi-modal framework to leverage strong pre-trained language models to address multiple shape-relevant tasks. Specifically, ShapeGPT employs a word-sentence-paragraph framework to discretize continuous shapes into shape words, further assembles these words for shape sentences, as well as integrates shape with instructional text for multi-modal paragraphs. To learn this shape-language model, we use a three-stage training scheme, including shape representation, multimodal alignment, and instruction-based generation, to align shape-language codebooks and learn the intricate correlations among these modalities. Extensive experiments demonstrate that ShapeGPT achieves comparable performance across shape-relevant tasks, including text-to-shape, shape-to-text, shape completion, and shape editing.

Prompting and contextual-based fine-tuning methods, which we call Prefix Learning, have been proposed to enhance the performance of language models on various downstream tasks that can match full parameter fine-tuning. There remains a limited theoretical understanding of how these methods work. In this paper, we aim to relieve this limitation by studying the learning ability of Prefix Learning from the perspective of prefix length. In particular, we approximate the infinite-long Prefix Learning optimization process by the Neural Tangent Kernel (NTK) technique. We formulate and solve it as a learning problem of the infinite-long prefix in a one-layer attention network. Our results confirm the over-parameterization property and arbitrary small loss convergence guarantee of the infinite-long Prefix Learning in attention. To the implementation end, we propose our NTK-Attention method, which is "equivalent" to attention computation with arbitrary prefix length efficiently. Its time complexity mainly depends on the sub-quadratic of input length (without prefix), and our method only requires d^2 + d extra parameters for representation, where d is the feature dimension. In addition, we conducted experiments that compare our NTK-Attention with full parameters fine-tuning, LoRA, and P-Tuning V2 methods across vision or natural language datasets. The results indicate our approach may be a promising parameter-efficient-fine-tuning method since it has demonstrated superior performance in numerous scenarios. Our code can be found at https://github.com/ChristianYang37/chiwun/tree/main/src/NTK-Attention.

The ability of Large Language Models (LLMs) to generate structured outputs, such as JSON, is crucial for their use in Compound AI Systems. However, evaluating and improving this capability remains challenging. In this work, we introduce StructuredRAG, a benchmark of six tasks designed to assess LLMs' proficiency in following response format instructions. We evaluate two state-of-the-art LLMs, Gemini 1.5 Pro and Llama 3 8B-instruct with 4-bit quantization using two distinct prompting strategies. We introduce these prompting strategies as f-String and Follow the Format (FF) prompting. Across 24 experiments, we find an average success rate of 82.55%. We further find a high variance in performance across tasks, models, and prompting strategies with success rates ranging from 0 to 100%. We find that Llama 3 8B-instruct often performs competitively with Gemini 1.5 Pro. We observe that task complexity significantly influences performance, with tasks involving lists or composite object outputs proving more challenging. Our findings highlight the need for further research into improving the reliability and consistency of structured output generation in LLMs. We have open-sourced our experimental code and results at github.com/weaviate/structured-rag.

Architecture optimization, which is a technique for finding an efficient neural network that meets certain requirements, generally reduces to a set of multiple-choice selection problems among alternative sub-structures or parameters. The discrete nature of the selection problem, however, makes this optimization difficult. To tackle this problem we introduce a novel concept of a trainable gate function. The trainable gate function, which confers a differentiable property to discretevalued variables, allows us to directly optimize loss functions that include non-differentiable discrete values such as 0-1 selection. The proposed trainable gate can be applied to pruning. Pruning can be carried out simply by appending the proposed trainable gate functions to each intermediate output tensor followed by fine-tuning the overall model, using any gradient-based training methods. So the proposed method can jointly optimize the selection of the pruned channels while fine-tuning the weights of the pruned model at the same time. Our experimental results demonstrate that the proposed method efficiently optimizes arbitrary neural networks in various tasks such as image classification, style transfer, optical flow estimation, and neural machine translation.

Reduced numerical precision is a common technique to reduce computational cost in many Deep Neural Networks (DNNs). While it has been observed that DNNs are resilient to small errors and noise, no general result exists that is capable of predicting a given DNN system architecture's sensitivity to reduced precision. In this project, we emulate arbitrary bit-width using a specified floating-point representation with a truncation method, which is applied to the neural network after each batch. We explore the impact of several model parameters on the network's training accuracy and show results on the MNIST dataset. We then present a preliminary theoretical investigation of the error scaling in both forward and backward propagations. We end with a discussion of the implications of these results as well as the potential for generalization to other network architectures.

Prompting interfaces allow users to quickly adjust the output of generative models in both vision and language. However, small changes and design choices in the prompt can lead to significant differences in the output. In this work, we develop a black-box framework for generating adversarial prompts for unstructured image and text generation. These prompts, which can be standalone or prepended to benign prompts, induce specific behaviors into the generative process, such as generating images of a particular object or generating high perplexity text.

We propose a two-stage deep learning framework for the inverse design of rectangular patch antennas. Our approach leverages generative modeling to learn a latent representation of antenna frequency response curves and conditions a subsequent generative model on these responses to produce feasible antenna geometries. We further demonstrate that leveraging search and optimization techniques at test-time improves the accuracy of the generated designs and enables consideration of auxiliary objectives such as manufacturability. Our approach generalizes naturally to different design criteria, and can be easily adapted to more complex geometric design spaces.

Multiple extensions of Recurrent Neural Networks (RNNs) have been proposed recently to address the difficulty of storing information over long time periods. In this paper, we experiment with the capacity of Neural Turing Machines (NTMs) to deal with these long-term dependencies on well-balanced strings of parentheses. We show that not only does the NTM emulate a stack with its heads and learn an algorithm to recognize such words, but it is also capable of strongly generalizing to much longer sequences.

A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data distributions that are outside of their restricted training sets, namely larger inputs and unseen data. We study these generalization issues at the level of numerical subroutines that comprise common algorithms like sorting, shortest paths, and minimum spanning trees. First, we observe that transformer-based sequence-to-sequence models can learn subroutines like sorting a list of numbers, but their performance rapidly degrades as the length of lists grows beyond those found in the training set. We demonstrate that this is due to attention weights that lose fidelity with longer sequences, particularly when the input numbers are numerically similar. To address the issue, we propose a learned conditional masking mechanism, which enables the model to strongly generalize far outside of its training range with near-perfect accuracy on a variety of algorithms. Second, to generalize to unseen data, we show that encoding numbers with a binary representation leads to embeddings with rich structure once trained on downstream tasks like addition or multiplication. This allows the embedding to handle missing data by faithfully interpolating numbers not seen during training.

Foundation segmentation models, while powerful, pose a significant risk: they enable users to effortlessly extract any objects from any digital content with a single click, potentially leading to copyright infringement or malicious misuse. To mitigate this risk, we introduce a new task "Anything Unsegmentable" to grant any image "the right to be unsegmented". The ambitious pursuit of the task is to achieve highly transferable adversarial attacks against all prompt-based segmentation models, regardless of model parameterizations and prompts. We highlight the non-transferable and heterogeneous nature of prompt-specific adversarial noises. Our approach focuses on disrupting image encoder features to achieve prompt-agnostic attacks. Intriguingly, targeted feature attacks exhibit better transferability compared to untargeted ones, suggesting the optimal update direction aligns with the image manifold. Based on the observations, we design a novel attack named Unsegment Anything by Simulating Deformation (UAD). Our attack optimizes a differentiable deformation function to create a target deformed image, which alters structural information while preserving achievable feature distance by adversarial example. Extensive experiments verify the effectiveness of our approach, compromising a variety of promptable segmentation models with different architectures and prompt interfaces. We release the code at https://github.com/jiahaolu97/anything-unsegmentable.

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural operators have emerged as a promising technique to solve elliptic PDEs more efficiently by directly mapping the input to solutions. However, existing networks typically cannot handle complex geometries and inhomogeneous boundary values present in the real world. Here we introduce Boundary-Embedded Neural Operators (BENO), a novel neural operator architecture that embeds the complex geometries and inhomogeneous boundary values into the solving of elliptic PDEs. Inspired by classical Green's function, BENO consists of two branches of Graph Neural Networks (GNNs) for interior source term and boundary values, respectively. Furthermore, a Transformer encoder maps the global boundary geometry into a latent vector which influences each message passing layer of the GNNs. We test our model extensively in elliptic PDEs with various boundary conditions. We show that all existing baseline methods fail to learn the solution operator. In contrast, our model, endowed with boundary-embedded architecture, outperforms state-of-the-art neural operators and strong baselines by an average of 60.96\%. Our source code can be found https://github.com/AI4Science-WestlakeU/beno.git.

We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter sigma describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for partial differential equations. Algorithms for approximating the solution to these systems are often the bottleneck in problems that require their solution, particularly for modern applications that require many millions of unknowns. Indeed, numerical linear algebra techniques have been investigated for many decades to alleviate this computational burden. Recently, data-driven techniques have also shown promise for these problems. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search directions. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We train the network using unsupervised learning with a loss function equal to the L^2 difference between an input and the system matrix times the network evaluation, where the unspecified constant in the approximate inverse is accounted for. We demonstrate the efficacy of our approach on spatially discretized Poisson equations with millions of degrees of freedom arising in computational fluid dynamics applications. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

Modern language models define distributions over strings, but downstream tasks often require different output formats. For instance, a model that generates byte-pair strings does not directly produce word-level predictions, and a DNA model does not directly produce amino-acid sequences. In such cases, a deterministic string-to-string transformation can convert the model's output to the desired form. This is a familiar pattern in probability theory: applying a function f to a random variable Xsim p yields a transformed random variable f(X) with an induced distribution. While such transformations are occasionally used in language modeling, prior work does not treat them as yielding new, fully functional language models. We formalize this perspective and introduce a general framework for language models derived from deterministic string-to-string transformations. We focus on transformations representable as finite-state transducers -- a commonly used state-machine abstraction for efficient string-to-string mappings. We develop algorithms that compose a language model with an FST to *marginalize* over source strings mapping to a given target, propagating probabilities through the transducer without altering model parameters and enabling *conditioning* on transformed outputs. We present an exact algorithm, an efficient approximation, and a theoretical analysis. We conduct experiments in three domains: converting language models from tokens to bytes, from tokens to words, and from DNA to amino acids. These experiments demonstrate inference-time adaptation of pretrained language models to match application-specific output requirements.

We carry out an information-theoretical analysis of a two-layer neural network trained from input-output pairs generated by a teacher network with matching architecture, in overparametrized regimes. Our results come in the form of bounds relating i) the mutual information between training data and network weights, or ii) the Bayes-optimal generalization error, to the same quantities but for a simpler (generalized) linear model for which explicit expressions are rigorously known. Our bounds, which are expressed in terms of the number of training samples, input dimension and number of hidden units, thus yield fundamental performance limits for any neural network (and actually any learning procedure) trained from limited data generated according to our two-layer teacher neural network model. The proof relies on rigorous tools from spin glasses and is guided by ``Gaussian equivalence principles'' lying at the core of numerous recent analyses of neural networks. With respect to the existing literature, which is either non-rigorous or restricted to the case of the learning of the readout weights only, our results are information-theoretic (i.e. are not specific to any learning algorithm) and, importantly, cover a setting where all the network parameters are trained.

In this paper, we establish a connection between the parameterization of flow-based and energy-based generative models, and present a new flow-based modeling approach called energy-based normalizing flow (EBFlow). We demonstrate that by optimizing EBFlow with score-matching objectives, the computation of Jacobian determinants for linear transformations can be entirely bypassed. This feature enables the use of arbitrary linear layers in the construction of flow-based models without increasing the computational time complexity of each training iteration from O(D^2L) to O(D^3L) for an L-layered model that accepts D-dimensional inputs. This makes the training of EBFlow more efficient than the commonly-adopted maximum likelihood training method. In addition to the reduction in runtime, we enhance the training stability and empirical performance of EBFlow through a number of techniques developed based on our analysis of the score-matching methods. The experimental results demonstrate that our approach achieves a significant speedup compared to maximum likelihood estimation while outperforming prior methods with a noticeable margin in terms of negative log-likelihood (NLL).

We show that both an LSTM and a unitary-evolution recurrent neural network (URN) can achieve encouraging accuracy on two types of syntactic patterns: context-free long distance agreement, and mildly context-sensitive cross serial dependencies. This work extends recent experiments on deeply nested context-free long distance dependencies, with similar results. URNs differ from LSTMs in that they avoid non-linear activation functions, and they apply matrix multiplication to word embeddings encoded as unitary matrices. This permits them to retain all information in the processing of an input string over arbitrary distances. It also causes them to satisfy strict compositionality. URNs constitute a significant advance in the search for explainable models in deep learning applied to NLP.

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently. In this work, we design a general solution operator for two different time-independent PDEs using graph neural networks (GNNs) and spectral graph convolutions. We train the networks on simulated data from a finite elements solver on a variety of shapes and inhomogeneities. In contrast to previous works, we focus on the ability of the trained operator to generalize to previously unseen scenarios. Specifically, we test generalization to meshes with different shapes and superposition of solutions for a different number of inhomogeneities. We find that training on a diverse dataset with lots of variation in the finite element meshes is a key ingredient for achieving good generalization results in all cases. With this, we believe that GNNs can be used to learn solution operators that generalize over a range of properties and produce solutions much faster than a generic solver. Our dataset, which we make publicly available, can be used and extended to verify the robustness of these models under varying conditions.

Previous studies have found that an adversary attacker can often infer unintended input information from intermediate-layer features. We study the possibility of preventing such adversarial inference, yet without too much accuracy degradation. We propose a generic method to revise the neural network to boost the challenge of inferring input attributes from features, while maintaining highly accurate outputs. In particular, the method transforms real-valued features into complex-valued ones, in which the input is hidden in a randomized phase of the transformed features. The knowledge of the phase acts like a key, with which any party can easily recover the output from the processing result, but without which the party can neither recover the output nor distinguish the original input. Preliminary experiments on various datasets and network structures have shown that our method significantly diminishes the adversary's ability in inferring about the input while largely preserves the resulting accuracy.

This paper does not introduce a novel method. Instead, it offers a fairer and more comprehensive comparison of KAN and MLP models across various tasks, including machine learning, computer vision, audio processing, natural language processing, and symbolic formula representation. Specifically, we control the number of parameters and FLOPs to compare the performance of KAN and MLP. Our main observation is that, except for symbolic formula representation tasks, MLP generally outperforms KAN. We also conduct ablation studies on KAN and find that its advantage in symbolic formula representation mainly stems from its B-spline activation function. When B-spline is applied to MLP, performance in symbolic formula representation significantly improves, surpassing or matching that of KAN. However, in other tasks where MLP already excels over KAN, B-spline does not substantially enhance MLP's performance. Furthermore, we find that KAN's forgetting issue is more severe than that of MLP in a standard class-incremental continual learning setting, which differs from the findings reported in the KAN paper. We hope these results provide insights for future research on KAN and other MLP alternatives. Project link: https://github.com/yu-rp/KANbeFair

Feature shaping refers to a family of methods that exhibit state-of-the-art performance for out-of-distribution (OOD) detection. These approaches manipulate the feature representation, typically from the penultimate layer of a pre-trained deep learning model, so as to better differentiate between in-distribution (ID) and OOD samples. However, existing feature-shaping methods usually employ rules manually designed for specific model architectures and OOD datasets, which consequently limit their generalization ability. To address this gap, we first formulate an abstract optimization framework for studying feature-shaping methods. We then propose a concrete reduction of the framework with a simple piecewise constant shaping function and show that existing feature-shaping methods approximate the optimal solution to the concrete optimization problem. Further, assuming that OOD data is inaccessible, we propose a formulation that yields a closed-form solution for the piecewise constant shaping function, utilizing solely the ID data. Through extensive experiments, we show that the feature-shaping function optimized by our method improves the generalization ability of OOD detection across a large variety of datasets and model architectures.