Daily Papers

The boundary representation (B-Rep) is the standard data structure used in Computer-Aided Design (CAD) for defining solid models. Despite recent progress, directly generating B-Reps end-to-end with precise geometry and watertight topology remains a challenge. This paper presents AutoBrep, a novel Transformer model that autoregressively generates B-Reps with high quality and validity. AutoBrep employs a unified tokenization scheme that encodes both geometric and topological characteristics of a B-Rep model as a sequence of discrete tokens. Geometric primitives (i.e., surfaces and curves) are encoded as latent geometry tokens, and their structural relationships are defined as special topological reference tokens. Sequence order in AutoBrep naturally follows a breadth first traversal of the B-Rep face adjacency graph. At inference time, neighboring faces and edges along with their topological structure are progressively generated. Extensive experiments demonstrate the advantages of our unified representation when coupled with next-token prediction for B-Rep generation. AutoBrep outperforms baselines with better quality and watertightness. It is also highly scalable to complex solids with good fidelity and inference speed. We further show that autocompleting B-Reps is natively supported through our unified tokenization, enabling user-controllable CAD generation with minimal changes. Code is available at https://github.com/AutodeskAILab/AutoBrep.

Adversarially perturbed images of text can cause sophisticated OCR systems to produce misleading or incorrect transcriptions from seemingly invisible changes to humans. Some of these perturbations even survive physical capture, posing security risks to high-stakes applications such as document processing, license plate recognition, and automated compliance systems. Existing defenses, such as adversarial training, input preprocessing, or post-recognition correction, are often model-specific, computationally expensive, and affect performance on unperturbed inputs while remaining vulnerable to unseen or adaptive attacks. To address these challenges, TopoReformer is introduced, a model-agnostic reformation pipeline that mitigates adversarial perturbations while preserving the structural integrity of text images. Topology studies properties of shapes and spaces that remain unchanged under continuous deformations, focusing on global structures such as connectivity, holes, and loops rather than exact distance. Leveraging these topological features, TopoReformer employs a topological autoencoder to enforce manifold-level consistency in latent space and improve robustness without explicit gradient regularization. The proposed method is benchmarked on EMNIST, MNIST, against standard adversarial attacks (FGSM, PGD, Carlini-Wagner), adaptive attacks (EOT, BDPA), and an OCR-specific watermark attack (FAWA).

The role of the attention mechanism in encoding linguistic knowledge has received special interest in NLP. However, the ability of the attention heads to judge the grammatical acceptability of a sentence has been underexplored. This paper approaches the paradigm of acceptability judgments with topological data analysis (TDA), showing that the geometric properties of the attention graph can be efficiently exploited for two standard practices in linguistics: binary judgments and linguistic minimal pairs. Topological features enhance the BERT-based acceptability classifier scores by 8%-24% on CoLA in three languages (English, Italian, and Swedish). By revealing the topological discrepancy between attention maps of minimal pairs, we achieve the human-level performance on the BLiMP benchmark, outperforming nine statistical and Transformer LM baselines. At the same time, TDA provides the foundation for analyzing the linguistic functions of attention heads and interpreting the correspondence between the graph features and grammatical phenomena.

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Mathematical symbols and descriptions appear in various forms across document section boundaries without explicit markup. In this paper, we present a new large-scale dataset that emphasizes extracting symbols and descriptions in scientific documents. Symlink annotates scientific papers of 5 different domains (i.e., computer science, biology, physics, mathematics, and economics). Our experiments on Symlink demonstrate the challenges of the symbol-description linking task for existing models and call for further research effort in this area. We will publicly release Symlink to facilitate future research.

In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.

Graphs are a fundamental data structure for representing relationships in real-world scenarios. With the success of Large Language Models (LLMs) across various natural language processing (NLP) tasks, there has been growing interest in integrating LLMs for graph learning. However, applying LLMs to graph-related tasks poses significant challenges, as these models are not inherently designed to capture the complex structural information present in graphs. Existing approaches address this challenge through two strategies: the chain of tasks approach, which uses Graph Neural Networks (GNNs) to encode the graph structure so that LLMs are relieved from understanding spatial positions; and Graph-to-Text Conversion, which translates graph structures into semantic text representations that LLMs can process. Despite their progress, these methods often struggle to fully preserve the topological information of graphs or require extensive computational resources, limiting their practical applicability. In this work, we introduce Node Tokenizer for Large Language Models (NT-LLM), a novel framework that efficiently encodes graph structures by selecting key nodes as anchors and representing each node based on its relative distance to these anchors. This position-anchored encoding effectively captures the graph topology, enabling enhanced reasoning capabilities in LLMs over graph data. Additionally, we implement a task-specific tuning procedure to further improve structural understanding within LLMs. Through extensive empirical evaluations, NT-LLM demonstrates significant performance improvements across a variety of graph-related tasks.

Despite the impressive advancements of Large Language Models (LLMs) in generating text, they are often limited by the knowledge contained in the input and prone to producing inaccurate or hallucinated content. To tackle these issues, Retrieval-augmented Generation (RAG) is employed as an effective strategy to enhance the available knowledge base and anchor the responses in reality by pulling additional texts from external databases. In real-world applications, texts are often linked through entities within a graph, such as citations in academic papers or comments in social networks. This paper exploits these topological relationships to guide the retrieval process in RAG. Specifically, we explore two kinds of topological connections: proximity-based, focusing on closely connected nodes, and role-based, which looks at nodes sharing similar subgraph structures. Our empirical research confirms their relevance to text relationships, leading us to develop a Topology-aware Retrieval-augmented Generation framework. This framework includes a retrieval module that selects texts based on their topological relationships and an aggregation module that integrates these texts into prompts to stimulate LLMs for text generation. We have curated established text-attributed networks and conducted comprehensive experiments to validate the effectiveness of this framework, demonstrating its potential to enhance RAG with topological awareness.

The impressive capabilities of recent generative models to create texts that are challenging to distinguish from the human-written ones can be misused for generating fake news, product reviews, and even abusive content. Despite the prominent performance of existing methods for artificial text detection, they still lack interpretability and robustness towards unseen models. To this end, we propose three novel types of interpretable topological features for this task based on Topological Data Analysis (TDA) which is currently understudied in the field of NLP. We empirically show that the features derived from the BERT model outperform count- and neural-based baselines up to 10\% on three common datasets, and tend to be the most robust towards unseen GPT-style generation models as opposed to existing methods. The probing analysis of the features reveals their sensitivity to the surface and syntactic properties. The results demonstrate that TDA is a promising line with respect to NLP tasks, specifically the ones that incorporate surface and structural information.

Multimodal large language models (MLLMs) have advanced rapidly in recent years. However, existing approaches for vision tasks often rely on indirect representations, such as generating coordinates as text for detection, which limits performance and prevents dense prediction tasks like segmentation. To overcome these challenges, we introduce Patch-as-Decodable Token (PaDT), a unified paradigm that enables MLLMs to directly generate both textual and diverse visual outputs. Central to PaDT are Visual Reference Tokens (VRTs), derived from visual patch embeddings of query images and interleaved seamlessly with LLM's output textual tokens. A lightweight decoder then transforms LLM's outputs into detection, segmentation, and grounding predictions. Unlike prior methods, PaDT processes VRTs independently at each forward pass and dynamically expands the embedding table, thus improving localization and differentiation among similar objects. We further tailor a training strategy for PaDT by randomly selecting VRTs for supervised fine-tuning and introducing a robust per-token cross-entropy loss. Our empirical studies across four visual perception and understanding tasks suggest PaDT consistently achieving state-of-the-art performance, even compared with significantly larger MLLM models. The code is available at https://github.com/Gorilla-Lab-SCUT/PaDT.

Recent research has evidenced the significant potentials of Large Language Models (LLMs) in handling challenging tasks within 3D scenes. However, current models are constrained to addressing object-centric tasks, where each question-answer pair focuses solely on an individual object. In real-world applications, users may pose queries involving multiple objects or expect for answers that precisely reference various objects. We introduce the use of object identifiers to freely reference objects during a conversation. While this solution appears straightforward, it presents two main challenges: 1) How to establish a reliable one-to-one correspondence between each object and its identifier? 2) How to incorporate complex spatial relationships among dozens of objects into the embedding space of the LLM? To address these challenges, we propose a two-stage alignment method, which involves learning an attribute-aware token and a relation-aware token for each object. These tokens capture the object's attributes and spatial relationships with surrounding objects in the 3D scene. Once the alignment is established, we can fine-tune our model on various downstream tasks using instruction tuning. Experiments conducted on traditional datasets like ScanQA, ScanRefer, and Nr3D/Sr3D showcase the effectiveness of our proposed method. Additionally, we create a 3D scene captioning dataset annotated with rich object identifiers, with the assistant of GPT-4. This dataset aims to further explore the capability of object identifiers in effective object referencing and precise scene understanding.

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a comprehensive framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. TDL has demonstrated theoretical and practical advantages that hold the promise of breaking ground in the applied sciences and beyond. However, the rapid growth of the TDL literature has also led to a lack of unification in notation and language across Topological Neural Network (TNN) architectures. This presents a real obstacle for building upon existing works and for deploying TNNs to new real-world problems. To address this issue, we provide an accessible introduction to TDL, and compare the recently published TNNs using a unified mathematical and graphical notation. Through an intuitive and critical review of the emerging field of TDL, we extract valuable insights into current challenges and exciting opportunities for future development.

We enhance the calculus of string diagrams for monoidal categories with hierarchical features in order to capture closed monoidal (and cartesian closed) structure. Using this new syntax we formulate an automatic differentiation algorithm for (applied) simply typed lambda calculus in the style of [Pearlmutter and Siskind 2008] and we prove for the first time its soundness. To give an efficient yet principled implementation of the AD algorithm we define a sound and complete representation of hierarchical string diagrams as a class of hierarchical hypergraphs we call hypernets.

Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit object-level reasoning and interconnectivity. In this paper, we propose a novel topological representation of an environment based on "image segments", which are semantically meaningful and open-vocabulary queryable, conferring several advantages over previous works based on pixel-level features. Unlike 3D scene graphs, we create a purely topological graph with segments as nodes, where edges are formed by a) associating segment-level descriptors between pairs of consecutive images and b) connecting neighboring segments within an image using their pixel centroids. This unveils a "continuous sense of a place", defined by inter-image persistence of segments along with their intra-image neighbours. It further enables us to represent and update segment-level descriptors through neighborhood aggregation using graph convolution layers, which improves robot localization based on segment-level retrieval. Using real-world data, we show how our proposed map representation can be used to i) generate navigation plans in the form of "hops over segments" and ii) search for target objects using natural language queries describing spatial relations of objects. Furthermore, we quantitatively analyze data association at the segment level, which underpins inter-image connectivity during mapping and segment-level localization when revisiting the same place. Finally, we show preliminary trials on segment-level `hopping' based zero-shot real-world navigation. Project page with supplementary details: oravus.github.io/RoboHop/

Graphs are ubiquitous structures found in numerous real-world applications, such as drug discovery, recommender systems, and social network analysis. To model graph-structured data, graph neural networks (GNNs) have become a popular tool. However, existing GNN architectures encounter challenges in cross-graph learning where multiple graphs have different feature spaces. To address this, recent approaches introduce text-attributed graphs (TAGs), where each node is associated with a textual description, which can be projected into a unified feature space using textual encoders. While promising, this method relies heavily on the availability of text-attributed graph data, which is difficult to obtain in practice. To bridge this gap, we propose a novel method named Topology-Aware Node description Synthesis (TANS), leveraging large language models (LLMs) to convert existing graphs into text-attributed graphs. The key idea is to integrate topological information into LLMs to explain how graph topology influences node semantics. We evaluate our TANS on text-rich, text-limited, and text-free graphs, demonstrating its applicability. Notably, on text-free graphs, our method significantly outperforms existing approaches that manually design node features, showcasing the potential of LLMs for preprocessing graph-structured data in the absence of textual information. The code and data are available at https://github.com/Zehong-Wang/TANS.

Graph neural networks achieve high accuracy in link prediction by jointly leveraging graph topology and node attributes. Topology, however, is represented indirectly; state-of-the-art methods based on subgraph classification label nodes with distance to the target link, so that, although topological information is present, it is tempered by pooling. This makes it challenging to leverage features like loops and motifs associated with network formation mechanisms. We propose a link prediction algorithm based on a new pooling scheme called WalkPool. WalkPool combines the expressivity of topological heuristics with the feature-learning ability of neural networks. It summarizes a putative link by random walk probabilities of adjacent paths. Instead of extracting transition probabilities from the original graph, it computes the transition matrix of a "predictive" latent graph by applying attention to learned features; this may be interpreted as feature-sensitive topology fingerprinting. WalkPool can leverage unsupervised node features or be combined with GNNs and trained end-to-end. It outperforms state-of-the-art methods on all common link prediction benchmarks, both homophilic and heterophilic, with and without node attributes. Applying WalkPool to a set of unsupervised GNNs significantly improves prediction accuracy, suggesting that it may be used as a general-purpose graph pooling scheme.

We consider molecule generation in 3D space using language models (LMs), which requires discrete tokenization of 3D molecular geometries. Although tokenization of molecular graphs exists, that for 3D geometries is largely unexplored. Here, we attempt to bridge this gap by proposing the Geo2Seq, which converts molecular geometries into SE(3)-invariant 1D discrete sequences. Geo2Seq consists of canonical labeling and invariant spherical representation steps, which together maintain geometric and atomic fidelity in a format conducive to LMs. Our experiments show that, when coupled with Geo2Seq, various LMs excel in molecular geometry generation, especially in controlled generation tasks.

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

GUI grounding, the task of mapping natural-language instructions to pixel coordinates, is crucial for autonomous agents, yet remains difficult for current VLMs. The core bottleneck is reliable patch-to-pixel mapping, which breaks when extrapolating to high-resolution displays unseen during training. Current approaches generate coordinates as text tokens directly from visual features, forcing the model to infer complex position-to-pixel mappings implicitly; as a result, accuracy degrades and failures proliferate on new resolutions. We address this with two complementary innovations. First, RULER tokens serve as explicit coordinate markers, letting the model reference positions similar to gridlines on a map and adjust rather than generate coordinates from scratch. Second, Interleaved MRoPE (I-MRoPE) improves spatial encoding by ensuring that width and height dimensions are represented equally, addressing the asymmetry of standard positional schemes. Experiments on ScreenSpot, ScreenSpot-V2, and ScreenSpot-Pro show consistent gains in grounding accuracy, with the largest improvements on high-resolution interfaces. By providing explicit spatial guidance rather than relying on implicit learning, our approach enables more reliable GUI automation across diverse resolutions and platforms.

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.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

This paper investigates how Transformer language models (LMs) fine-tuned for acceptability classification capture linguistic features. Our approach uses the best practices of topological data analysis (TDA) in NLP: we construct directed attention graphs from attention matrices, derive topological features from them, and feed them to linear classifiers. We introduce two novel features, chordality, and the matching number, and show that TDA-based classifiers outperform fine-tuning baselines. We experiment with two datasets, CoLA and RuCoLA in English and Russian, typologically different languages. On top of that, we propose several black-box introspection techniques aimed at detecting changes in the attention mode of the LMs during fine-tuning, defining the LM's prediction confidences, and associating individual heads with fine-grained grammar phenomena. Our results contribute to understanding the behavior of monolingual LMs in the acceptability classification task, provide insights into the functional roles of attention heads, and highlight the advantages of TDA-based approaches for analyzing LMs. We release the code and the experimental results for further uptake.

Current Large Multimodal Models (LMMs) empowered visual grounding typically rely on <SEG> tokens as a text prompt to jointly optimize the vision-language model (e.g., LLaVA) and the downstream task-specific model (e.g., SAM). However, we observe that little research has looked into how it works.In this work, we first visualize the similarity maps, which are obtained by computing the semantic similarity between the <SEG> token and the image token embeddings derived from the last hidden layer in both the LLaVA encoder and SAM decoder. Intriguingly, we have found that a striking consistency holds in terms of activation responses in the similarity map, which reveals that what the <SEG> token contributes to is semantic similarity within image-text pairs. Specifically, the <SEG> token, a placeholder expanded in text vocabulary, extensively queries among individual tokenized image patches to match the semantics of an object from text to the paired image, while the Large Language Models (LLMs) are being fine-tuned. Upon the above findings, we present READ, which facilitates LMMs' resilient REAsoning capability of where to attenD under the guidance of highly activated points borrowed from similarity maps. Remarkably, READ features an intuitive design, Similarity as Points module (SasP), which can be seamlessly applied to <SEG>-like paradigms in a plug-and-play fashion. Also, extensive experiments have been conducted on ReasonSeg and RefCOCO(+/g) datasets. To validate whether READ suffers from catastrophic forgetting of previous skills after fine-tuning, we further assess its generation ability on an augmented FP-RefCOCO(+/g) dataset. All codes and models are publicly available at https://github.com/rui-qian/READ.

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

This work introduces TopoBenchmarkX, a modular open-source library designed to standardize benchmarking and accelerate research in Topological Deep Learning (TDL). TopoBenchmarkX maps the TDL pipeline into a sequence of independent and modular components for data loading and processing, as well as model training, optimization, and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBenchmarkX is that it allows for the transformation and lifting between topological domains. This enables, for example, to obtain richer data representations and more fine-grained analyses by mapping the topology and features of a graph to higher-order topological domains such as simplicial and cell complexes. The range of applicability of TopoBenchmarkX is demonstrated by benchmarking several TDL architectures for various tasks and datasets.

DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it differentiable, probabilistic or quantum. This report gives an overview of the library and the new developments released in its version 1.0. In particular, we showcase the implementation of diagram equality for a large fragment of the hierarchy of graphical languages for monoidal categories, as well as a new syntax for defining string diagrams as Python functions.

Referring Expression Segmentation (RES) is a widely explored multi-modal task, which endeavors to segment the pre-existing object within a single image with a given linguistic expression. However, in broader real-world scenarios, it is not always possible to determine if the described object exists in a specific image. Typically, we have a collection of images, some of which may contain the described objects. The current RES setting curbs its practicality in such situations. To overcome this limitation, we propose a more realistic and general setting, named Group-wise Referring Expression Segmentation (GRES), which expands RES to a collection of related images, allowing the described objects to be present in a subset of input images. To support this new setting, we introduce an elaborately compiled dataset named Grouped Referring Dataset (GRD), containing complete group-wise annotations of target objects described by given expressions. We also present a baseline method named Grouped Referring Segmenter (GRSer), which explicitly captures the language-vision and intra-group vision-vision interactions to achieve state-of-the-art results on the proposed GRES and related tasks, such as Co-Salient Object Detection and RES. Our dataset and codes will be publicly released in https://github.com/yixuan730/group-res.

Token embeddings, a mapping from discrete lexical symbols to continuous vectors, are at the heart of any language model (LM). However, lexical symbol meanings can also be determined and even redefined by their structural role in a long context. In this paper, we ask: is it possible for a language model to be performant without any fixed token embeddings? Such a language model would have to rely entirely on the co-occurence and repetition of tokens in the context rather than the a priori identity of any token. To answer this, we study lexinvariantlanguage models that are invariant to lexical symbols and therefore do not need fixed token embeddings in practice. First, we prove that we can construct a lexinvariant LM to converge to the true language model at a uniform rate that is polynomial in terms of the context length, with a constant factor that is sublinear in the vocabulary size. Second, to build a lexinvariant LM, we simply encode tokens using random Gaussian vectors, such that each token maps to the same representation within each sequence but different representations across sequences. Empirically, we demonstrate that it can indeed attain perplexity comparable to that of a standard language model, given a sufficiently long context. We further explore two properties of the lexinvariant language models: First, given text generated from a substitution cipher of English, it implicitly implements Bayesian in-context deciphering and infers the mapping to the underlying real tokens with high accuracy. Second, it has on average 4X better accuracy over synthetic in-context reasoning tasks. Finally, we discuss regularizing standard language models towards lexinvariance and potential practical applications.

Retrieving graphs from a large corpus, that contain a subgraph isomorphic to a given query graph, is a core operation in many real-world applications. While recent multi-vector graph representations and scores based on set alignment and containment can provide accurate subgraph isomorphism tests, their use in retrieval remains limited by their need to score corpus graphs exhaustively. We introduce CORGII (Contextual Representation of Graphs for Inverted Indexing), a graph indexing framework in which, starting with a contextual dense graph representation, a differentiable discretization module computes sparse binary codes over a learned latent vocabulary. This text document-like representation allows us to leverage classic, highly optimized inverted indices, while supporting soft (vector) set containment scores. Pushing this paradigm further, we replace the classical, fixed impact weight of a `token' on a graph (such as TFIDF or BM25) with a data-driven, trainable impact weight. Finally, we explore token expansion to support multi-probing the index for smoother accuracy-efficiency tradeoffs. To our knowledge, CORGII is the first indexer of dense graph representations using discrete tokens mapping to efficient inverted lists. Extensive experiments show that CORGII provides better trade-offs between accuracy and efficiency, compared to several baselines.

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

We present TopoMortar, a brick wall dataset that is the first dataset specifically designed to evaluate topology-focused image segmentation methods, such as topology loss functions. TopoMortar enables to investigate in two ways whether methods incorporate prior topological knowledge. First, by eliminating challenges seen in real-world data, such as small training set, noisy labels, and out-of-distribution test-set images, that, as we show, impact the effectiveness of topology losses. Second, by allowing to assess in the same dataset topology accuracy across dataset challenges, isolating dataset-related effects from the effect of incorporating prior topological knowledge. In these two experiments, it is deliberately difficult to improve topology accuracy without actually using topology information, thus, permitting to attribute an improvement in topology accuracy to the incorporation of prior topological knowledge. To this end, TopoMortar includes three types of labels (accurate, noisy, pseudo-labels), two fixed training sets (large and small), and in-distribution and out-of-distribution test-set images. We compared eight loss functions on TopoMortar, and we found that clDice achieved the most topologically accurate segmentations, Skeleton Recall loss performed best particularly with noisy labels, and the relative advantageousness of the other loss functions depended on the experimental setting. Additionally, we show that simple methods, such as data augmentation and self-distillation, can elevate Cross entropy Dice loss to surpass most topology loss functions, and that those simple methods can enhance topology loss functions as well. clDice and Skeleton Recall loss, both skeletonization-based loss functions, were also the fastest to train, making this type of loss function a promising research direction. TopoMortar and our code can be found at https://github.com/jmlipman/TopoMortar

Although text-to-image (T2I) models exhibit remarkable generation capabilities, they frequently fail to accurately bind semantically related objects or attributes in the input prompts; a challenge termed semantic binding. Previous approaches either involve intensive fine-tuning of the entire T2I model or require users or large language models to specify generation layouts, adding complexity. In this paper, we define semantic binding as the task of associating a given object with its attribute, termed attribute binding, or linking it to other related sub-objects, referred to as object binding. We introduce a novel method called Token Merging (ToMe), which enhances semantic binding by aggregating relevant tokens into a single composite token. This ensures that the object, its attributes and sub-objects all share the same cross-attention map. Additionally, to address potential confusion among main objects with complex textual prompts, we propose end token substitution as a complementary strategy. To further refine our approach in the initial stages of T2I generation, where layouts are determined, we incorporate two auxiliary losses, an entropy loss and a semantic binding loss, to iteratively update the composite token to improve the generation integrity. We conducted extensive experiments to validate the effectiveness of ToMe, comparing it against various existing methods on the T2I-CompBench and our proposed GPT-4o object binding benchmark. Our method is particularly effective in complex scenarios that involve multiple objects and attributes, which previous methods often fail to address. The code will be publicly available at https://github.com/hutaihang/ToMe.

Text-to-Image (T2I) models often suffer from issues such as semantic leakage, incorrect feature binding, and omissions of key concepts in the generated image. This work studies these phenomena by looking into the role of information flow between textual token representations. To this end, we generate images by applying the diffusion component on a subset of contextual token representations in a given prompt and observe several interesting phenomena. First, in many cases, a word or multiword expression is fully represented by one or two tokens, while other tokens are redundant. For example, in "San Francisco's Golden Gate Bridge", the token "gate" alone captures the full expression. We demonstrate the redundancy of these tokens by removing them after textual encoding and generating an image from the resulting representation. Surprisingly, we find that this process not only maintains image generation performance but also reduces errors by 21\% compared to standard generation. We then show that information can also flow between different expressions in a sentence, which often leads to semantic leakage. Based on this observation, we propose a simple, training-free method to mitigate semantic leakage: replacing the leaked item's representation after the textual encoding with its uncontextualized representation. Remarkably, this simple approach reduces semantic leakage by 85\%. Overall, our work provides a comprehensive analysis of information flow across textual tokens in T2I models, offering both novel insights and practical benefits.

Tokenization is the first - and often underappreciated - layer of computation in language models. While Chain-of-Thought (CoT) prompting enables transformer models to approximate recurrent computation by externalizing intermediate steps, we show that the success of such reasoning is fundamentally bounded by the structure of tokenized inputs. This work presents a theoretical and empirical investigation into how tokenization schemes, particularly subword-based methods like byte-pair encoding (BPE), impede symbolic computation by merging or obscuring atomic reasoning units. We introduce the notion of Token Awareness to formalize how poor token granularity disrupts logical alignment and prevents models from generalizing symbolic procedures. Through systematic evaluation on arithmetic and symbolic tasks, we demonstrate that token structure dramatically affect reasoning performance, causing failure even with CoT, while atomically-aligned formats unlock strong generalization, allowing small models (e.g., GPT-4o-mini) to outperform larger systems (e.g., o1) in structured reasoning. Our findings reveal that symbolic reasoning ability in LLMs is not purely architectural, but deeply conditioned on token-level representations.

Byte Pair Encoding (BPE) serves as a foundation method for text tokenization in the Natural Language Processing (NLP) field. Despite its wide adoption, the original BPE algorithm harbors an inherent flaw: it inadvertently introduces a frequency imbalance for tokens in the text corpus. Since BPE iteratively merges the most frequent token pair in the text corpus while keeping all tokens that have been merged in the vocabulary, it unavoidably holds tokens that primarily represent subwords of complete words and appear infrequently on their own in the text corpus. We term such tokens as Scaffold Tokens. Due to their infrequent appearance in the text corpus, Scaffold Tokens pose a learning imbalance issue for language models. To address that issue, we propose Scaffold-BPE, which incorporates a dynamic scaffold token removal mechanism by parameter-free, computation-light, and easy-to-implement modifications to the original BPE. This novel approach ensures the exclusion of low-frequency Scaffold Tokens from the token representations for the given texts, thereby mitigating the issue of frequency imbalance and facilitating model training. On extensive experiments across language modeling tasks and machine translation tasks, Scaffold-BPE consistently outperforms the original BPE, well demonstrating its effectiveness and superiority.

While language models are increasingly utilized in materials science, typical models rely on frequency-centric tokenization methods originally developed for natural language processing. However, these methods frequently produce excessive fragmentation and semantic loss, failing to maintain the structural and semantic integrity of material concepts. To address this issue, we propose MATTER, a novel tokenization approach that integrates material knowledge into tokenization. Based on MatDetector trained on our materials knowledge base and a re-ranking method prioritizing material concepts in token merging, MATTER maintains the structural integrity of identified material concepts and prevents fragmentation during tokenization, ensuring their semantic meaning remains intact. The experimental results demonstrate that MATTER outperforms existing tokenization methods, achieving an average performance gain of 4% and 2% in the generation and classification tasks, respectively. These results underscore the importance of domain knowledge for tokenization strategies in scientific text processing. Our code is available at https://github.com/yerimoh/MATTER

Tokenization plays a critical role in language modeling, yet existing approaches such as Byte-Pair Encoding (BPE) or WordPiece operate purely on frequency statistics, ignoring the underlying semantic structure of text. This leads to over-tokenization of semantically redundant spans and underutilization of contextual coherence, particularly in long-context scenarios. In this work, we propose SemToken, a semantic-aware tokenization framework that jointly reduces token redundancy and improves computation efficiency. SemToken first extracts contextual semantic embeddings via lightweight encoders and performs local semantic clustering to merge semantically equivalent tokens. Then, it allocates heterogeneous token granularity based on semantic density, allowing finer-grained tokenization in content-rich regions and coarser compression in repetitive or low-entropy spans. SemToken can be seamlessly integrated with modern language models and attention acceleration methods. Experiments on long-context language modeling benchmarks such as WikiText-103 and LongBench show that SemToken achieves up to 2.4times reduction in token count and 1.9times speedup, with negligible or no degradation in perplexity and downstream accuracy. Our findings suggest that semantic structure offers a promising new axis for optimizing tokenization and computation in large language models.

This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since November 21, 2025 and has as of January 4, 2026, produced 160k lines of formalized topology. Most of it (about 130k lines) have been done in two weeks,from December 22 to January 4, for an LLM subscription cost of about \$100. This includes a 3k-line proof of Urysohn's lemma, a 2k-line proof of Urysohn's Metrization theorem, over 10k-line proof of the Tietze extension theorem, and many more (in total over 1.5k lemmas/theorems). The approach is quite simple and cheap: build a long-running feedback loop between an LLM and a reasonably fast proof checker equipped with a core foundational library. The LLM is now instantiated as ChatGPT (mostly 5.2) or Claude Sonnet (4.5) run through the respective Codex or Claude Code command line interfaces. The proof checker is Chad Brown's higher-order set theory system Megalodon, and the core library is Brown's formalization of basic set theory and surreal numbers (including reals, etc). The rest is some prompt engineering and technical choices which we describe here. Based on the fast progress, low cost, virtually unknown ITP/library, and the simple setup available to everyone, we believe that (auto)formalization may become quite easy and ubiquitous in 2026, regardless of which proof assistant is used.

We introduce Kosmos-2, a Multimodal Large Language Model (MLLM), enabling new capabilities of perceiving object descriptions (e.g., bounding boxes) and grounding text to the visual world. Specifically, we represent refer expressions as links in Markdown, i.e., ``[text span](bounding boxes)'', where object descriptions are sequences of location tokens. Together with multimodal corpora, we construct large-scale data of grounded image-text pairs (called GrIT) to train the model. In addition to the existing capabilities of MLLMs (e.g., perceiving general modalities, following instructions, and performing in-context learning), Kosmos-2 integrates the grounding capability into downstream applications. We evaluate Kosmos-2 on a wide range of tasks, including (i) multimodal grounding, such as referring expression comprehension, and phrase grounding, (ii) multimodal referring, such as referring expression generation, (iii) perception-language tasks, and (iv) language understanding and generation. This work lays out the foundation for the development of Embodiment AI and sheds light on the big convergence of language, multimodal perception, action, and world modeling, which is a key step toward artificial general intelligence. Data, demo, and pretrained models are available at https://aka.ms/kosmos-2.

We propose a novel approach for learning interchangeable tokens in language models to obtain an extendable vocabulary that can generalize to new tokens. Our method is designed to address alpha-equivalence, the principle that renaming bound variables in a syntactic expression preserves semantics. This property arises in many formal languages such as temporal logics, in which all proposition symbols represent the same concept but are distinguishable from each other. To handle such tokens, we develop a dual-part embedding approach. The first part is shared across all interchangeable tokens, thereby enforcing that they represent the same core concept. The second part is randomly generated for each token, which enables distinguishability. We evaluate our method in a Transformer encoder-decoder model on two tasks: solving linear temporal logic formulae and copying with extendable vocabulary. Our method demonstrates promising generalization capabilities in addition to introducing a favorable inductive bias for alpha-equivalence.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

Recent advancements in large language models (LLMs) have significantly enhanced their reasoning capabilities. However, they continue to struggle with basic character-level tasks, such as counting letters in words, a problem rooted in their tokenization process. While existing benchmarks have highlighted this weakness through basic character operations, such failures are often dismissed due to lacking practical relevance. Yet, many real-world applications, such as navigating text-based maps or interpreting structured tables, rely heavily on precise sub-token understanding. In this regard, we introduce SubTokenTest, a comprehensive benchmark that assesses sub-token understanding through practical, utility-driven tasks. Our benchmark includes ten tasks across four domains and isolates tokenization-related failures by decoupling performance from complex reasoning. We provide a comprehensive evaluation of nine advanced LLMs. Additionally, we investigate the impact of test-time scaling on sub-token reasoning and explore how character-level information is encoded within the hidden states.

To fully understand the behavior of a large language model (LLM) requires our understanding of its input space. If this input space differs from our assumption, our understanding of and conclusions about the LLM is likely flawed, regardless of its architecture. Here, we elucidate the structure of the token embeddings, the input domain for LLMs, both empirically and theoretically. We present a generalized and statistically testable model where the neighborhood of each token splits into well-defined signal and noise dimensions. This model is based on a generalization of a manifold called a fiber bundle, so we denote our hypothesis test as the ``fiber bundle null.'' Failing to reject the null is uninformative, but rejecting it at a specific token indicates that token has a statistically significant local structure, and so is of interest to us. By running our test over several open-source LLMs, each with unique token embeddings, we find that the null is frequently rejected, and so the token subspace is provably not a fiber bundle and hence also not a manifold. As a consequence of our findings, when an LLM is presented with two semantically equivalent prompts, and if one prompt contains a token implicated by our test, that prompt will likely exhibit more output variability proportional to the local signal dimension of the token.

Computer-Aided Design (CAD) is a foundational component of industrial prototyping, where models are defined not by raw coordinates but by construction sequences such as sketches and extrusions. This sequential structure enables both efficient prototype initialization and subsequent editing. Text-guided CAD prototyping, which unifies Text-to-CAD generation and CAD editing, has the potential to streamline the entire design pipeline. However, prior work has not explored this setting, largely because standard large language model (LLM) tokenizers decompose CAD sequences into natural-language word pieces, failing to capture primitive-level CAD semantics and hindering attention modules from modeling geometric structure. We conjecture that a multimodal tokenization strategy, aligned with CAD's primitive and structural nature, can provide more effective representations. To this end, we propose CAD-Tokenizer, a framework that represents CAD data with modality-specific tokens using a sequence-based VQ-VAE with primitive-level pooling and constrained decoding. This design produces compact, primitive-aware representations that align with CAD's structural nature. Applied to unified text-guided CAD prototyping, CAD-Tokenizer significantly improves instruction following and generation quality, achieving better quantitative and qualitative performance over both general-purpose LLMs and task-specific baselines.

Information flows by routes inside the network via mechanisms implemented in the model. These routes can be represented as graphs where nodes correspond to token representations and edges to operations inside the network. We automatically build these graphs in a top-down manner, for each prediction leaving only the most important nodes and edges. In contrast to the existing workflows relying on activation patching, we do this through attribution: this allows us to efficiently uncover existing circuits with just a single forward pass. Additionally, the applicability of our method is far beyond patching: we do not need a human to carefully design prediction templates, and we can extract information flow routes for any prediction (not just the ones among the allowed templates). As a result, we can talk about model behavior in general, for specific types of predictions, or different domains. We experiment with Llama 2 and show that the role of some attention heads is overall important, e.g. previous token heads and subword merging heads. Next, we find similarities in Llama 2 behavior when handling tokens of the same part of speech. Finally, we show that some model components can be specialized on domains such as coding or multilingual texts.

Graphs are able to model interconnected entities in many online services, supporting a wide range of applications on the Web. This raises an important question: How can we train a graph foundational model on multiple source domains and adapt to an unseen target domain? A major obstacle is that graphs from different domains often exhibit divergent characteristics. Some studies leverage large language models to align multiple domains based on textual descriptions associated with the graphs, limiting their applicability to text-attributed graphs. For text-free graphs, a few recent works attempt to align different feature distributions across domains, while generally neglecting structural differences. In this work, we propose a novel Structure Alignment framework for text-free Multi-domain Graph Pre-Training and cross-domain adaptation (SAMGPT). It is designed to learn multi-domain knowledge from graphs originating in multiple source domains, which can then be adapted to address applications in an unseen target domain. Specifically, we introduce a set of structure tokens to harmonize structure-based aggregation across source domains during the pre-training phase. Next, for cross-domain adaptation, we design dual prompts, namely, holistic prompts and specific prompts, which adapt unified multi-domain structural knowledge and fine-grained, domain-specific information, respectively, to a target domain. Finally, we conduct comprehensive experiments on seven public datasets to evaluate and analyze the effectiveness of SAMGPT.

Effectively representing 3D scenes for Multimodal Large Language Models (MLLMs) is crucial yet challenging. Existing approaches commonly only rely on 2D image features and use varied tokenization approaches. This work presents a rigorous study of 3D token structures, systematically comparing video-based and point-based representations while maintaining consistent model backbones and parameters. We propose a novel approach that enriches visual tokens by incorporating 3D point cloud features from a Sonata pretrained Point Transformer V3 encoder. Our experiments demonstrate that merging explicit 3D features significantly boosts performance. Furthermore, we show that point-based token structures can rival video-based ones when the points are cleverly sampled and ordered. Our best models from both structures achieve state-of-the-art results on multiple 3D understanding benchmarks. We emphasize our analysis of token structures as a key contribution, alongside transparent reporting of results averaged over multiple seeds, a practice we believe is vital for robust progress in the field.

Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

Tokenization is an important preprocessing step in the training and inference of large language models (LLMs). While there has been extensive research on the expressive power of the neural achitectures used in LLMs, the impact of tokenization has not been well understood. In this work, we demonstrate that tokenization, irrespective of the algorithm used, acts as an inverse homomorphism between strings and tokens. This suggests that the character space of the source language and the token space of the tokenized language are homomorphic, preserving the structural properties of the source language. Additionally, we explore the concept of proper tokenization, which refers to an unambiguous tokenization returned from the tokenizer. Our analysis reveals that the expressiveness of neural architectures in recognizing context-free languages is not affected by tokenization.

Verifiable formal languages like Lean have profoundly impacted mathematical reasoning, particularly through the use of large language models (LLMs) for automated reasoning. A significant challenge in training LLMs for these formal languages is the lack of parallel datasets that align natural language with formal language proofs. To address this challenge, this paper introduces a novel framework for translating the Mathlib4 corpus (a unified library of mathematics in formal language Lean 4) into natural language. Building upon this, we employ a dual augmentation strategy that combines tactic-based and informal-based approaches, leveraging the Lean-jixia system, a Lean 4 analyzer. We present the results of this pipeline on Mathlib4 as Herald (Hierarchy and Retrieval-based Translated Lean Dataset). We also propose the Herald Translator, which is fine-tuned on Herald. Herald translator achieves a 93.2% accuracy (Pass@128) on formalizing statements in the miniF2F-test and a 22.5% accuracy on our internal graduate-level textbook dataset, outperforming InternLM2-Math-Plus-7B (74.0% and 7.5%) and TheoremLlama (50.1% and 4.0%). Furthermore, we propose a section-level translation framework for real-world applications. As a direct application of Herald translator, we have successfully translated a template section in the Stack project, marking a notable progress in the automatic formalization of graduate-level mathematical literature. Our model, along with the datasets, will be open-sourced to the public soon.

The Boundary representation (B-rep) format is the de-facto shape representation in computer-aided design (CAD) to model solid and sheet objects. Recent approaches to generating CAD models have focused on learning sketch-and-extrude modeling sequences that are executed by a solid modeling kernel in postprocess to recover a B-rep. In this paper we present a new approach that enables learning from and synthesizing B-reps without the need for supervision through CAD modeling sequence data. Our method SolidGen, is an autoregressive neural network that models the B-rep directly by predicting the vertices, edges, and faces using Transformer-based and pointer neural networks. Key to achieving this is our Indexed Boundary Representation that references B-rep vertices, edges and faces in a well-defined hierarchy to capture the geometric and topological relations suitable for use with machine learning. SolidGen can be easily conditioned on contexts e.g., class labels, images, and voxels thanks to its probabilistic modeling of the B-rep distribution. We demonstrate qualitatively, quantitatively, and through perceptual evaluation by human subjects that SolidGen can produce high quality, realistic CAD models.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the discriminative power of distinguishing isomorphisms of graphs, which plays a crucial role in boosting their predictive performances. To address this challenge, we introduce 'Topology-Informed Graph Transformer (TIGT)', a novel transformer enhancing both discriminative power in detecting graph isomorphisms and the overall performance of Graph Transformers. TIGT consists of four components: A topological positional embedding layer using non-isomorphic universal covers based on cyclic subgraphs of graphs to ensure unique graph representation: A dual-path message-passing layer to explicitly encode topological characteristics throughout the encoder layers: A global attention mechanism: And a graph information layer to recalibrate channel-wise graph features for better feature representation. TIGT outperforms previous Graph Transformers in classifying synthetic dataset aimed at distinguishing isomorphism classes of graphs. Additionally, mathematical analysis and empirical evaluations highlight our model's competitive edge over state-of-the-art Graph Transformers across various benchmark datasets.

Referring expressions usually describe an object using properties of the object and relationships of the object with other objects. We propose a technique that integrates context between objects to understand referring expressions. Our approach uses an LSTM to learn the probability of a referring expression, with input features from a region and a context region. The context regions are discovered using multiple-instance learning (MIL) since annotations for context objects are generally not available for training. We utilize max-margin based MIL objective functions for training the LSTM. Experiments on the Google RefExp and UNC RefExp datasets show that modeling context between objects provides better performance than modeling only object properties. We also qualitatively show that our technique can ground a referring expression to its referred region along with the supporting context region.

This paper proposes a fundamentally new paradigm for image generation through set-based tokenization and distribution modeling. Unlike conventional methods that serialize images into fixed-position latent codes with a uniform compression ratio, we introduce an unordered token set representation to dynamically allocate coding capacity based on regional semantic complexity. This TokenSet enhances global context aggregation and improves robustness against local perturbations. To address the critical challenge of modeling discrete sets, we devise a dual transformation mechanism that bijectively converts sets into fixed-length integer sequences with summation constraints. Further, we propose Fixed-Sum Discrete Diffusion--the first framework to simultaneously handle discrete values, fixed sequence length, and summation invariance--enabling effective set distribution modeling. Experiments demonstrate our method's superiority in semantic-aware representation and generation quality. Our innovations, spanning novel representation and modeling strategies, advance visual generation beyond traditional sequential token paradigms. Our code and models are publicly available at https://github.com/Gengzigang/TokenSet.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Recent advances in 3D point cloud transformers have led to state-of-the-art results in tasks such as semantic segmentation and reconstruction. However, these models typically rely on dense token representations, incurring high computational and memory costs during training and inference. In this work, we present the finding that tokens are remarkably redundant, leading to substantial inefficiency. We introduce gitmerge3D, a globally informed graph token merging method that can reduce the token count by up to 90-95% while maintaining competitive performance. This finding challenges the prevailing assumption that more tokens inherently yield better performance and highlights that many current models are over-tokenized and under-optimized for scalability. We validate our method across multiple 3D vision tasks and show consistent improvements in computational efficiency. This work is the first to assess redundancy in large-scale 3D transformer models, providing insights into the development of more efficient 3D foundation architectures. Our code and checkpoints are publicly available at https://gitmerge3d.github.io

HAL (Hyper Articles en Ligne) is the French national publication repository, used by most higher education and research organizations for their open science policy. As a digital library, it is a rich repository of scholarly documents, but its potential for advanced research has been underutilized. We present HALvest, a unique dataset that bridges the gap between citation networks and the full text of papers submitted on HAL. We craft our dataset by filtering HAL for scholarly publications, resulting in approximately 700,000 documents, spanning 34 languages across 13 identified domains, suitable for language model training, and yielding approximately 16.5 billion tokens (with 8 billion in French and 7 billion in English, the most represented languages). We transform the metadata of each paper into a citation network, producing a directed heterogeneous graph. This graph includes uniquely identified authors on HAL, as well as all open submitted papers, and their citations. We provide a baseline for authorship attribution using the dataset, implement a range of state-of-the-art models in graph representation learning for link prediction, and discuss the usefulness of our generated knowledge graph structure.

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

Recent works on Generalized Referring Expression Segmentation (GRES) struggle with handling complex expressions referring to multiple distinct objects. This is because these methods typically employ an end-to-end foreground-background segmentation and lack a mechanism to explicitly differentiate and associate different object instances to the text query. To this end, we propose InstAlign, a method that incorporates object-level reasoning into the segmentation process. Our model leverages both text and image inputs to extract a set of object-level tokens that capture both the semantic information in the input prompt and the objects within the image. By modeling the text-object alignment via instance-level supervision, each token uniquely represents an object segment in the image, while also aligning with relevant semantic information from the text. Extensive experiments on the gRefCOCO and Ref-ZOM benchmarks demonstrate that our method significantly advances state-of-the-art performance, setting a new standard for precise and flexible GRES.

Referring Expression Segmentation (RES) aims to generate a segmentation mask for the object described by a given language expression. Existing classic RES datasets and methods commonly support single-target expressions only, i.e., one expression refers to one target object. Multi-target and no-target expressions are not considered. This limits the usage of RES in practice. In this paper, we introduce a new benchmark called Generalized Referring Expression Segmentation (GRES), which extends the classic RES to allow expressions to refer to an arbitrary number of target objects. Towards this, we construct the first large-scale GRES dataset called gRefCOCO that contains multi-target, no-target, and single-target expressions. GRES and gRefCOCO are designed to be well-compatible with RES, facilitating extensive experiments to study the performance gap of the existing RES methods on the GRES task. In the experimental study, we find that one of the big challenges of GRES is complex relationship modeling. Based on this, we propose a region-based GRES baseline ReLA that adaptively divides the image into regions with sub-instance clues, and explicitly models the region-region and region-language dependencies. The proposed approach ReLA achieves new state-of-the-art performance on the both newly proposed GRES and classic RES tasks. The proposed gRefCOCO dataset and method are available at https://henghuiding.github.io/GRES.

Recent work has demonstrated that semantics specified by pretraining data influence how representations of different concepts are organized in a large language model (LLM). However, given the open-ended nature of LLMs, e.g., their ability to in-context learn, we can ask whether models alter these pretraining semantics to adopt alternative, context-specified ones. Specifically, if we provide in-context exemplars wherein a concept plays a different role than what the pretraining data suggests, do models reorganize their representations in accordance with these novel semantics? To answer this question, we take inspiration from the theory of conceptual role semantics and define a toy "graph tracing" task wherein the nodes of the graph are referenced via concepts seen during training (e.g., apple, bird, etc.) and the connectivity of the graph is defined via some predefined structure (e.g., a square grid). Given exemplars that indicate traces of random walks on the graph, we analyze intermediate representations of the model and find that as the amount of context is scaled, there is a sudden re-organization from pretrained semantic representations to in-context representations aligned with the graph structure. Further, we find that when reference concepts have correlations in their semantics (e.g., Monday, Tuesday, etc.), the context-specified graph structure is still present in the representations, but is unable to dominate the pretrained structure. To explain these results, we analogize our task to energy minimization for a predefined graph topology, providing evidence towards an implicit optimization process to infer context-specified semantics. Overall, our findings indicate scaling context-size can flexibly re-organize model representations, possibly unlocking novel capabilities.

Unsupervised text representation learning (TRL) is a fundamental task in natural language processing, which is beneficial for improving search and recommendations with the web's unlabeled texts. A recent empirical study finds that the high-quality representation aligns with the key token of the input text, uncovering the potential connection between representation space and vocabulary space. Inspired by the findings, we revisit the generative tasks and develop an unsupervised generative framework for TRL, Text2Token. The framework is based on the token target prediction task, utilizing carefully constructed target token distribution as supervisory signals. To construct the high-quality target token distribution, we analyze the token-alignment properties with advanced embedders and identify two essential categories of key tokens: (1) the meaningful tokens in the text and (2) semantically derived tokens beyond the text. Based on these insights, we propose two methods -- data-driven and model-derived -- to construct synthetic token targets from data or the LLM backbone. Experiments on the MTEB v2 benchmark demonstrate that Text2Token achieves performance competitive with the state-of-the-art embedder with unsupervised contrastive learning, LLM2Vec. Our analysis further shows that vocabulary and representation spaces optimize together and toward the optimum solution during training, providing new ideas and insights for future work.

Text-Attributed Graphs (TAGs) augment graph structures with natural language descriptions, facilitating detailed depictions of data and their interconnections across various real-world settings. However, existing TAG datasets predominantly feature textual information only at the nodes, with edges typically represented by mere binary or categorical attributes. This lack of rich textual edge annotations significantly limits the exploration of contextual relationships between entities, hindering deeper insights into graph-structured data. To address this gap, we introduce Textual-Edge Graphs Datasets and Benchmark (TEG-DB), a comprehensive and diverse collection of benchmark textual-edge datasets featuring rich textual descriptions on nodes and edges. The TEG-DB datasets are large-scale and encompass a wide range of domains, from citation networks to social networks. In addition, we conduct extensive benchmark experiments on TEG-DB to assess the extent to which current techniques, including pre-trained language models, graph neural networks, and their combinations, can utilize textual node and edge information. Our goal is to elicit advancements in textual-edge graph research, specifically in developing methodologies that exploit rich textual node and edge descriptions to enhance graph analysis and provide deeper insights into complex real-world networks. The entire TEG-DB project is publicly accessible as an open-source repository on Github, accessible at https://github.com/Zhuofeng-Li/TEG-Benchmark.

The quadratic computational complexity to the number of tokens limits the practical applications of Vision Transformers (ViTs). Several works propose to prune redundant tokens to achieve efficient ViTs. However, these methods generally suffer from (i) dramatic accuracy drops, (ii) application difficulty in the local vision transformer, and (iii) non-general-purpose networks for downstream tasks. In this work, we propose a novel Semantic Token ViT (STViT), for efficient global and local vision transformers, which can also be revised to serve as backbone for downstream tasks. The semantic tokens represent cluster centers, and they are initialized by pooling image tokens in space and recovered by attention, which can adaptively represent global or local semantic information. Due to the cluster properties, a few semantic tokens can attain the same effect as vast image tokens, for both global and local vision transformers. For instance, only 16 semantic tokens on DeiT-(Tiny,Small,Base) can achieve the same accuracy with more than 100% inference speed improvement and nearly 60% FLOPs reduction; on Swin-(Tiny,Small,Base), we can employ 16 semantic tokens in each window to further speed it up by around 20% with slight accuracy increase. Besides great success in image classification, we also extend our method to video recognition. In addition, we design a STViT-R(ecover) network to restore the detailed spatial information based on the STViT, making it work for downstream tasks, which is powerless for previous token sparsification methods. Experiments demonstrate that our method can achieve competitive results compared to the original networks in object detection and instance segmentation, with over 30% FLOPs reduction for backbone. Code is available at http://github.com/changsn/STViT-R

We propose a method that can generate an unambiguous description (known as a referring expression) of a specific object or region in an image, and which can also comprehend or interpret such an expression to infer which object is being described. We show that our method outperforms previous methods that generate descriptions of objects without taking into account other potentially ambiguous objects in the scene. Our model is inspired by recent successes of deep learning methods for image captioning, but while image captioning is difficult to evaluate, our task allows for easy objective evaluation. We also present a new large-scale dataset for referring expressions, based on MS-COCO. We have released the dataset and a toolbox for visualization and evaluation, see https://github.com/mjhucla/Google_Refexp_toolbox

We show that standard Transformers without graph-specific modifications can lead to promising results in graph learning both in theory and practice. Given a graph, we simply treat all nodes and edges as independent tokens, augment them with token embeddings, and feed them to a Transformer. With an appropriate choice of token embeddings, we prove that this approach is theoretically at least as expressive as an invariant graph network (2-IGN) composed of equivariant linear layers, which is already more expressive than all message-passing Graph Neural Networks (GNN). When trained on a large-scale graph dataset (PCQM4Mv2), our method coined Tokenized Graph Transformer (TokenGT) achieves significantly better results compared to GNN baselines and competitive results compared to Transformer variants with sophisticated graph-specific inductive bias. Our implementation is available at https://github.com/jw9730/tokengt.

We explore the use of topological data analysis (TDA) combined with machine learning for discriminating standard model backgrounds from the invisible decay of the Z^prime boson associated with monophoton emission at a 3 TeV muon collider. Reconstructed events are mapped into a six-dimensional kinematic space and aggregated into bags of events, from which persistent homology is used to extract Betti number distributions. Within the Multiple Instance Learning paradigm, classifiers trained on these topological descriptors demonstrate significantly improved classification accuracy compared to the conventional ML approaches based on event-wise kinematic inputs. We also draw exclusion contours at 95\% CL in the (m_{Z^prime}, m_chi) parameter space, highlighting the potential of topological features to extend the discovery reach of future collider experiments.

Transformer models underpin many recent advances in practical machine learning applications, yet understanding their internal behavior continues to elude researchers. Given the size and complexity of these models, forming a comprehensive picture of their inner workings remains a significant challenge. To this end, we set out to understand small transformer models in a more tractable setting: that of solving mazes. In this work, we focus on the abstractions formed by these models and find evidence for the consistent emergence of structured internal representations of maze topology and valid paths. We demonstrate this by showing that the residual stream of only a single token can be linearly decoded to faithfully reconstruct the entire maze. We also find that the learned embeddings of individual tokens have spatial structure. Furthermore, we take steps towards deciphering the circuity of path-following by identifying attention heads (dubbed adjacency heads), which are implicated in finding valid subsequent tokens.

We present Omni-RGPT, a multimodal large language model designed to facilitate region-level comprehension for both images and videos. To achieve consistent region representation across spatio-temporal dimensions, we introduce Token Mark, a set of tokens highlighting the target regions within the visual feature space. These tokens are directly embedded into spatial regions using region prompts (e.g., boxes or masks) and simultaneously incorporated into the text prompt to specify the target, establishing a direct connection between visual and text tokens. To further support robust video understanding without requiring tracklets, we introduce an auxiliary task that guides Token Mark by leveraging the consistency of the tokens, enabling stable region interpretation across the video. Additionally, we introduce a large-scale region-level video instruction dataset (RegVID-300k). Omni-RGPT achieves state-of-the-art results on image and video-based commonsense reasoning benchmarks while showing strong performance in captioning and referring expression comprehension tasks.

Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap, an objective that is insufficient for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the correct topology of the segmented structures. However, so far, none of the existing approaches achieve a spatially correct matching between the topological features of ground truth and prediction. In this work, we propose the first topologically and feature-wise accurate metric and loss function for supervised image segmentation, which we term Betti matching. We show how induced matchings guarantee the spatially correct matching between barcodes in a segmentation setting. Furthermore, we propose an efficient algorithm to compute the Betti matching of images. We show that the Betti matching error is an interpretable metric to evaluate the topological correctness of segmentations, which is more sensitive than the well-established Betti number error. Moreover, the differentiability of the Betti matching loss enables its use as a loss function. It improves the topological performance of segmentation networks across six diverse datasets while preserving the volumetric performance. Our code is available in https://github.com/nstucki/Betti-matching.

Large Vision-Language Models (LVLMs) have advanced multimodal learning but face high computational costs due to the large number of visual tokens, motivating token pruning to improve inference efficiency. The key challenge lies in identifying which tokens are truly important. Most existing approaches rely on attention-based criteria to estimate token importance. However, they inherently suffer from certain limitations, such as positional bias. In this work, we explore a new perspective on token importance based on token transitions in LVLMs. We observe that the transition of token representations provides a meaningful signal of semantic information. Based on this insight, we propose TransPrune, a training-free and efficient token pruning method. Specifically, TransPrune progressively prunes tokens by assessing their importance through a combination of Token Transition Variation (TTV)-which measures changes in both the magnitude and direction of token representations-and Instruction-Guided Attention (IGA), which measures how strongly the instruction attends to image tokens via attention. Extensive experiments demonstrate that TransPrune achieves comparable multimodal performance to original LVLMs, such as LLaVA-v1.5 and LLaVA-Next, across eight benchmarks, while reducing inference TFLOPs by more than half. Moreover, TTV alone can serve as an effective criterion without relying on attention, achieving performance comparable to attention-based methods. The code will be made publicly available upon acceptance of the paper at https://github.com/liaolea/TransPrune.

A central question for neuroscience is how to characterize brain representations of perceptual and cognitive content. An ideal characterization should distinguish different functional regions with robustness to noise and idiosyncrasies of individual brains that do not correspond to computational differences. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. Here we explore a further step of abstraction: from the geometry to the topology of brain representations. We propose topological representational similarity analysis (tRSA), an extension of representational similarity analysis (RSA) that uses a family of geo-topological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this new family of statistics in terms of the sensitivity and specificity for model selection using both simulations and functional MRI (fMRI) data. In the simulations, the ground truth is a data-generating layer representation in a neural network model and the models are the same and other layers in different model instances (trained from different random seeds). In fMRI, the ground truth is a visual area and the models are the same and other areas measured in different subjects. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.

Referring expression segmentation is a fundamental task in computer vision that integrates natural language understanding with precise visual localization of target regions. Considering aerial imagery (e.g., modern aerial photos collected through drones, historical photos from aerial archives, high-resolution satellite imagery, etc.) presents unique challenges because spatial resolution varies widely across datasets, the use of color is not consistent, targets often shrink to only a few pixels, and scenes contain very high object densities and objects with partial occlusions. This work presents Aerial-D, a new large-scale referring expression segmentation dataset for aerial imagery, comprising 37,288 images with 1,522,523 referring expressions that cover 259,709 annotated targets, spanning across individual object instances, groups of instances, and semantic regions covering 21 distinct classes that range from vehicles and infrastructure to land coverage types. The dataset was constructed through a fully automatic pipeline that combines systematic rule-based expression generation with a Large Language Model (LLM) enhancement procedure that enriched both the linguistic variety and the focus on visual details within the referring expressions. Filters were additionally used to simulate historic imaging conditions for each scene. We adopted the RSRefSeg architecture, and trained models on Aerial-D together with prior aerial datasets, yielding unified instance and semantic segmentation from text for both modern and historical images. Results show that the combined training achieves competitive performance on contemporary benchmarks, while maintaining strong accuracy under monochrome, sepia, and grainy degradations that appear in archival aerial photography. The dataset, trained models, and complete software pipeline are publicly available at https://luispl77.github.io/aerial-d .

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.

Representation learning on text-attributed graphs (TAGs) integrates structural connectivity with rich textual semantics, enabling applications in diverse domains. Current methods largely rely on contrastive learning to maximize cross-modal similarity, assuming tighter coupling between graph and text representations improves transfer performance. However, our empirical analysis reveals that both natural gap expansion and forced gap reduction result in performance degradation by disrupting pre-trained knowledge structures and impairing generalization. This arises from the geometric incompatibility between encoders, where graph encoders capture topological patterns, while text encoders capture semantic structures. Over-alignment compresses these distinct spaces into shared subspaces, causing structure collapse that diminishes both topological reasoning and semantic understanding. We propose LLM4GTA, a gap-aware alignment framework that preserves representation gaps as geometric necessities for maintaining modality-specific knowledge and improving transfer performance. LLM4GTA includes an adaptive gap preservation module to prevent over-alignment by monitoring similarity evolution and an intra-modal compensation mechanism that boosts discriminative power using auxiliary classifiers in graph space. Extensive experiments show significant improvements over existing methods in zero-shot and few-shot scenarios.

Recently, Vision Language Models (VLMs) have increasingly emphasized document visual grounding to achieve better human-computer interaction, accessibility, and detailed understanding. However, its application to visualizations such as charts remains under-explored due to the inherent complexity of interleaved visual-numerical relationships in chart images. Existing chart understanding methods primarily focus on answering questions without explicitly identifying the visual elements that support their predictions. To bridge this gap, we introduce RefChartQA, a novel benchmark that integrates Chart Question Answering (ChartQA) with visual grounding, enabling models to refer elements at multiple granularities within chart images. Furthermore, we conduct a comprehensive evaluation by instruction-tuning 5 state-of-the-art VLMs across different categories. Our experiments demonstrate that incorporating spatial awareness via grounding improves response accuracy by over 15%, reducing hallucinations, and improving model reliability. Additionally, we identify key factors influencing text-spatial alignment, such as architectural improvements in TinyChart, which leverages a token-merging module for enhanced feature fusion. Our dataset is open-sourced for community development and further advancements. All models and code will be publicly available at https://github.com/moured/RefChartQA.

We introduce a novel visual tokenization framework that embeds a provable PCA-like structure into the latent token space. While existing visual tokenizers primarily optimize for reconstruction fidelity, they often neglect the structural properties of the latent space -- a critical factor for both interpretability and downstream tasks. Our method generates a 1D causal token sequence for images, where each successive token contributes non-overlapping information with mathematically guaranteed decreasing explained variance, analogous to principal component analysis. This structural constraint ensures the tokenizer extracts the most salient visual features first, with each subsequent token adding diminishing yet complementary information. Additionally, we identified and resolved a semantic-spectrum coupling effect that causes the unwanted entanglement of high-level semantic content and low-level spectral details in the tokens by leveraging a diffusion decoder. Experiments demonstrate that our approach achieves state-of-the-art reconstruction performance and enables better interpretability to align with the human vision system. Moreover, auto-regressive models trained on our token sequences achieve performance comparable to current state-of-the-art methods while requiring fewer tokens for training and inference.

We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a natural language theorem statement, and a natural language proof. The problems are primarily drawn from popular undergraduate pure mathematics textbooks and cover topics such as real and complex analysis, linear algebra, abstract algebra, and topology. We intend for ProofNet to be a challenging benchmark that will drive progress in autoformalization and automatic theorem proving. We report baseline results on statement autoformalization via in-context learning. Moreover, we introduce two novel statement autoformalization methods: prompt retrieval and distilled backtranslation.

Tokenization is a fundamental component of language models for code. It involves breaking down the input into units that are later passed to the language model stack to learn high-dimensional representations used in various contexts, from classification to generation. However, the output of these tokenizers is often longer than that traditionally used in compilers and interpreters. This could result in undesirable effects, such as increased computational overhead. In this work, we investigate the effect of merging the hidden representations of subtokens that belong to the same semantic unit, such as subtokens that form a single identifier. We propose two strategies: one based on averaging the representations and another that leverages a learning-based approach. Both methods can be seamlessly integrated with existing language models for code. We conduct experiments using six language models for code: CodeBERT, GraphCodeBERT, UniXCoder, CdoeT5, CodeT5+ (220M), and CodeT5+ (770M), across three software engineering tasks: vulnerability detection, code classification, and code translation. Results show that these strategies can reduce the number of floating-point operations by 1% to 19%. Regarding downstream performance, the most significant degradation was observed in the vulnerability detection task, where the F1 score decreased by 1.82 points compared to the baseline. In contrast, for code translation, we observed an improvement of 2.47 points in CodeBLEU. This work contributes to the broader effort of improving language models for code across multiple dimensions, including both computational efficiency and downstream performance.

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle (symmetries in) geometric complexes, extending the scope of TNNs and PH to spatial settings. Theoretically, we show that PH descriptors can provably enhance the expressivity of simplicial message-passing networks. Empirically, (continuous and E(n)-equivariant extensions of) TopNets achieve strong performance across diverse tasks, including antibody design, molecular dynamics simulation, and drug property prediction.

The exploitation of syntactic graphs (SyGs) as a word's context has been shown to be beneficial for distributional semantic models (DSMs), both at the level of individual word representations and in deriving phrasal representations via composition. However, notwithstanding the potential performance benefit, the syntactically-aware DSMs proposed to date have huge numbers of parameters (compared to conventional DSMs) and suffer from data sparsity. Furthermore, the encoding of the SyG links (i.e., the syntactic relations) has been largely limited to linear maps. The knowledge graphs' literature, on the other hand, has proposed light-weight models employing different geometric transformations (GTs) to encode edges in a knowledge graph (KG). Our work explores the possibility of adopting this family of models to encode SyGs. Furthermore, we investigate which GT better encodes syntactic relations, so that these representations can be used to enhance phrase-level composition via syntactic contextualisation.

Computer-aided design (CAD) is the digital construction of 2D and 3D objects, and is central to a wide range of engineering and manufacturing applications like automobile and aviation. Despite its importance, CAD modeling remains largely a time-intensive, manual task. Recent works have attempted to automate this process with small transformer-based models and handcrafted CAD sequence representations. However, there has been little effort to leverage the potential of large language models (LLMs) for sequential CAD design. In this work, we introduce a new large-scale dataset of more than 170k CAD models annotated with high-quality, human-like descriptions generated with our pipeline based on GPT-4.1. Using this dataset, we fine-tune powerful code-LLMs to generate CAD sequences represented in a JSON-based format from natural language descriptions, demonstrating the viability and effectiveness of this approach for text-conditioned CAD generation. Because simple metrics often fail to reflect the quality of generated objects, we introduce geometric and topological metrics based on sphericity, mean curvature, and Euler characteristic to provide richer structural insights. Our experiments and ablation studies on both synthetic and human-annotated data demonstrate that CADmium is able to automate CAD design, drastically speeding up the design of new objects. The dataset, code, and fine-tuned models are available online.

When used with deep learning, the symbolic music modality is often coupled with language model architectures. To do so, the music needs to be tokenized, i.e. converted into a sequence of discrete tokens. This can be achieved by different approaches, as music can be composed of simultaneous tracks, of simultaneous notes with several attributes. Until now, the proposed tokenizations rely on small vocabularies of tokens describing the note attributes and time events, resulting in fairly long token sequences, and a sub-optimal use of the embedding space of language models. Recent research has put efforts on reducing the overall sequence length by merging embeddings or combining tokens. In this paper, we show that Byte Pair Encoding, a compression technique widely used for natural language, significantly decreases the sequence length while increasing the vocabulary size. By doing so, we leverage the embedding capabilities of such models with more expressive tokens, resulting in both better results and faster inference in generation and classification tasks. The source code is shared on Github, along with a companion website. Finally, BPE is directly implemented in MidiTok, allowing the reader to easily benefit from this method.

Autoregressive visual generation models typically rely on tokenizers to compress images into tokens that can be predicted sequentially. A fundamental dilemma exists in token representation: discrete tokens enable straightforward modeling with standard cross-entropy loss, but suffer from information loss and tokenizer training instability; continuous tokens better preserve visual details, but require complex distribution modeling, complicating the generation pipeline. In this paper, we propose TokenBridge, which bridges this gap by maintaining the strong representation capacity of continuous tokens while preserving the modeling simplicity of discrete tokens. To achieve this, we decouple discretization from the tokenizer training process through post-training quantization that directly obtains discrete tokens from continuous representations. Specifically, we introduce a dimension-wise quantization strategy that independently discretizes each feature dimension, paired with a lightweight autoregressive prediction mechanism that efficiently model the resulting large token space. Extensive experiments show that our approach achieves reconstruction and generation quality on par with continuous methods while using standard categorical prediction. This work demonstrates that bridging discrete and continuous paradigms can effectively harness the strengths of both approaches, providing a promising direction for high-quality visual generation with simple autoregressive modeling. Project page: https://yuqingwang1029.github.io/TokenBridge.

Reference Expression Segmentation (RES) aims to segment image regions specified by referring expressions and has become popular with the rise of multimodal large models (MLLMs). While MLLMs excel in semantic understanding, their token-generation paradigm struggles with pixel-level dense prediction. Existing RES methods either couple MLLMs with the parameter-heavy Segment Anything Model (SAM) with 632M network parameters or adopt SAM-free lightweight pipelines that sacrifice accuracy. To address the trade-off between performance and cost, we specifically propose MLLMSeg, a novel framework that fully exploits the inherent visual detail features encoded in the MLLM vision encoder without introducing an extra visual encoder. Besides, we propose a detail-enhanced and semantic-consistent feature fusion module (DSFF) that fully integrates the detail-related visual feature with the semantic-related feature output by the large language model (LLM) of MLLM. Finally, we establish a light-weight mask decoder with only 34M network parameters that optimally leverages detailed spatial features from the visual encoder and semantic features from the LLM to achieve precise mask prediction. Extensive experiments demonstrate that our method generally surpasses both SAM-based and SAM-free competitors, striking a better balance between performance and cost. Code is available at https://github.com/jcwang0602/MLLMSeg.

With the introduction of transformer-based models for vision and language tasks, such as LLaVA and Chameleon, there has been renewed interest in the discrete tokenized representation of images. These models often treat image patches as discrete tokens, analogous to words in natural language, learning joint alignments between visual and human languages. However, little is known about the statistical behavior of these visual languages - whether they follow similar frequency distributions, grammatical structures, or topologies as natural languages. In this paper, we take a natural-language-centric approach to analyzing discrete visual languages and uncover striking similarities and fundamental differences. We demonstrate that, although visual languages adhere to Zipfian distributions, higher token innovation drives greater entropy and lower compression, with tokens predominantly representing object parts, indicating intermediate granularity. We also show that visual languages lack cohesive grammatical structures, leading to higher perplexity and weaker hierarchical organization compared to natural languages. Finally, we demonstrate that, while vision models align more closely with natural languages than other models, this alignment remains significantly weaker than the cohesion found within natural languages. Through these experiments, we demonstrate how understanding the statistical properties of discrete visual languages can inform the design of more effective computer vision models.

Recent mesh generation approaches typically tokenize triangle meshes into sequences of tokens and train autoregressive models to generate these tokens sequentially. Despite substantial progress, such token sequences inevitably reuse vertices multiple times to fully represent manifold meshes, as each vertex is shared by multiple faces. This redundancy leads to excessively long token sequences and inefficient generation processes. In this paper, we propose an efficient framework that generates artistic meshes by treating vertices and faces separately, significantly reducing redundancy. We employ an autoregressive model solely for vertex generation, decreasing the token count to approximately 23\% of that required by the most compact existing tokenizer. Next, we leverage a bidirectional transformer to complete the mesh in a single step by capturing inter-vertex relationships and constructing the adjacency matrix that defines the mesh faces. To further improve the generation quality, we introduce a fidelity enhancer to refine vertex positioning into more natural arrangements and propose a post-processing framework to remove undesirable edge connections. Experimental results show that our method achieves more than 8times faster speed on mesh generation compared to state-of-the-art approaches, while producing higher mesh quality.

Answering complex real-world questions often requires accurate retrieval from textual knowledge graphs (TKGs). The scarcity of annotated data, along with intricate topological structures, makes this task particularly challenging. As the nature of relational path information could enhance the inference ability of Large Language Models (LLMs), efficiently retrieving more complex relational path information from TKGs presents another key challenge. To tackle these challenges, we first develop a Dataset for LLMs Complex Reasoning over Textual Knowledge Graphs (RiTeK) with a broad topological structure coverage.We synthesize realistic user queries that integrate diverse topological structures, relational information, and complex textual descriptions. We conduct rigorous expert evaluation to validate the quality of our synthesized queries. And then, we introduce an enhanced Monte Carlo Tree Search (MCTS) method, Relational MCTS, to automatically extract relational path information from textual graphs for specific queries. Our dataset mainly covers the medical domain as the relation types and entity are complex and publicly available. Experimental results indicate that RiTeK poses significant challenges for current retrieval and LLM systems, while the proposed Relational MCTS method enhances LLM inference ability and achieves state-of-the-art performance on RiTeK.

The quality of subword tokenization is critical for Large Language Models, yet evaluating tokenizers for morphologically rich Uralic languages is hampered by the lack of clean morpheme lexicons. We introduce SampoNLP, a corpus-free toolkit for morphological lexicon creation using MDL-inspired Self-Referential Atomicity Scoring, which filters composite forms through internal structural cues - suited for low-resource settings. Using the high-purity lexicons generated by SampoNLP for Finnish, Hungarian, and Estonian, we conduct a systematic evaluation of BPE tokenizers across a range of vocabulary sizes (8k-256k). We propose a unified metric, the Integrated Performance Score (IPS), to navigate the trade-off between morpheme coverage and over-splitting. By analyzing the IPS curves, we identify the "elbow points" of diminishing returns and provide the first empirically grounded recommendations for optimal vocabulary sizes (k) in these languages. Our study not only offers practical guidance but also quantitatively demonstrates the limitations of standard BPE for highly agglutinative languages. The SampoNLP library and all generated resources are made publicly available: https://github.com/AragonerUA/SampoNLP

Despite the widespread use of Transformer-based text embedding models in NLP tasks, surprising 'sticky tokens' can undermine the reliability of embeddings. These tokens, when repeatedly inserted into sentences, pull sentence similarity toward a certain value, disrupting the normal distribution of embedding distances and degrading downstream performance. In this paper, we systematically investigate such anomalous tokens, formally defining them and introducing an efficient detection method, Sticky Token Detector (STD), based on sentence and token filtering. Applying STD to 40 checkpoints across 14 model families, we discover a total of 868 sticky tokens. Our analysis reveals that these tokens often originate from special or unused entries in the vocabulary, as well as fragmented subwords from multilingual corpora. Notably, their presence does not strictly correlate with model size or vocabulary size. We further evaluate how sticky tokens affect downstream tasks like clustering and retrieval, observing significant performance drops of up to 50%. Through attention-layer analysis, we show that sticky tokens disproportionately dominate the model's internal representations, raising concerns about tokenization robustness. Our findings show the need for better tokenization strategies and model design to mitigate the impact of sticky tokens in future text embedding applications.

Typically, tokenization is the very first step in most text processing works. As a token serves as an atomic unit that embeds the contextual information of text, how to define a token plays a decisive role in the performance of a model.Even though Byte Pair Encoding (BPE) has been considered the de facto standard tokenization method due to its simplicity and universality, it still remains unclear whether BPE works best across all languages and tasks. In this paper, we test several tokenization strategies in order to answer our primary research question, that is, "What is the best tokenization strategy for Korean NLP tasks?" Experimental results demonstrate that a hybrid approach of morphological segmentation followed by BPE works best in Korean to/from English machine translation and natural language understanding tasks such as KorNLI, KorSTS, NSMC, and PAWS-X. As an exception, for KorQuAD, the Korean extension of SQuAD, BPE segmentation turns out to be the most effective.

Deep learning approaches to natural language processing have made great strides in recent years. While these models produce symbols that convey vast amounts of diverse knowledge, it is unclear how such symbols are grounded in data from the world. In this paper, we explore the development of a private language for visual data representation by training emergent language (EL) encoders/decoders in both i) a traditional referential game environment and ii) a contrastive learning environment utilizing a within-class matching training paradigm. An additional classification layer utilizing neural machine translation and random forest classification was used to transform symbolic representations (sequences of integer symbols) to class labels. These methods were applied in two experiments focusing on object recognition and action recognition. For object recognition, a set of sketches produced by human participants from real imagery was used (Sketchy dataset) and for action recognition, 2D trajectories were generated from 3D motion capture systems (MOVI dataset). In order to interpret the symbols produced for data in each experiment, gradient-weighted class activation mapping (Grad-CAM) methods were used to identify pixel regions indicating semantic features which contribute evidence towards symbols in learned languages. Additionally, a t-distributed stochastic neighbor embedding (t-SNE) method was used to investigate embeddings learned by CNN feature extractors.

Few images on the Web receive alt-text descriptions that would make them accessible to blind and low vision (BLV) users. Image-based NLG systems have progressed to the point where they can begin to address this persistent societal problem, but these systems will not be fully successful unless we evaluate them on metrics that guide their development correctly. Here, we argue against current referenceless metrics -- those that don't rely on human-generated ground-truth descriptions -- on the grounds that they do not align with the needs of BLV users. The fundamental shortcoming of these metrics is that they do not take context into account, whereas contextual information is highly valued by BLV users. To substantiate these claims, we present a study with BLV participants who rated descriptions along a variety of dimensions. An in-depth analysis reveals that the lack of context-awareness makes current referenceless metrics inadequate for advancing image accessibility. As a proof-of-concept, we provide a contextual version of the referenceless metric CLIPScore which begins to address the disconnect to the BLV data. An accessible HTML version of this paper is available at https://elisakreiss.github.io/contextual-description-evaluation/paper/reflessmetrics.html

We define and develop a homotopy invariant notion for the topological complexity of a map f:X to Y, denoted TC(f), that interacts with TC(X) and TC(Y) in the same way cat(f) interacts with cat(X) and cat(Y). Furthermore, TC(f) and cat(f) satisfy the same inequalities as TC(X) and cat(X). We compare it to other invariants defined in the papers [15,16,17,18,20]. We apply TC(f) to studying group homomorphisms f:Hto G.

Positional encoding mechanisms enable Transformers to model sequential structure and long-range dependencies in text. While absolute positional encodings struggle with extrapolation to longer sequences due to fixed positional representations, and relative approaches like Alibi exhibit performance degradation on extremely long contexts, the widely-used Rotary Positional Encoding (RoPE) introduces oscillatory attention patterns that hinder stable long-distance dependency modelling. We address these limitations through a geometric reformulation of positional encoding. Drawing inspiration from Lorentz transformations in hyperbolic geometry, we propose Hyperbolic Rotary Positional Encoding (HoPE), which leverages hyperbolic functions to implement Lorentz rotations on token representations. Theoretical analysis demonstrates that RoPE is a special case of our generalized formulation. HoPE fundamentally resolves RoPE's slation issues by enforcing monotonic decay of attention weights with increasing token distances. Extensive experimental results, including perplexity evaluations under several extended sequence benchmarks, show that HoPE consistently exceeds existing positional encoding methods. These findings underscore HoPE's enhanced capacity for representing and generalizing long-range dependencies. Data and code will be available.

In recent years, general visual foundation models (VFMs) have witnessed increasing adoption, particularly as image encoders for popular multi-modal large language models (MLLMs). However, without semantically fine-grained supervision, these models still encounter fundamental prediction errors in the context of downstream text-image-related tasks, i.e., perception, understanding and reasoning with images containing small and dense texts. To bridge this gap, we develop TokenOCR, the first token-level visual foundation model specifically tailored for text-image-related tasks, designed to support a variety of traditional downstream applications. To facilitate the pretraining of TokenOCR, we also devise a high-quality data production pipeline that constructs the first token-level image text dataset, TokenIT, comprising 20 million images and 1.8 billion token-mask pairs. Furthermore, leveraging this foundation with exceptional image-as-text capability, we seamlessly replace previous VFMs with TokenOCR to construct a document-level MLLM, TokenVL, for VQA-based document understanding tasks. Finally, extensive experiments demonstrate the effectiveness of TokenOCR and TokenVL. Code, datasets, and weights will be available at https://token-family.github.io/TokenOCR_project.

We present the KL3M tokenizers, a family of specialized tokenizers for legal, financial, and governmental text. Despite established work on tokenization, specialized tokenizers for professional domains remain understudied. Our paper offers two main contributions to this area. First, we introduce domain-specific BPE tokenizers for legal, financial, and governmental text. Our kl3m-004-128k-cased tokenizer uses 9-17% fewer tokens than GPT-4o and Llama3 for domain-specific documents, despite having a smaller vocabulary. For specialized terminology, our cased tokenizer is even more efficient, using up to 83% fewer tokens for legal terms and 39% fewer tokens for financial terms. Second, we develop character-level BPE tokenizers (4K, 8K, and 16K vocabulary sizes) for text correction tasks like OCR post-processing. These tokenizers keep consistent token boundaries between error-containing and correct text, making it easier for models to learn correction patterns. These tokenizers help professional applications by fitting more text in context windows, reducing computational needs, and preserving the meaning of domain-specific terms. Our analysis shows these efficiency gains directly benefit the processing of long legal and financial documents. We release all tokenizers and code through GitHub and Hugging Face to support further research in specialized tokenization.

Large Language Models (LLMs) excel at complex reasoning through search algorithms, yet current strategies often suffer from massive token consumption due to redundant exploration of semantically equivalent steps. Existing semantic similarity methods struggle to accurately identify such equivalence in domain-specific contexts like mathematical reasoning. To address this, we propose EquivPruner, a simple yet effective approach that identifies and prunes semantically equivalent actions during LLM reasoning search. We also introduce MathEquiv, the first dataset we created for mathematical statement equivalence, which enables the training of a lightweight equivalence detector. Extensive experiments across various models and tasks demonstrate that EquivPruner significantly reduces token consumption, improving searching efficiency and often bolstering reasoning accuracy. For instance, when applied to Qwen2.5-Math-7B-Instruct on GSM8K, EquivPruner reduced token consumption by 48.1\% while also improving accuracy. Our code is available at https://github.com/Lolo1222/EquivPruner.

There is growing evidence that pretraining on high quality, carefully thought-out tokens such as code or mathematics plays an important role in improving the reasoning abilities of large language models. For example, Minerva, a PaLM model finetuned on billions of tokens of mathematical documents from arXiv and the web, reported dramatically improved performance on problems that require quantitative reasoning. However, because all known open source web datasets employ preprocessing that does not faithfully preserve mathematical notation, the benefits of large scale training on quantitive web documents are unavailable to the research community. We introduce OpenWebMath, an open dataset inspired by these works containing 14.7B tokens of mathematical webpages from Common Crawl. We describe in detail our method for extracting text and LaTeX content and removing boilerplate from HTML documents, as well as our methods for quality filtering and deduplication. Additionally, we run small-scale experiments by training 1.4B parameter language models on OpenWebMath, showing that models trained on 14.7B tokens of our dataset surpass the performance of models trained on over 20x the amount of general language data. We hope that our dataset, openly released on the Hugging Face Hub, will help spur advances in the reasoning abilities of large language models.

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

Using natural language to query visual information is a fundamental need in real-world applications. Text-Image Retrieval (TIR) retrieves a target image from a gallery based on an image-level description, while Referring Expression Comprehension (REC) localizes a target object within a given image using an instance-level description. However, real-world applications often present more complex demands. Users typically query an instance-level description across a large gallery and expect to receive both relevant image and the corresponding instance location. In such scenarios, TIR struggles with fine-grained descriptions and object-level localization, while REC is limited in its ability to efficiently search large galleries and lacks an effective ranking mechanism. In this paper, we introduce a new task called Referring Expression Instance Retrieval (REIR), which supports both instance-level retrieval and localization based on fine-grained referring expressions. First, we propose a large-scale benchmark for REIR, named REIRCOCO, constructed by prompting advanced vision-language models to generate high-quality referring expressions for instances in the MSCOCO and RefCOCO datasets. Second, we present a baseline method, Contrastive Language-Instance Alignment with Relation Experts (CLARE), which employs a dual-stream architecture to address REIR in an end-to-end manner. Given a referring expression, the textual branch encodes it into a query embedding. The visual branch detects candidate objects and extracts their instance-level visual features. The most similar candidate to the query is selected for bounding box prediction. CLARE is first trained on object detection and REC datasets to establish initial grounding capabilities, then optimized via Contrastive Language-Instance Alignment (CLIA) for improved retrieval across images. We will release our code and benchmark publicly.

Traditional reference segmentation tasks have predominantly focused on silent visual scenes, neglecting the integral role of multimodal perception and interaction in human experiences. In this work, we introduce a novel task called Reference Audio-Visual Segmentation (Ref-AVS), which seeks to segment objects within the visual domain based on expressions containing multimodal cues. Such expressions are articulated in natural language forms but are enriched with multimodal cues, including audio and visual descriptions. To facilitate this research, we construct the first Ref-AVS benchmark, which provides pixel-level annotations for objects described in corresponding multimodal-cue expressions. To tackle the Ref-AVS task, we propose a new method that adequately utilizes multimodal cues to offer precise segmentation guidance. Finally, we conduct quantitative and qualitative experiments on three test subsets to compare our approach with existing methods from related tasks. The results demonstrate the effectiveness of our method, highlighting its capability to precisely segment objects using multimodal-cue expressions. Dataset is available at https://gewu-lab.github.io/Ref-AVS{https://gewu-lab.github.io/Ref-AVS}.

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding quality without labels remains an open challenge. In this work, we propose Persistence, a topology-aware metric based on persistent homology that quantifies the geometric structure and topological richness of embedding spaces in a fully unsupervised manner. Unlike metrics that assume linear separability or rely on covariance structure, Persistence captures global and multi-scale organization. Empirical results across diverse domains show that Persistence consistently achieves top-tier correlations with downstream performance, outperforming existing unsupervised metrics and enabling reliable model and hyperparameter selection.

Recent progress in Sign Language Translation (SLT) has focussed primarily on improving the representational capacity of large language models to incorporate Sign Language features. This work explores an alternative direction: enhancing the geometric properties of skeletal representations themselves. We propose Geo-Sign, a method that leverages the properties of hyperbolic geometry to model the hierarchical structure inherent in sign language kinematics. By projecting skeletal features derived from Spatio-Temporal Graph Convolutional Networks (ST-GCNs) into the Poincar\'e ball model, we aim to create more discriminative embeddings, particularly for fine-grained motions like finger articulations. We introduce a hyperbolic projection layer, a weighted Fr\'echet mean aggregation scheme, and a geometric contrastive loss operating directly in hyperbolic space. These components are integrated into an end-to-end translation framework as a regularisation function, to enhance the representations within the language model. This work demonstrates the potential of hyperbolic geometry to improve skeletal representations for Sign Language Translation, improving on SOTA RGB methods while preserving privacy and improving computational efficiency. Code available here: https://github.com/ed-fish/geo-sign.

This paper presents the release of EmojiNet, the largest machine-readable emoji sense inventory that links Unicode emoji representations to their English meanings extracted from the Web. EmojiNet is a dataset consisting of: (i) 12,904 sense labels over 2,389 emoji, which were extracted from the web and linked to machine-readable sense definitions seen in BabelNet, (ii) context words associated with each emoji sense, which are inferred through word embedding models trained over Google News corpus and a Twitter message corpus for each emoji sense definition, and (iii) recognizing discrepancies in the presentation of emoji on different platforms, specification of the most likely platform-based emoji sense for a selected set of emoji. The dataset is hosted as an open service with a REST API and is available at http://emojinet.knoesis.org/. The development of this dataset, evaluation of its quality, and its applications including emoji sense disambiguation and emoji sense similarity are discussed.

Transformers have become an indispensable module for text generation models since their great success in machine translation. Previous works attribute the~success of transformers to the query-key-value dot-product attention, which provides a robust inductive bias by the fully connected token graphs. However, we found that self-attention has a severe limitation. When predicting the (i+1)-th token, self-attention only takes the i-th token as an information collector, and it tends to give a high attention weight to those tokens similar to itself. Therefore, most of the historical information that occurred before the i-th token is not taken into consideration. Based on this observation, in this paper, we propose a new architecture, called bird-eye transformer(BET), which goes one step further to improve the performance of transformers by reweighting self-attention to encourage it to focus more on important historical information. We have conducted experiments on multiple text generation tasks, including machine translation (2 datasets) and language models (3 datasets). These experimental~results show that our proposed model achieves a better performance than the baseline transformer architectures on~all~datasets. The code is released at: https://sites.google.com/view/bet-transformer/home.

AI-driven geometric problem solving is a complex vision-language task that requires accurate diagram interpretation, mathematical reasoning, and robust cross-modal grounding. A foundational yet underexplored capability for this task is the ability to identify and interpret geometric elements based on natural language queries. To address this, we introduce the task of Referring Expression Comprehension (REC) for geometric problems, which evaluates whether models can localize points, shapes, and spatial relations in diagrams in response to textual prompts. We present GeoRef, a benchmark dataset constructed from existing geometric problem corpora, featuring diverse, high-quality annotations and queries. Due to the lack of annotated data for this task, we generate a large-scale synthetic training dataset using a structured geometric formal language, enabling broad coverage of geometric concepts and facilitating model adaptation. We explore two fine-tuning approaches: Supervised Fine-Tuning (SFT) and Group Relative Policy Optimization (GRPO). Our results show that GRPO significantly outperforms SFT by better aligning model behavior with task-specific rewards. Furthermore, we propose a verify-and-regenerate mechanism that detects incorrect predictions and re-infers answers using contextual reasoning history, further boosting accuracy. Notably, even state-of-the-art Multimodal Large Language Models (MLLMs) struggle with this task, underscoring the necessity of explicitly evaluating and strengthening geometric grounding as a prerequisite for robust geometric problem solving. Moreover, models trained on GeoRef demonstrate measurable improvements on downstream geometric reasoning tasks, highlighting the broader value of REC as a foundation for multimodal mathematical understanding.

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

The field of face recognition (FR) has undergone significant advancements with the rise of deep learning. Recently, the success of unsupervised learning and graph neural networks has demonstrated the effectiveness of data structure information. Considering that the FR task can leverage large-scale training data, which intrinsically contains significant structure information, we aim to investigate how to encode such critical structure information into the latent space. As revealed from our observations, directly aligning the structure information between the input and latent spaces inevitably suffers from an overfitting problem, leading to a structure collapse phenomenon in the latent space. To address this problem, we propose TopoFR, a novel FR model that leverages a topological structure alignment strategy called PTSA and a hard sample mining strategy named SDE. Concretely, PTSA uses persistent homology to align the topological structures of the input and latent spaces, effectively preserving the structure information and improving the generalization performance of FR model. To mitigate the impact of hard samples on the latent space structure, SDE accurately identifies hard samples by automatically computing structure damage score (SDS) for each sample, and directs the model to prioritize optimizing these samples. Experimental results on popular face benchmarks demonstrate the superiority of our TopoFR over the state-of-the-art methods. Code and models are available at: https://github.com/modelscope/facechain/tree/main/face_module/TopoFR.

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/}.

We introduce Mesh Silksong, a compact and efficient mesh representation tailored to generate the polygon mesh in an auto-regressive manner akin to silk weaving. Existing mesh tokenization methods always produce token sequences with repeated vertex tokens, wasting the network capability. Therefore, our approach tokenizes mesh vertices by accessing each mesh vertice only once, reduces the token sequence's redundancy by 50\%, and achieves a state-of-the-art compression rate of approximately 22\%. Furthermore, Mesh Silksong produces polygon meshes with superior geometric properties, including manifold topology, watertight detection, and consistent face normals, which are critical for practical applications. Experimental results demonstrate the effectiveness of our approach, showcasing not only intricate mesh generation but also significantly improved geometric integrity.

Text-based foundation models have become an important part of scientific discovery, with molecular foundation models accelerating advancements in material science and molecular design.However, existing models are constrained by closed-vocabulary tokenizers that capture only a fraction of molecular space. In this work, we systematically evaluate 34 tokenizers, including 19 chemistry-specific ones, and reveal significant gaps in their coverage of the SMILES molecular representation. To assess the impact of tokenizer choice, we introduce n-gram language models as a low-cost proxy and validate their effectiveness by pretraining and finetuning 18 RoBERTa-style encoders for molecular property prediction. To overcome the limitations of existing tokenizers, we propose two new tokenizers -- Smirk and Smirk-GPE -- with full coverage of the OpenSMILES specification. The proposed tokenizers systematically integrate nuclear, electronic, and geometric degrees of freedom; facilitating applications in pharmacology, agriculture, biology, and energy storage. Our results highlight the need for open-vocabulary modeling and chemically diverse benchmarks in cheminformatics.

We introduce methods to quantify how Large Language Models (LLMs) encode and store contextual information, revealing that tokens often seen as minor (e.g., determiners, punctuation) carry surprisingly high context. Notably, removing these tokens -- especially stopwords, articles, and commas -- consistently degrades performance on MMLU and BABILong-4k, even if removing only irrelevant tokens. Our analysis also shows a strong correlation between contextualization and linearity, where linearity measures how closely the transformation from one layer's embeddings to the next can be approximated by a single linear mapping. These findings underscore the hidden importance of filler tokens in maintaining context. For further exploration, we present LLM-Microscope, an open-source toolkit that assesses token-level nonlinearity, evaluates contextual memory, visualizes intermediate layer contributions (via an adapted Logit Lens), and measures the intrinsic dimensionality of representations. This toolkit illuminates how seemingly trivial tokens can be critical for long-range understanding.

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.

Artificial general intelligence on graphs has shown significant advancements across various applications, yet the traditional 'Pre-train & Fine-tune' paradigm faces inefficiencies and negative transfer issues, particularly in complex and few-shot settings. Graph prompt learning emerges as a promising alternative, leveraging lightweight prompts to manipulate data and fill the task gap by reformulating downstream tasks to the pretext. However, several critical challenges still remain: how to unify diverse graph prompt models, how to evaluate the quality of graph prompts, and to improve their usability for practical comparisons and selection. In response to these challenges, we introduce the first comprehensive benchmark for graph prompt learning. Our benchmark integrates SIX pre-training methods and FIVE state-of-the-art graph prompt techniques, evaluated across FIFTEEN diverse datasets to assess performance, flexibility, and efficiency. We also present 'ProG', an easy-to-use open-source library that streamlines the execution of various graph prompt models, facilitating objective evaluations. Additionally, we propose a unified framework that categorizes existing graph prompt methods into two main approaches: prompts as graphs and prompts as tokens. This framework enhances the applicability and comparison of graph prompt techniques. The code is available at: https://github.com/sheldonresearch/ProG.

Retrieval-Augmented Generation (RAG) systems face significant performance gaps when applied to technical domains requiring precise information extraction from complex documents. Current evaluation methodologies relying on document-level metrics inadequately capture token-resolution retrieval accuracy that is critical for domain-related documents. We propose a framework combining granular evaluation metrics with synthetic data generation to optimize domain-specific RAG performance. First, we introduce token-aware metrics Precision Omega and Intersection-over-Union (IoU) that quantify context preservation versus information density trade-offs inherent in technical texts. Second, we develop a reasoning model-driven pipeline using instruction-tuned LLMs (DeepSeek-R1, DeepSeek-R1 distilled variants, and Phi-4) to generate context-anchored QA pairs with discontinuous reference spans across three specialized corpora: SEC 10-K filings (finance), biomedical abstracts (PubMed), and APT threat reports (cybersecurity). Our empirical analysis reveals critical insights: smaller chunks (less than 10 tokens) improve precision by 31-42% (IoU = 0.071 vs. baseline 0.053) at recall costs (-18%), while domain-specific embedding strategies yield 22% variance in optimal chunk sizing (5-20 tokens). The DeepSeek-R1-Distill-Qwen-32B model demonstrates superior concept alignment (+14% mean IoU over alternatives), though no configuration universally dominates. Financial texts favor larger chunks for risk factor coverage (Recall = 0.81 at size = 20), whereas cybersecurity content benefits from atomic segmentation, Precision Omega = 0.28 at size = 5. Our code is available on https://github.com/aryan-jadon/Synthetic-Data-Generation-and-Evaluation-using-Reasoning-Model

We present a unified, promptable model capable of simultaneously segmenting, recognizing, and captioning anything. Unlike SAM, we aim to build a versatile region representation in the wild via visual prompting. To achieve this, we train a generalizable model with massive segmentation masks, e.g., SA-1B masks, and semantic priors from a pre-trained CLIP model with 5 billion parameters. Specifically, we construct a promptable image decoder by adding a semantic token to each mask token. The semantic token is responsible for learning the semantic priors in a predefined concept space. Through joint optimization of segmentation on mask tokens and concept prediction on semantic tokens, our model exhibits strong regional recognition and localization capabilities. For example, an additional 38M-parameter causal text decoder trained from scratch sets a new record with a CIDEr score of 150.7 on the Visual Genome region captioning task. We believe this model can be a versatile region-level image tokenizer, capable of encoding general-purpose region context for a broad range of perception tasks. Code and models are available at https://github.com/baaivision/tokenize-anything.