arXiv subjects

Liping Yuan

Publications and source records attributed to Liping Yuan.

17 recordsLinked to original sources

arXiv2026

On the m-point convexity

Let $S\subset \mathbb{R}^d$ $(d\geq 2)$. A set $S$ is said to be $m$-point convex, if for every $m$ distinct points in $S$, at least one of the line-segments determined by them lies in $S$. We also say that $S$ has property $P_m$. Let ${x,y,z}\in \mathbb{R}^{d}$. If $\mathrm{conv}\{x,y,z\}$ is a right triangle, then $\{x,y,z\}$ is called a {\it right triple}. A set $S$ is said to have the right-$3$-point property,if, for every right triple of $S$, at least one of the line-segments determined by them belongs to $S$. In particular, it has the double right-$3$-point property, if, for every right triple in $S$, at least two of the line-segments determined by them belong to $S$. In this paper, we further investigate $m$-point convex sets and establish the relationship between the sets with the double right-$3$-point property and convex sets in $\mathbb{R}^d$.

math.CO↗

arXiv2026

The orthogonal connectedness of polyhedral surfaces

Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doing so, we also encounter polytopes which are not orthogonally decomposable.

math.CO↗

arXiv2025

Excursions in Sylvester-Gallai land

The Sylvester-Gallai theorem states that for a finite set of points in the plane, if every line determined by any two of these points also contains a third, then the set is necessarily made of collinear points. In this paper, we first provide a counterexample in the plane when the point set is countably infinite but bounded. Then we consider a variant of the Sylvester-Gallai theorem where instead of a finite point set we have a finite family of convex sets in $\mathbb{R}^d$ ($d\geq 2$). Finally, we present another variant of the Sylvester-Gallai theorem, when instead of point sets we have a finite family of line-segments in the plane.

math.CO↗

arXiv2025

On Klee's problem of convex bodies in Banach spaces

It is well known that every convex body in a finite dimensional normed space can be uniformly approximated by strictly convex and smooth convex bodies. However, in the case of infinite dimensions, little progress has been made since Klee asked how it is in the case of infinite dimensions in 1959. In this paper, we show that for an infinite dimensional Banach space $X$, (1) every convex body can be uniformly approximated by strictly convex bodies if and only if $X$ admits an equivalent strictly convex norm; (2) every convex body can be uniformly approximated by Gâteaux smooth convex bodies if the dual $X^*$ of $X$ admits an equivalent strictly convex dual norm; in particular, (3) if $X$ is either separable, or reflexive, then every convex body in $X$ can be uniformly approximated by strictly convex and smooth convex bodies. They are done by showing that some correspondences among the sets of all convex bodies endowed with the Hausdorff metric, all continuous coercive Minkowski functionals and Fenchel's transform defined on all quadratic homogenous continuous convex functions equipped with the metric induced by the sup-norm of all bounded continuous functions defined on the closed unit ball $B_X$ are actually locally Lipschitz isomorphisms.

math.FA↗

arXiv2025

Seed1.5-VL Technical Report

We present Seed1.5-VL, a vision-language foundation model designed to advance general-purpose multimodal understanding and reasoning. Seed1.5-VL is composed with a 532M-parameter vision encoder and a Mixture-of-Experts (MoE) LLM of 20B active parameters. Despite its relatively compact architecture, it delivers strong performance across a wide spectrum of public VLM benchmarks and internal evaluation suites, achieving the state-of-the-art performance on 38 out of 60 public benchmarks. Moreover, in agent-centric tasks such as GUI control and gameplay, Seed1.5-VL outperforms leading multimodal systems, including OpenAI CUA and Claude 3.7. Beyond visual and video understanding, it also demonstrates strong reasoning abilities, making it particularly effective for multimodal reasoning challenges such as visual puzzles. We believe these capabilities will empower broader applications across diverse tasks. In this report, we mainly provide a comprehensive review of our experiences in building Seed1.5-VL across model design, data construction, and training at various stages, hoping that this report can inspire further research. Seed1.5-VL is now accessible at https://www.volcengine.com/ (Volcano Engine Model ID: doubao-1-5-thinking-vision-pro-250428)

cs.CV↗

arXiv2025

Orthogonally connected sets

In this paper, we further investigate the orthogonally connected sets and establish necessary and sufficient conditions for a set to be staircase connected.

math.CO↗

arXiv2025

Tarsier2: Advancing Large Vision-Language Models from Detailed Video Description to Comprehensive Video Understanding

We introduce Tarsier2, a state-of-the-art large vision-language model (LVLM) designed for generating detailed and accurate video descriptions, while also exhibiting superior general video understanding capabilities. Tarsier2 achieves significant advancements through three key upgrades: (1) Scaling pre-training data from 11M to 40M video-text pairs, enriching both volume and diversity; (2) Performing fine-grained temporal alignment during supervised fine-tuning; (3) Using model-based sampling to automatically construct preference data and applying DPO training for optimization. Extensive experiments show that Tarsier2-7B consistently outperforms leading proprietary models, including GPT-4o and Gemini 1.5 Pro, in detailed video description tasks. On the DREAM-1K benchmark, Tarsier2-7B improves F1 by 2.8% over GPT-4o and 5.8% over Gemini-1.5-Pro. In human side-by-side evaluations, Tarsier2-7B shows a +8.6% performance advantage over GPT-4o and +24.9% over Gemini-1.5-Pro. Tarsier2-7B also sets new state-of-the-art results across 15 public benchmarks, spanning tasks such as video question-answering, video grounding, hallucination test, and embodied question-answering, demonstrating its versatility as a robust generalist vision-language model.

cs.CV↗

arXiv2024

Tarsier: Recipes for Training and Evaluating Large Video Description Models

Generating fine-grained video descriptions is a fundamental challenge in video understanding. In this work, we introduce Tarsier, a family of large-scale video-language models designed to generate high-quality video descriptions. Tarsier employs CLIP-ViT to encode frames separately and then uses an LLM to model temporal relationships. Despite its simple architecture, we demonstrate that with a meticulously designed two-stage training procedure, the Tarsier models exhibit substantially stronger video description capabilities than any existing open-source model, showing a $+51.4\%$ advantage in human side-by-side evaluation over the strongest model. Additionally, they are comparable to state-of-the-art proprietary models, with a $+12.3\%$ advantage against GPT-4V and a $-6.7\%$ disadvantage against Gemini 1.5 Pro. When upgraded to Tarsier2 by building upon SigLIP and Qwen2-7B, it further improves significantly with a $+4.8\%$ advantage against GPT-4o. Besides video description, Tarsier proves to be a versatile generalist model, achieving new state-of-the-art results across nine public benchmarks, including multi-choice VQA, open-ended VQA, and zero-shot video captioning. Our second contribution is the introduction of a new benchmark -- DREAM-1K (https://tarsier-vlm.github.io/) for evaluating video description models, consisting of a new challenging dataset featuring videos from diverse sources and varying complexity, along with an automatic method specifically designed to assess the quality of fine-grained video descriptions. We make our models and evaluation benchmark publicly available at https://github.com/bytedance/tarsier.

cs.CV↗

arXiv2024

Boximator: Generating Rich and Controllable Motions for Video Synthesis

Generating rich and controllable motion is a pivotal challenge in video synthesis. We propose Boximator, a new approach for fine-grained motion control. Boximator introduces two constraint types: hard box and soft box. Users select objects in the conditional frame using hard boxes and then use either type of boxes to roughly or rigorously define the object's position, shape, or motion path in future frames. Boximator functions as a plug-in for existing video diffusion models. Its training process preserves the base model's knowledge by freezing the original weights and training only the control module. To address training challenges, we introduce a novel self-tracking technique that greatly simplifies the learning of box-object correlations. Empirically, Boximator achieves state-of-the-art video quality (FVD) scores, improving on two base models, and further enhanced after incorporating box constraints. Its robust motion controllability is validated by drastic increases in the bounding box alignment metric. Human evaluation also shows that users favor Boximator generation results over the base model.

cs.CV↗

arXiv2023

SparseGAN: Sparse Generative Adversarial Network for Text Generation

It is still a challenging task to learn a neural text generation model under the framework of generative adversarial networks (GANs) since the entire training process is not differentiable. The existing training strategies either suffer from unreliable gradient estimations or imprecise sentence representations. Inspired by the principle of sparse coding, we propose a SparseGAN that generates semantic-interpretable, but sparse sentence representations as inputs to the discriminator. The key idea is that we treat an embedding matrix as an over-complete dictionary, and use a linear combination of very few selected word embeddings to approximate the output feature representation of the generator at each time step. With such semantic-rich representations, we not only reduce unnecessary noises for efficient adversarial training, but also make the entire training process fully differentiable. Experiments on multiple text generation datasets yield performance improvements, especially in sequence-level metrics, such as BLEU.

cs.CL↗

arXiv2021

On the Transferability of Adversarial Attacksagainst Neural Text Classifier

Deep neural networks are vulnerable to adversarial attacks, where a small perturbation to an input alters the model prediction. In many cases, malicious inputs intentionally crafted for one model can fool another model. In this paper, we present the first study to systematically investigate the transferability of adversarial examples for text classification models and explore how various factors, including network architecture, tokenization scheme, word embedding, and model capacity, affect the transferability of adversarial examples. Based on these studies, we propose a genetic algorithm to find an ensemble of models that can be used to induce adversarial examples to fool almost all existing models. Such adversarial examples reflect the defects of the learning process and the data bias in the training set. Finally, we derive word replacement rules that can be used for model diagnostics from these adversarial examples.

cs.LG↗

arXiv2021

Certified Robustness to Text Adversarial Attacks by Randomized [MASK]

Recently, few certified defense methods have been developed to provably guarantee the robustness of a text classifier to adversarial synonym substitutions. However, all existing certified defense methods assume that the defenders are informed of how the adversaries generate synonyms, which is not a realistic scenario. In this paper, we propose a certifiably robust defense method by randomly masking a certain proportion of the words in an input text, in which the above unrealistic assumption is no longer necessary. The proposed method can defend against not only word substitution-based attacks, but also character-level perturbations. We can certify the classifications of over 50% texts to be robust to any perturbation of 5 words on AGNEWS, and 2 words on SST2 dataset. The experimental results show that our randomized smoothing method significantly outperforms recently proposed defense methods across multiple datasets.

cs.CL↗

arXiv2021

Alleviate Exposure Bias in Sequence Prediction \\ with Recurrent Neural Networks

A popular strategy to train recurrent neural networks (RNNs), known as ``teacher forcing'' takes the ground truth as input at each time step and makes the later predictions partly conditioned on those inputs. Such training strategy impairs their ability to learn rich distributions over entire sequences because the chosen inputs hinders the gradients back-propagating to all previous states in an end-to-end manner. We propose a fully differentiable training algorithm for RNNs to better capture long-term dependencies by recovering the probability of the whole sequence. The key idea is that at each time step, the network takes as input a ``bundle'' of similar words predicted at the previous step instead of a single ground truth. The representations of these similar words forms a convex hull, which can be taken as a kind of regularization to the input. Smoothing the inputs by this way makes the whole process trainable and differentiable. This design makes it possible for the model to explore more feasible combinations (possibly unseen sequences), and can be interpreted as a computationally efficient approximation to the beam search. Experiments on multiple sequence generation tasks yield performance improvements, especially in sequence-level metrics, such as BLUE or ROUGE-2.

cs.CL↗

arXiv2019

Locating diametral points

Let $K$ be a convex body in $\mathbb{R} ^d$, with $d = 2,3$. We determine sharp sufficient conditions for a set $E$ composed of $1$, $2$, or $3$ points of ${\rm bd}K$, to contain at least one endpoint of a diameter of $K$ (for $d=2,3$). We extend this also to convex surfaces, with their intrinsic metric. Our conditions are upper bounds on the sum of the complete angles at the points in $E$. We also show that such criteria do not exist for $n\geq 4$ points.

math.MG↗

arXiv2017

A note on discrete lattice-periodic sets with an application to Archimedean tilings

Cao & Yuan obtained a Blichfeldt-type result for the vertex set of the edge-to-edge tiling of the plane by regular hexagons. Observing that every Archimedean tiling is the union of translates of a fixed lattice, we take a more general viewpoint and investigate basic questions for such point sets about the homogeneous and inhomogeneous problem in the Geometry of Numbers. The Archimedean tilings nicely exemplify our results.

math.CO↗

arXiv2014

Volumes of convex lattice polytopes and a question of V. I. Arnold

We show by a direct construction that there are at least $\exp\{cV^{(d-1)/(d+1)}\}$ convex lattice polytopes in $\mathbb{R}^d$ of volume $V$ that are different in the sense that none of them can be carried to an other one by a lattice preserving affine transformation. This is achieved by considering the family $\mathcal{P}^d(r)$ (to be defined in the text) of convex lattice polytopes whose volumes are between $0$ and $r^d/d!$. Namely we prove that for $P \in \mathcal{P}^d(r)$, $d!\mathrm{vol\;} P$ takes all possible integer values between $cr^{d-1}$ and $r^d$ where $c>0$ is a constant depending only on $d$.

math.CO↗

arXiv2012

Acute Triangulations of the Cuboctahedral Surface

In this paper we prove that the surface of the cuboctahedron can be triangulated into 8 non-obtuse triangles and 12 acute triangles. Furthermore, we show that both bounds are the best possible.

math.CO↗