arXiv subjects

Ian Zhang

Publications and source records attributed to Ian Zhang.

9 recordsLinked to original sources

arXiv2026

Hallucination Rates in Language Generation

Language generation in the limit is an elegant model introduced by Kleinberg and Mullainathan [KM24] to formally study language generation by an algorithm that learns solely based on example strings. In this model, an algorithm is said to correctly generate from a language if it never makes an error after some finite time. In contrast, even sophisticated language models are known to regularly hallucinate in practice. In this paper, we initiate the study of language generation in the limit with (infinite) hallucination, i.e., the algorithm may generate incorrect strings infinitely often, but the errors occur at a limited rate (possibly even with 0-measure). We first show that hallucination, even at rate 0, makes generation in the limit strictly more powerful: there are language collections that cannot be generated with finite error but can be generated with infinite error, even when errors occur on a 0-measure set of time-steps. Furthermore, while all countable collections are generatable with finite error, we show a strict hierarchy of (uncountable) language collections characterized by the hallucination rate. This hierarchy extends to breadth, the fraction of the target language generated. While all countable collections can attain the optimal breadth of 1/2 [KW26b], we show strict separation at every breadth and hallucination rate. Finally, we study generation in the limit without repetition, where the algorithm may not repeat strings. This lets us compare the sets of correct and incorrect strings generated, rather than the fractions of correct and incorrect time-steps. Once again, we demonstrate a strict hierarchy at every hallucination rate and breadth. Taken together, these results reveal rich structure in language collections generatable in the limit with hallucination and establish hallucination rate as an important parameter in the theoretical study of language generation.

cs.DS↗

arXiv2026

Characterizing the Effect of Noise in Language Generation in the Limit

Kleinberg and Mullainathan recently proposed a formal framework for studying the phenomenon of language generation, called language generation in the limit. In this model, an adversary gives an enumeration of example strings from an unknown target language, and the algorithm is tasked with correctly generating unseen strings from the target language within finite time. Refined notions of non-uniform and uniform generation were later introduced by Li, Raman, and Tewari (2025), and a noisy model was introduced by Raman and Raman (2025), which allows the adversary to insert extraneous strings. A natural question in the noisy model is to quantify the effect of noise, by studying the impact of each additional extraneous string. We show two complementary results in this setting. We first show that for both uniform and non-uniform generation, a single noisy string strictly reduces the set of collections that can be generated, thus answering an open question in Raman and Raman (2025). Then, we show for both uniform and non-uniform generation that generation with a single noisy string is equivalent to generation with any finite amount of noise, sharply contrasting with the strict hierarchy for noisy generation in the limit shown by Bai, Panigrahi, and Zhang (2026). Finally, we leverage our previous results to provide the first known characterization for non-uniform noise-dependent generatability.

cs.DS↗

arXiv2025

Deliberation via Matching

We study deliberative social choice, where voters engage in small-group discussions to output collective preferences that are then aggregated by a social choice rule. We introduce a simple deliberation-via-matching protocol. In this protocol, for each pair of candidates, we form a maximum matching among voters who disagree on that pair, and have each matched pair deliberate. We then aggregate the resulting individual and deliberative preferences using the weighted uncovered set tournament rule. We show that this protocol has a tight distortion bound of $3$ within the metric distortion framework. In the absence of deliberation, general deterministic social choice rules can achieve this distortion, whereas deterministic tournament rules face a strictly larger lower bound of $3.11$. Our result closes this gap: Pairwise deliberation allows a tournament-based rule to attain distortion $3$. Conceptually, this shows that tournament rules can match the power of general deterministic social choice rules once they are given the minimal added power of pairwise deliberations. We prove this bound via a novel bilinear relaxation of the non-linear program capturing optimal distortion, whose vertices we can explicitly enumerate, leading to an analytic proof. Loosely speaking, our key technical insight is that the distortion objective, as a function of metric distances to any three alternatives, is both supermodular and convex. This characterization therefore provides a new analytical tool for studying the distortion of deliberative protocols, and may be of independent interest. Finally, although our analysis is for the full protocol, we show that this mechanism also admits a lightweight sampling-based implementation, yielding a high-probability approximation to the deterministic guarantee with arbitrary accuracy and low per-voter complexity.

cs.GT↗

arXiv2025

Language Generation in the Limit: Noise, Loss, and Feedback

Kleinberg and Mullainathan (2024) recently proposed a formal framework called language generation in the limit and showed that given a sequence of example strings from an unknown target language drawn from any countable collection, an algorithm can correctly generate unseen strings from the target language within finite time. This notion was further refined by Li, Raman, and Tewari (2024), who defined stricter categories of non-uniform and uniform generation. They showed that a finite union of uniformly generatable collections is generatable in the limit, and asked if the same is true for non-uniform generation. We begin by resolving the question in the negative: we give a uniformly generatable collection and a non-uniformly generatable collection whose union is not generatable in the limit. We then use facets of this construction to further our understanding of several variants of language generation. The first two, generation with noise and without samples, were introduced by Raman and Raman (2025) and Li, Raman, and Tewari (2024) respectively. We show the equivalence of these models for uniform and non-uniform generation, and provide a characterization of non-uniform noisy generation. The former paper asked if there is any separation between noisy and non-noisy generation in the limit -- we show that such a separation exists even with a single noisy string. Finally, we study the framework of generation with feedback, introduced by Charikar and Pabbaraju (2025), where the algorithm is strengthened by allowing it to ask membership queries. We show finite queries add no power, but infinite queries yield a strictly more powerful model. In summary, the results in this paper resolve the union-closedness of language generation in the limit, and leverage those techniques (and others) to give precise characterizations for natural variants that incorporate noise, loss, and feedback.

cs.DS↗

arXiv2025

Fish Mouth Inspired Origami Gripper for Robust Multi-Type Underwater Grasping

Robotic grasping and manipulation in underwater environments present unique challenges for robotic hands traditionally used on land. These challenges stem from dynamic water conditions, a wide range of object properties from soft to stiff, irregular object shapes, and varying surface frictions. One common approach involves developing finger-based hands with embedded compliance using underactuation and soft actuators. This study introduces an effective alternative solution that does not rely on finger-based hand designs. We present a fish mouth inspired origami gripper that utilizes a single degree of freedom to perform a variety of robust grasping tasks underwater. The innovative structure transforms a simple uniaxial pulling motion into a grasping action based on the Yoshimura crease pattern folding. The origami gripper offers distinct advantages, including scalable and optimizable design, grasping compliance, and robustness, with four grasping types: pinch, power grasp, simultaneous grasping of multiple objects, and scooping from the seabed. In this work, we detail the design, modeling, fabrication, and validation of a specialized underwater gripper capable of handling various marine creatures, including jellyfish, crabs, and abalone. By leveraging an origami and bio-inspired approach, the presented gripper demonstrates promising potential for robotic grasping and manipulation in underwater environments.

cs.RO↗

arXiv2025

Global-Local Interface for On-Demand Teleoperation

Teleoperation is a critical method for human-robot interface, holds significant potential for enabling robotic applications in industrial and unstructured environments. Existing teleoperation methods have distinct strengths and limitations in flexibility, range of workspace and precision. To fuse these advantages, we introduce the Global-Local (G-L) Teleoperation Interface. This interface decouples robotic teleoperation into global behavior, which ensures the robot motion range and intuitiveness, and local behavior, which enhances human operator's dexterity and capability for performing fine tasks. The G-L interface enables efficient teleoperation not only for conventional tasks like pick-and-place, but also for challenging fine manipulation and large-scale movements. Based on the G-L interface, we constructed a single-arm and a dual-arm teleoperation system with different remote control devices, then demonstrated tasks requiring large motion range, precise manipulation or dexterous end-effector control. Extensive experiments validated the user-friendliness, accuracy, and generalizability of the proposed interface.

cs.RO↗

arXiv2024

Fair Division via the Cake-Cutting Share

In this paper, we consider the classic fair division problem of allocating $m$ divisible items to $n$ agents with linear valuations over the items. We define novel notions of fair shares from the perspective of individual agents via the cake-cutting process. These shares generalize the notion of proportionality by taking into account the valuations of other agents via constraints capturing envy. We study what fraction (approximation) of these shares are achievable in the worst case, and present tight and non-trivial approximation bounds as a function of $n$ and $m$. In particular, we show a tight approximation bound of $\Theta(\sqrt{n})$ for various notions of such shares. We show this bound via a novel application of dual fitting, which may be of independent interest. We also present a bound of $O(m^{2/3})$ for a strict notion of share, with an almost matching lower bound. We further develop weaker notions of shares whose approximation bounds interpolate smoothly between proportionality and the shares described above. We finally present empirical results showing that our definitions lead to more reasonable shares than the standard fair share notion of proportionality.

cs.GT↗

arXiv2024

Markov Processes for Enhanced Deepfake Generation and Detection

New and existing methods for generating, and especially detecting, deepfakes are investigated and compared on the simple problem of authenticating coin flip data. Importantly, an alternative approach to deepfake generation and detection, which uses a Markov Observation Model (MOM) is introduced and compared on detection ability to the traditional Generative Adversarial Network (GAN) approach as well as Support Vector Machine (SVM), Branching Particle Filtering (BPF) and human alternatives. MOM was also compared on generative and discrimination ability to GAN, filtering and humans (as SVM does not have generative ability). Humans are shown to perform the worst, followed in order by GAN, SVM, BPF and MOM, which was the best at the detection of deepfakes. Unsurprisingly, the order was maintained on the generation problem with removal of SVM as it does not have generation ability.

stat.AP↗

arXiv2021

A coarse-to-fine framework for unsupervised multi-contrast MR image deformable registration with dual consistency constraint

Multi-contrast magnetic resonance (MR) image registration is useful in the clinic to achieve fast and accurate imaging-based disease diagnosis and treatment planning. Nevertheless, the efficiency and performance of the existing registration algorithms can still be improved. In this paper, we propose a novel unsupervised learning-based framework to achieve accurate and efficient multi-contrast MR image registrations. Specifically, an end-to-end coarse-to-fine network architecture consisting of affine and deformable transformations is designed to improve the robustness and achieve end-to-end registration. Furthermore, a dual consistency constraint and a new prior knowledge-based loss function are developed to enhance the registration performances. The proposed method has been evaluated on a clinical dataset containing 555 cases, and encouraging performances have been achieved. Compared to the commonly utilized registration methods, including VoxelMorph, SyN, and LT-Net, the proposed method achieves better registration performance with a Dice score of 0.8397 in identifying stroke lesions. With regards to the registration speed, our method is about 10 times faster than the most competitive method of SyN (Affine) when testing on a CPU. Moreover, we prove that our method can still perform well on more challenging tasks with lacking scanning information data, showing high robustness for the clinical application.

eess.IV↗