Xin Lyu

Edith Cohen, Xin Lyu, Jelani Nelson et al.

The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(ξ^{-1} \log(1/β))$ (for generalization error $ξ$ with confidence $1-β$). The private version of the problem, however, is more challenging and in particular, the sample complexity must depend on the size $|X|$ of the domain. Progress on quantifying this dependence, via lower and upper bounds, was made in a line of works over the past decade. In this paper, we finally close the gap for approximate-DP and provide a nearly tight upper bound of $\tilde{O}(\log^* |X|)$, which matches a lower bound by Alon et al (that applies even with improper learning) and improves over a prior upper bound of $\tilde{O}((\log^* |X|)^{1.5})$ by Kaplan et al. We also provide matching upper and lower bounds of $\tildeΘ(2^{\log^*|X|})$ for the additive error of private quasi-concave optimization (a related and more general problem). Our improvement is achieved via the novel Reorder-Slice-Compute paradigm for private data analysis which we believe will have further applications.

Xin Lyu, Avishay Tal, Hongxun Wu et al.

In his breakthrough paper, Raz showed that any parity learning algorithm requires either quadratic memory or an exponential number of samples [FOCS'16, JACM'19]. A line of work that followed extended this result to a large class of learning problems. Until recently, all these results considered learning in the streaming model, where each sample is drawn independently, and the learner is allowed a single pass over the stream of samples. Garg, Raz, and Tal [CCC'19] considered a stronger model, allowing multiple passes over the stream. In the $2$-pass model, they showed that learning parities of size $n$ requires either a memory of size $n^{1.5}$ or at least $2^{\sqrt{n}}$ samples. (Their result also generalizes to other learning problems.) In this work, for any constant $q$, we prove tight memory-sample lower bounds for any parity learning algorithm that makes $q$ passes over the stream of samples. We show that such a learner requires either $Ω(n^{2})$ memory size or at least $2^{Ω(n)}$ samples. Beyond establishing a tight lower bound, this is the first non-trivial lower bound for $q$-pass learning for any $q\ge 3$. Similar to prior work, our results extend to any learning problem with many nearly-orthogonal concepts. We complement the lower bound with an upper bound, showing that parity learning with $q$ passes can be done efficiently with $O(n^2/\log q)$ memory.

GLM-V Team, Wenyi Hong, Wenmeng Yu et al.

We present GLM-4.1V-Thinking and GLM-4.5V, a family of vision-language models (VLMs) designed to advance general-purpose multimodal understanding and reasoning. In this report, we share our key findings in the development of the reasoning-centric training framework. We first develop a capable vision foundation model with significant potential through large-scale pre-training, which arguably sets the upper bound for the final performance. We then propose Reinforcement Learning with Curriculum Sampling (RLCS) to unlock the full potential of the model, leading to comprehensive capability enhancement across a diverse range of tasks, including STEM problem solving, video understanding, content recognition, coding, grounding, GUI-based agents, and long document interpretation. In a comprehensive evaluation across 42 public benchmarks, GLM-4.5V achieves state-of-the-art performance on nearly all tasks among open-source models of similar size, and demonstrates competitive or even superior results compared to closed-source models such as Gemini-2.5-Flash on challenging tasks including Coding and GUI Agents. Meanwhile, the smaller GLM-4.1V-9B-Thinking remains highly competitive-achieving superior results to the much larger Qwen2.5-VL-72B on 29 benchmarks. We open-source both GLM-4.1V-9B-Thinking and GLM-4.5V. Code, models and more information are released at https://github.com/zai-org/GLM-V.

Edith Cohen, Xin Lyu, Jelani Nelson et al.

One of the most basic problems for studying the "price of privacy over time" is the so called private counter problem, introduced by Dwork et al. (2010) and Chan et al. (2010). In this problem, we aim to track the number of events that occur over time, while hiding the existence of every single event. More specifically, in every time step $t\in[T]$ we learn (in an online fashion) that $Δ_t\geq 0$ new events have occurred, and must respond with an estimate $n_t\approx\sum_{j=1}^t Δ_j$. The privacy requirement is that all of the outputs together, across all time steps, satisfy event level differential privacy. The main question here is how our error needs to depend on the total number of time steps $T$ and the total number of events $n$. Dwork et al. (2015) showed an upper bound of $O\left(\log(T)+\log^2(n)\right)$, and Henzinger et al. (2023) showed a lower bound of $Ω\left(\min\{\log n, \log T\}\right)$. We show a new lower bound of $Ω\left(\min\{n,\log T\}\right)$, which is tight w.r.t. the dependence on $T$, and is tight in the sparse case where $\log^2 n=O(\log T)$. Our lower bound has the following implications: $\bullet$ We show that our lower bound extends to the "online thresholds problem", where the goal is to privately answer many "quantile queries" when these queries are presented one-by-one. This resolves an open question of Bun et al. (2017). $\bullet$ Our lower bound implies, for the first time, a separation between the number of mistakes obtainable by a private online learner and a non-private online learner. This partially resolves a COLT'22 open question published by Sanyal and Ramponi. $\bullet$ Our lower bound also yields the first separation between the standard model of private online learning and a recently proposed relaxed variant of it, called private online prediction.

Fan Zhang, Zhaohan Wang, Xin Lyu et al.

Speech-driven gesture generation is an emerging field within virtual human creation. However, a significant challenge lies in accurately determining and processing the multitude of input features (such as acoustic, semantic, emotional, personality, and even subtle unknown features). Traditional approaches, reliant on various explicit feature inputs and complex multimodal processing, constrain the expressiveness of resulting gestures and limit their applicability. To address these challenges, we present Persona-Gestor, a novel end-to-end generative model designed to generate highly personalized 3D full-body gestures solely relying on raw speech audio. The model combines a fuzzy feature extractor and a non-autoregressive Adaptive Layer Normalization (AdaLN) transformer diffusion architecture. The fuzzy feature extractor harnesses a fuzzy inference strategy that automatically infers implicit, continuous fuzzy features. These fuzzy features, represented as a unified latent feature, are fed into the AdaLN transformer. The AdaLN transformer introduces a conditional mechanism that applies a uniform function across all tokens, thereby effectively modeling the correlation between the fuzzy features and the gesture sequence. This module ensures a high level of gesture-speech synchronization while preserving naturalness. Finally, we employ the diffusion model to train and infer various gestures. Extensive subjective and objective evaluations on the Trinity, ZEGGS, and BEAT datasets confirm our model's superior performance to the current state-of-the-art approaches. Persona-Gestor improves the system's usability and generalization capabilities, setting a new benchmark in speech-driven gesture synthesis and broadening the horizon for virtual human technology. Supplementary videos and code can be accessed at https://zf223669.github.io/Diffmotion-v2-website/

Edith Cohen, Benjamin Cohen-Wang, Xin Lyu et al.

The Private Aggregation of Teacher Ensembles (PATE) framework enables privacy-preserving machine learning by aggregating responses from disjoint subsets of sensitive data. Adaptations of PATE to tasks with inherent output diversity such as text generation, where the desired output is a sample from a distribution, face a core tension: as diversity increases, samples from different teachers are less likely to agree, but lower agreement results in reduced utility for the same privacy requirements. Yet suppressing diversity to artificially increase agreement is undesirable, as it distorts the output of the underlying model, and thus reduces output quality. We propose Hot PATE, a variant of PATE designed for diverse generative settings. We formalize the notion of a diversity-preserving ensemble sampler and introduce an efficient sampler that provably transfers diversity without incurring additional privacy cost. Hot PATE requires only API access to proprietary models and can be used as a drop-in replacement for existing Cold PATE samplers. Our empirical evaluations corroborate and quantify the benefits, showing significant improvements in the privacy utility trade-off on evaluated in-context learning tasks, both in preserving diversity and in returning relevant responses.

Xin Lyu, Hongxun Wu, Junzhao Yang

We study the cost of parallelizing weak-to-strong boosting algorithms for learning, following the recent work of Karbasi and Larsen. Our main results are two-fold: - First, we prove a tight lower bound, showing that even "slight" parallelization of boosting requires an exponential blow-up in the complexity of training. Specifically, let $γ$ be the weak learner's advantage over random guessing. The famous \textsc{AdaBoost} algorithm produces an accurate hypothesis by interacting with the weak learner for $\tilde{O}(1 / γ^2)$ rounds where each round runs in polynomial time. Karbasi and Larsen showed that "significant" parallelization must incur exponential blow-up: Any boosting algorithm either interacts with the weak learner for $Ω(1 / γ)$ rounds or incurs an $\exp(d / γ)$ blow-up in the complexity of training, where $d$ is the VC dimension of the hypothesis class. We close the gap by showing that any boosting algorithm either has $Ω(1 / γ^2)$ rounds of interaction or incurs a smaller exponential blow-up of $\exp(d)$. -Complementing our lower bound, we show that there exists a boosting algorithm using $\tilde{O}(1/(t γ^2))$ rounds, and only suffer a blow-up of $\exp(d \cdot t^2)$. Plugging in $t = ω(1)$, this shows that the smaller blow-up in our lower bound is tight. More interestingly, this provides the first trade-off between the parallelism and the total work required for boosting.

Xin Lyu

We consider online and PAC learning of Littlestone classes subject to the constraint of approximate differential privacy. Our main result is a private learner to online-learn a Littlestone class with a mistake bound of $\tilde{O}(d^{9.5}\cdot \log(T))$ in the realizable case, where $d$ denotes the Littlestone dimension and $T$ the time horizon. This is a doubly-exponential improvement over the state-of-the-art [GL'21] and comes polynomially close to the lower bound for this task. The advancement is made possible by a couple of ingredients. The first is a clean and refined interpretation of the ``irreducibility'' technique from the state-of-the-art private PAC-learner for Littlestone classes [GGKM'21]. Our new perspective also allows us to improve the PAC-learner of [GGKM'21] and give a sample complexity upper bound of $\widetilde{O}(\frac{d^5 \log(1/δβ)}{\varepsilon α})$ where $α$ and $β$ denote the accuracy and confidence of the PAC learner, respectively. This improves over [GGKM'21] by factors of $\frac{d}α$ and attains an optimal dependence on $α$. Our algorithm uses a private sparse selection algorithm to \emph{sample} from a pool of strongly input-dependent candidates. However, unlike most previous uses of sparse selection algorithms, where one only cares about the utility of output, our algorithm requires understanding and manipulating the actual distribution from which an output is drawn. In the proof, we use a sparse version of the Exponential Mechanism from [GKM'21] which behaves nicely under our framework and is amenable to a very easy utility proof.

Vitaly Feldman, Guy Kornowski, Xin Lyu

Recent research demonstrated that training large language models involves memorization of a significant fraction of training data. Such memorization can lead to privacy violations when training on sensitive user data and thus motivates the study of data memorization's role in learning. In this work, we develop a general approach for proving lower bounds on excess data memorization, that relies on a new connection between strong data processing inequalities and data memorization. We then demonstrate that several simple and natural binary classification problems exhibit a trade-off between the number of samples available to a learning algorithm, and the amount of information about the training data that a learning algorithm needs to memorize to be accurate. In particular, $Ω(d)$ bits of information about the training data need to be memorized when $O(1)$ $d$-dimensional examples are available, which then decays as the number of examples grows at a problem-specific rate. Further, our lower bounds are generally matched (up to logarithmic factors) by simple learning algorithms. We also extend our lower bounds to more general mixture-of-clusters models. Our definitions and results build on the work of Brown et al. (2021) and address several limitations of the lower bounds in their work.

Xin Lyu, Kunal Talwar · apple-ml

Fingerprinting codes are a crucial tool for proving lower bounds in differential privacy. They have been used to prove tight lower bounds for several fundamental questions, especially in the ``low accuracy'' regime. Unlike reconstruction/discrepancy approaches however, they are more suited for query sets that arise naturally from the fingerprinting codes construction. In this work, we propose a general framework for proving fingerprinting type lower bounds, that allows us to tailor the technique to the geometry of the query set. Our approach allows us to prove several new results, including the following. First, we show that any (sample- and population-)accurate algorithm for answering $Q$ arbitrary adaptive counting queries over a universe $\mathcal{X}$ to accuracy $α$ needs $Ω(\frac{\sqrt{\log |\mathcal{X}|}\cdot \log Q}{α^3})$ samples, matching known upper bounds. This shows that the approaches based on differential privacy are optimal for this question, and improves significantly on the previously known lower bounds of $\frac{\log Q}{α^2}$ and $\min(\sqrt{Q}, \sqrt{\log |\mathcal{X}|})/α^2$. Second, we show that any $(\varepsilon,δ)$-DP algorithm for answering $Q$ counting queries to accuracy $α$ needs $Ω(\frac{\sqrt{ \log|\mathcal{X}| \log(1/δ)} \log Q}{\varepsilonα^2})$ samples, matching known upper bounds up to constants. Our framework allows for proving this bound via a direct correlation analysis and improves the prior bound of [BUV'14] by $\sqrt{\log(1/δ)}$. Third, we characterize the sample complexity of answering a set of random $0$-$1$ queries under approximate differential privacy. We give new upper and lower bounds in different regimes. By combining them with known results, we can complete the whole picture.

Fan Zhang, Siyuan Zhao, Naye Ji et al.

Speech-driven gesture generation using transformer-based generative models represents a rapidly advancing area within virtual human creation. However, existing models face significant challenges due to their quadratic time and space complexities, limiting scalability and efficiency. To address these limitations, we introduce DiM-Gestor, an innovative end-to-end generative model leveraging the Mamba-2 architecture. DiM-Gestor features a dual-component framework: (1) a fuzzy feature extractor and (2) a speech-to-gesture mapping module, both built on the Mamba-2. The fuzzy feature extractor, integrated with a Chinese Pre-trained Model and Mamba-2, autonomously extracts implicit, continuous speech features. These features are synthesized into a unified latent representation and then processed by the speech-to-gesture mapping module. This module employs an Adaptive Layer Normalization (AdaLN)-enhanced Mamba-2 mechanism to uniformly apply transformations across all sequence tokens. This enables precise modeling of the nuanced interplay between speech features and gesture dynamics. We utilize a diffusion model to train and infer diverse gesture outputs. Extensive subjective and objective evaluations conducted on the newly released Chinese Co-Speech Gestures dataset corroborate the efficacy of our proposed model. Compared with Transformer-based architecture, the assessments reveal that our approach delivers competitive results and significantly reduces memory usage, approximately 2.4 times, and enhances inference speeds by 2 to 4 times. Additionally, we released the CCG dataset, a Chinese Co-Speech Gestures dataset, comprising 15.97 hours (six styles across five scenarios) of 3D full-body skeleton gesture motion performed by professional Chinese TV broadcasters.

Edith Cohen, Xin Lyu, Jelani Nelson et al.

CountSketch is a popular dimensionality reduction technique that maps vectors to a lower dimension using randomized linear measurements. The sketch supports recovering $\ell_2$-heavy hitters of a vector (entries with $v[i]^2 \geq \frac{1}{k}\|\boldsymbol{v}\|^2_2$). We study the robustness of the sketch in adaptive settings where input vectors may depend on the output from prior inputs. Adaptive settings arise in processes with feedback or with adversarial attacks. We show that the classic estimator is not robust, and can be attacked with a number of queries of the order of the sketch size. We propose a robust estimator (for a slightly modified sketch) that allows for quadratic number of queries in the sketch size, which is an improvement factor of $\sqrt{k}$ (for $k$ heavy hitters) over prior work.