Haotian Jiang

Haotian Jiang, Qianxiao Li, Zhong Li et al.

We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation paradigms, and the insights one can gain from these results. We also outline some future research directions towards building a theory of sequence modelling.

Sally Dong, Haotian Jiang, Yin Tat Lee et al.

Many fundamental problems in machine learning can be formulated by the convex program \[ \min_{θ\in R^d}\ \sum_{i=1}^{n}f_{i}(θ), \] where each $f_i$ is a convex, Lipschitz function supported on a subset of $d_i$ coordinates of $θ$. One common approach to this problem, exemplified by stochastic gradient descent, involves sampling one $f_i$ term at every iteration to make progress. This approach crucially relies on a notion of uniformity across the $f_i$'s, formally captured by their condition number. In this work, we give an algorithm that minimizes the above convex formulation to $ε$-accuracy in $\widetilde{O}(\sum_{i=1}^n d_i \log (1 /ε))$ gradient computations, with no assumptions on the condition number. The previous best algorithm independent of the condition number is the standard cutting plane method, which requires $O(nd \log (1/ε))$ gradient computations. As a corollary, we improve upon the evaluation oracle complexity for decomposable submodular minimization by Axiotis et al. (ICML 2021). Our main technical contribution is an adaptive procedure to select an $f_i$ term at every iteration via a novel combination of cutting-plane and interior-point methods.

Venkat Varada, Mina Ghashami, Jitesh Mehta et al.

Entity Resolution (ER) in voice assistants is a prime component during run time that resolves entities in users request to real world entities. ER involves two major functionalities 1. Relevance generation and 2. Ranking. In this paper we propose a low cost relevance generation framework by generating features using customer implicit and explicit feedback signals. The generated relevance datasets can serve as test sets to measure ER performance. We also introduce a set of metrics that accurately measures the performance of ER systems in various dimensions. They provide great interpretability to deep dive and identifying root cause of ER issues, whether the problem is in relevance generation or ranking.

Mengjie Xu, Yitao Zhu, Haotian Jiang et al.

Multi-view object tracking (MVOT) offers promising solutions to challenges such as occlusion and target loss, which are common in traditional single-view tracking. However, progress has been limited by the lack of comprehensive multi-view datasets and effective cross-view integration methods. To overcome these limitations, we compiled a Multi-View object Tracking (MVTrack) dataset of 234K high-quality annotated frames featuring 27 distinct objects across various scenes. In conjunction with this dataset, we introduce a novel MVOT method, Multi-View Integration Tracker (MITracker), to efficiently integrate multi-view object features and provide stable tracking outcomes. MITracker can track any object in video frames of arbitrary length from arbitrary viewpoints. The key advancements of our method over traditional single-view approaches come from two aspects: (1) MITracker transforms 2D image features into a 3D feature volume and compresses it into a bird's eye view (BEV) plane, facilitating inter-view information fusion; (2) we propose an attention mechanism that leverages geometric information from fused 3D feature volume to refine the tracking results at each view. MITracker outperforms existing methods on the MVTrack and GMTD datasets, achieving state-of-the-art performance. The code and the new dataset will be available at https://mii-laboratory.github.io/MITracker/.

Penghao Yu, Haotian Jiang, Zeyu Bao et al.

Transformer has become the dominant architecture for sequence modeling, yet a detailed understanding of how its structural parameters influence expressive power remains limited. In this work, we study the approximation properties of transformers, with particular emphasis on the role of the number of attention heads. Our analysis begins with the introduction of a generalized $D$-retrieval task, which we prove to be dense in the space of continuous functions, thereby providing the basis for our theoretical framework. We then establish both upper and lower bounds on the parameter complexity required for $ε$-approximation. Specifically, we show that transformers with sufficiently many heads admit efficient approximation, whereas with too few heads, the number of parameters must scale at least as $O(1/ε^{cT})$, for some constant $c$ and sequence length $T$. To the best of our knowledge, this constitutes the first rigorous lower bound of this type in a nonlinear and practically relevant setting. We further examine the single-head case and demonstrate that an embedding dimension of order $O(T)$ allows complete memorization of the input, where approximation is entirely achieved by the feed-forward block. Finally, we validate our theoretical findings with experiments on both synthetic data and real-world tasks, illustrating the practical relevance of our results.

Ruoxi Yu, Haotian Jiang, Jingpu Cheng et al.

Transformers have achieved remarkable successes across a wide range of applications, yet the theoretical foundation of their model efficiency remains underexplored. In this work, we investigate how the model parameters -- mainly attention heads and head dimensions -- should be allocated across layers to balance expressivity and efficiency. We first provide mathematical analysis on the role of early layers in information extraction from an approximation perspective, with a theoretical characterization on the trade-off between the number of heads and head dimension under a fixed parameter budget. In addition, we uncover and prove the \emph{saturation} behavior of softmax activations: Continuously increasing head dimensions can lead to diminishing returns in learning errors, particularly for long sequences. Supported by both theory and experiments, this saturation pattern suggests that later layers can operate more efficiently with reduced parameters. Combining these insights, we propose principled strategies for allocating attention heads and dimensions across Transformers' layers, shedding light on theoretically-grounded model efficiency of Transformer-based architectures.

Haotian Jiang, Qianxiao Li

The Transformer architecture is widely applied in sequence modeling applications, yet the theoretical understanding of its working principles remains limited. In this work, we investigate the approximation rate for single-layer Transformers with one head. We consider a class of non-linear relationships and identify a novel notion of complexity measures to establish an explicit Jackson-type approximation rate estimate for the Transformer. This rate reveals the structural properties of the Transformer and suggests the types of sequential relationships it is best suited for approximating. In particular, the results on approximation rates enable us to concretely analyze the differences between the Transformer and classical sequence modeling methods, such as recurrent neural networks.

Yangsibo Huang, Haotian Jiang, Daogao Liu et al.

In this paper, we study the setting in which data owners train machine learning models collaboratively under a privacy notion called joint differential privacy [Kearns et al., 2018]. In this setting, the model trained for each data owner $j$ uses $j$'s data without privacy consideration and other owners' data with differential privacy guarantees. This setting was initiated in [Jain et al., 2021] with a focus on linear regressions. In this paper, we study this setting for stochastic convex optimization (SCO). We present an algorithm that is a variant of DP-SGD [Song et al., 2013; Abadi et al., 2016] and provides theoretical bounds on its population loss. We compare our algorithm to several baselines and discuss for what parameter setups our algorithm is more preferred. We also empirically study joint differential privacy in the multi-class classification problem over two public datasets. Our empirical findings are well-connected to the insights from our theoretical results.

Haotian Jiang, Zhong Li, Qianxiao Li

We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem. In the recurrent setting, recent results reveal an intricate connection between approximation efficiency and memory structures in the data generation process. In this paper, we derive parallel results for convolutional architectures, with WaveNet being a prime example. Our results reveal that in this new setting, approximation efficiency is not only characterised by memory, but also additional fine structures in the target relationship. This leads to a novel definition of spectrum-based regularity that measures the complexity of temporal relationships under the convolutional approximation scheme. These analyses provide a foundation to understand the differences between architectural choices for time series modelling and can give theoretically grounded guidance for practical applications.