arXiv subjects

Weihao Kong

Publications and source records attributed to Weihao Kong.

At least 19 recordsLinked to original sources

arXiv2026

Hardwired-Neurons Language Processing Units as General-Purpose Cognitive Substrates

The rapid advancement of Large Language Models (LLMs) has established language as a core general-purpose cognitive substrate, driving the demand for specialized Language Processing Units (LPUs) tailored for LLM inference. To overcome the growing energy consumption of LLM inference systems, this paper proposes a Hardwired-Neurons Language Processing Unit (HNLPU), which physically hardwires LLM weight parameters into the computational fabric, achieving several orders of magnitude computational efficiency improvement by extreme specialization. However, a significant challenge still lies in the scale of modern LLMs. A straightforward hardwiring of gpt-oss 120 B would require fabricating photomask sets valued at over 6 billion dollars, rendering this straightforward solution economically impractical. Addressing this challenge, we propose the novel Metal-Embedding methodology. Instead of embedding weights in a 2D grid of silicon device cells, Metal-Embedding embeds weight parameters into the 3D topology of metal wires. This brings two benefits: (1) a 15x increase in density, and (2) 60 out of 70 photomask layers are homogeneous across chips, including all EUV photomasks. In total, Metal-Embedding reduced the photomask cost by 112x, bringing the Non-Recurring Engineering (NRE) cost of HNLPU into an economically viable range. Experimental results show that HNLPU achieved 249,960 tokens/s (5,555x/85x that of GPU/WSE), 36 tokens/J (1,047x/283x that of GPU/WSE), 13,232 mm2 total die area, $59.46 M-123.5 M estimated NRE at 5 nm technology. Analysis shows that HNLPU achieved 41.7-80.4x improvement in cost-effectiveness and 357x reduction in carbon footprint compared to OpenAI-scale H100 clusters, under an annual weight updating assumption.

cs.AR↗

arXiv2024

Insufficient Statistics Perturbation: Stable Estimators for Private Least Squares

We present a sample- and time-efficient differentially private algorithm for ordinary least squares, with error that depends linearly on the dimension and is independent of the condition number of $X^\top X$, where $X$ is the design matrix. All prior private algorithms for this task require either $d^{3/2}$ examples, error growing polynomially with the condition number, or exponential time. Our near-optimal accuracy guarantee holds for any dataset with bounded statistical leverage and bounded residuals. Technically, we build on the approach of Brown et al. (2023) for private mean estimation, adding scaled noise to a carefully designed stable nonprivate estimator of the empirical regression vector.

cs.LG↗

arXiv2024

A decoder-only foundation model for time-series forecasting

Motivated by recent advances in large language models for Natural Language Processing (NLP), we design a time-series foundation model for forecasting whose out-of-the-box zero-shot performance on a variety of public datasets comes close to the accuracy of state-of-the-art supervised forecasting models for each individual dataset. Our model is based on pretraining a patched-decoder style attention model on a large time-series corpus, and can work well across different forecasting history lengths, prediction lengths and temporal granularities.

cs.CL↗

arXiv2024

Long-term Forecasting with TiDE: Time-series Dense Encoder

Recent work has shown that simple linear models can outperform several Transformer based approaches in long term time-series forecasting. Motivated by this, we propose a Multi-layer Perceptron (MLP) based encoder-decoder model, Time-series Dense Encoder (TiDE), for long-term time-series forecasting that enjoys the simplicity and speed of linear models while also being able to handle covariates and non-linear dependencies. Theoretically, we prove that the simplest linear analogue of our model can achieve near optimal error rate for linear dynamical systems (LDS) under some assumptions. Empirically, we show that our method can match or outperform prior approaches on popular long-term time-series forecasting benchmarks while being 5-10x faster than the best Transformer based model.

stat.ML↗

arXiv2023

A Combinatorial Approach to Robust PCA

We study the problem of recovering Gaussian data under adversarial corruptions when the noises are low-rank and the corruptions are on the coordinate level. Concretely, we assume that the Gaussian noises lie in an unknown $k$-dimensional subspace $U \subseteq \mathbb{R}^d$, and $s$ randomly chosen coordinates of each data point fall into the control of an adversary. This setting models the scenario of learning from high-dimensional yet structured data that are transmitted through a highly-noisy channel, so that the data points are unlikely to be entirely clean. Our main result is an efficient algorithm that, when $ks^2 = O(d)$, recovers every single data point up to a nearly-optimal $\ell_1$ error of $\tilde O(ks/d)$ in expectation. At the core of our proof is a new analysis of the well-known Basis Pursuit (BP) method for recovering a sparse signal, which is known to succeed under additional assumptions (e.g., incoherence or the restricted isometry property) on the underlying subspace $U$. In contrast, we present a novel approach via studying a natural combinatorial problem and show that, over the randomness in the support of the sparse signal, a high-probability error bound is possible even if the subspace $U$ is arbitrary.

cs.DS↗

arXiv2023

Transformers can optimally learn regression mixture models

Mixture models arise in many regression problems, but most methods have seen limited adoption partly due to these algorithms' highly-tailored and model-specific nature. On the other hand, transformers are flexible, neural sequence models that present the intriguing possibility of providing general-purpose prediction methods, even in this mixture setting. In this work, we investigate the hypothesis that transformers can learn an optimal predictor for mixtures of regressions. We construct a generative process for a mixture of linear regressions for which the decision-theoretic optimal procedure is given by data-driven exponential weights on a finite set of parameters. We observe that transformers achieve low mean-squared error on data generated via this process. By probing the transformer's output at inference time, we also show that transformers typically make predictions that are close to the optimal predictor. Our experiments also demonstrate that transformers can learn mixtures of regressions in a sample-efficient fashion and are somewhat robust to distribution shifts. We complement our experimental observations by proving constructively that the decision-theoretic optimal procedure is indeed implementable by a transformer.

cs.LG↗

arXiv2023

Linear Regression using Heterogeneous Data Batches

In many learning applications, data are collected from multiple sources, each providing a \emph{batch} of samples that by itself is insufficient to learn its input-output relationship. A common approach assumes that the sources fall in one of several unknown subgroups, each with an unknown input distribution and input-output relationship. We consider one of this setup's most fundamental and important manifestations where the output is a noisy linear combination of the inputs, and there are $k$ subgroups, each with its own regression vector. Prior work~\cite{kong2020meta} showed that with abundant small-batches, the regression vectors can be learned with only few, $\tildeΩ( k^{3/2})$, batches of medium-size with $\tildeΩ(\sqrt k)$ samples each. However, the paper requires that the input distribution for all $k$ subgroups be isotropic Gaussian, and states that removing this assumption is an ``interesting and challenging problem". We propose a novel gradient-based algorithm that improves on the existing results in several ways. It extends the applicability of the algorithm by: (1) allowing the subgroups' underlying input distributions to be different, unknown, and heavy-tailed; (2) recovering all subgroups followed by a significant proportion of batches even for infinite $k$; (3) removing the separation requirement between the regression vectors; (4) reducing the number of batches and allowing smaller batch sizes.

cs.LG↗

arXiv2023

Dirichlet Proportions Model for Hierarchically Coherent Probabilistic Forecasting

Probabilistic, hierarchically coherent forecasting is a key problem in many practical forecasting applications -- the goal is to obtain coherent probabilistic predictions for a large number of time series arranged in a pre-specified tree hierarchy. In this paper, we present an end-to-end deep probabilistic model for hierarchical forecasting that is motivated by a classical top-down strategy. It jointly learns the distribution of the root time series, and the (dirichlet) proportions according to which each parent time-series is split among its children at any point in time. The resulting forecasts are naturally coherent, and provide probabilistic predictions over all time series in the hierarchy. We experiment on several public datasets and demonstrate significant improvements of up to 26% on most datasets compared to state-of-the-art baselines. Finally, we also provide theoretical justification for the superiority of our top-down approach compared to the more traditional bottom-up modeling.

cs.LG↗

arXiv2023

Estimating Optimal Policy Value in General Linear Contextual Bandits

In many bandit problems, the maximal reward achievable by a policy is often unknown in advance. We consider the problem of estimating the optimal policy value in the sublinear data regime before the optimal policy is even learnable. We refer to this as $V^*$ estimation. It was recently shown that fast $V^*$ estimation is possible but only in disjoint linear bandits with Gaussian covariates. Whether this is possible for more realistic context distributions has remained an open and important question for tasks such as model selection. In this paper, we first provide lower bounds showing that this general problem is hard. However, under stronger assumptions, we give an algorithm and analysis proving that $\widetilde{\mathcal{O}}(\sqrt{d})$ sublinear estimation of $V^*$ is indeed information-theoretically possible, where $d$ is the dimension. We then present a more practical, computationally efficient algorithm that estimates a problem-dependent upper bound on $V^*$ that holds for general distributions and is tight when the context distribution is Gaussian. We prove our algorithm requires only $\widetilde{\mathcal{O}}(\sqrt{d})$ samples to estimate the upper bound. We use this upper bound and the estimator to obtain novel and improved guarantees for several applications in bandit model selection and testing for treatment effects.

cs.LG↗

arXiv2023

Near Optimal Private and Robust Linear Regression

We study the canonical statistical estimation problem of linear regression from $n$ i.i.d.~examples under $(\varepsilon,δ)$-differential privacy when some response variables are adversarially corrupted. We propose a variant of the popular differentially private stochastic gradient descent (DP-SGD) algorithm with two innovations: a full-batch gradient descent to improve sample complexity and a novel adaptive clipping to guarantee robustness. When there is no adversarial corruption, this algorithm improves upon the existing state-of-the-art approach and achieves a near optimal sample complexity. Under label-corruption, this is the first efficient linear regression algorithm to guarantee both $(\varepsilon,δ)$-DP and robustness. Synthetic experiments confirm the superiority of our approach.

cs.LG↗

arXiv2022

Efficient List-Decodable Regression using Batches

We begin the study of list-decodable linear regression using batches. In this setting only an $α\in (0,1]$ fraction of the batches are genuine. Each genuine batch contains $\ge n$ i.i.d. samples from a common unknown distribution and the remaining batches may contain arbitrary or even adversarial samples. We derive a polynomial time algorithm that for any $n\ge \tilde Ω(1/α)$ returns a list of size $\mathcal O(1/α^2)$ such that one of the items in the list is close to the true regression parameter. The algorithm requires only $\tilde{\mathcal{O}}(d/α^2)$ genuine batches and works under fairly general assumptions on the distribution. The results demonstrate the utility of batch structure, which allows for the first polynomial time algorithm for list-decodable regression, which may be impossible for the non-batch setting, as suggested by a recent SQ lower bound \cite{diakonikolas2021statistical} for the non-batch setting.

cs.LG↗

arXiv2022

Trimmed Maximum Likelihood Estimation for Robust Learning in Generalized Linear Models

We study the problem of learning generalized linear models under adversarial corruptions. We analyze a classical heuristic called the iterative trimmed maximum likelihood estimator which is known to be effective against label corruptions in practice. Under label corruptions, we prove that this simple estimator achieves minimax near-optimal risk on a wide range of generalized linear models, including Gaussian regression, Poisson regression and Binomial regression. Finally, we extend the estimator to the more challenging setting of label and covariate corruptions and demonstrate its robustness and optimality in that setting as well.

cs.LG↗

arXiv2022

DP-PCA: Statistically Optimal and Differentially Private PCA

We study the canonical statistical task of computing the principal component from $n$ i.i.d.~data in $d$ dimensions under $(\varepsilon,δ)$-differential privacy. Although extensively studied in literature, existing solutions fall short on two key aspects: ($i$) even for Gaussian data, existing private algorithms require the number of samples $n$ to scale super-linearly with $d$, i.e., $n=Ω(d^{3/2})$, to obtain non-trivial results while non-private PCA requires only $n=O(d)$, and ($ii$) existing techniques suffer from a non-vanishing error even when the randomness in each data point is arbitrarily small. We propose DP-PCA, which is a single-pass algorithm that overcomes both limitations. It is based on a private minibatch gradient ascent method that relies on {\em private mean estimation}, which adds minimal noise required to ensure privacy by adapting to the variance of a given minibatch of gradients. For sub-Gaussian data, we provide nearly optimal statistical error rates even for $n=\tilde O(d)$. Furthermore, we provide a lower bound showing that sub-Gaussian style assumption is necessary in obtaining the optimal error rate.

cs.LG↗

arXiv2021

Robust and Differentially Private Mean Estimation

In statistical learning and analysis from shared data, which is increasingly widely adopted in platforms such as federated learning and meta-learning, there are two major concerns: privacy and robustness. Each participating individual should be able to contribute without the fear of leaking one's sensitive information. At the same time, the system should be robust in the presence of malicious participants inserting corrupted data. Recent algorithmic advances in learning from shared data focus on either one of these threats, leaving the system vulnerable to the other. We bridge this gap for the canonical problem of estimating the mean from i.i.d. samples. We introduce PRIME, which is the first efficient algorithm that achieves both privacy and robustness for a wide range of distributions. We further complement this result with a novel exponential time algorithm that improves the sample complexity of PRIME, achieving a near-optimal guarantee and matching a known lower bound for (non-robust) private mean estimation. This proves that there is no extra statistical cost to simultaneously guaranteeing privacy and robustness.

cs.LG↗

arXiv2021

Differential privacy and robust statistics in high dimensions

We introduce a universal framework for characterizing the statistical efficiency of a statistical estimation problem with differential privacy guarantees. Our framework, which we call High-dimensional Propose-Test-Release (HPTR), builds upon three crucial components: the exponential mechanism, robust statistics, and the Propose-Test-Release mechanism. Gluing all these together is the concept of resilience, which is central to robust statistical estimation. Resilience guides the design of the algorithm, the sensitivity analysis, and the success probability analysis of the test step in Propose-Test-Release. The key insight is that if we design an exponential mechanism that accesses the data only via one-dimensional robust statistics, then the resulting local sensitivity can be dramatically reduced. Using resilience, we can provide tight local sensitivity bounds. These tight bounds readily translate into near-optimal utility guarantees in several cases. We give a general recipe for applying HPTR to a given instance of a statistical estimation problem and demonstrate it on canonical problems of mean estimation, linear regression, covariance estimation, and principal component analysis. We introduce a general utility analysis technique that proves that HPTR nearly achieves the optimal sample complexity under several scenarios studied in the literature.

math.ST↗

arXiv2021

Fisher-Pitman permutation tests based on nonparametric Poisson mixtures with application to single cell genomics

This paper investigates the theoretical and empirical performance of Fisher-Pitman-type permutation tests for assessing the equality of unknown Poisson mixture distributions. Building on nonparametric maximum likelihood estimators (NPMLEs) of the mixing distribution, these tests are theoretically shown to be able to adapt to complicated unspecified structures of count data and also consistent against their corresponding ANOVA-type alternatives; the latter is a result in parallel to classic claims made by Robinson (Robinson, 1973). The studied methods are then applied to a single-cell RNA-seq data obtained from different cell types from brain samples of autism subjects and healthy controls; empirically, they unveil genes that are differentially expressed between autism and control subjects yet are missed using common tests. For justifying their use, rate optimality of NPMLEs is also established in settings similar to nonparametric Gaussian (Wu and Yang, 2020a) and binomial mixtures (Tian et al., 2017; Vinayak et al., 2019).

stat.ME↗

arXiv2021

SPECTRE: Defending Against Backdoor Attacks Using Robust Statistics

Modern machine learning increasingly requires training on a large collection of data from multiple sources, not all of which can be trusted. A particularly concerning scenario is when a small fraction of poisoned data changes the behavior of the trained model when triggered by an attacker-specified watermark. Such a compromised model will be deployed unnoticed as the model is accurate otherwise. There have been promising attempts to use the intermediate representations of such a model to separate corrupted examples from clean ones. However, these defenses work only when a certain spectral signature of the poisoned examples is large enough for detection. There is a wide range of attacks that cannot be protected against by the existing defenses. We propose a novel defense algorithm using robust covariance estimation to amplify the spectral signature of corrupted data. This defense provides a clean model, completely removing the backdoor, even in regimes where previous methods have no hope of detecting the poisoned examples. Code and pre-trained models are available at https://github.com/SewoongLab/spectre-defense .

cs.LG↗

arXiv2020

Online Model Selection for Reinforcement Learning with Function Approximation

Deep reinforcement learning has achieved impressive successes yet often requires a very large amount of interaction data. This result is perhaps unsurprising, as using complicated function approximation often requires more data to fit, and early theoretical results on linear Markov decision processes provide regret bounds that scale with the dimension of the linear approximation. Ideally, we would like to automatically identify the minimal dimension of the approximation that is sufficient to encode an optimal policy. Towards this end, we consider the problem of model selection in RL with function approximation, given a set of candidate RL algorithms with known regret guarantees. The learner's goal is to adapt to the complexity of the optimal algorithm without knowing it \textit{a priori}. We present a meta-algorithm that successively rejects increasingly complex models using a simple statistical test. Given at least one candidate that satisfies realizability, we prove the meta-algorithm adapts to the optimal complexity with $\tilde{O}(L^{5/6} T^{2/3})$ regret compared to the optimal candidate's $\tilde{O}(\sqrt T)$ regret, where $T$ is the number of episodes and $L$ is the number of algorithms. The dimension and horizon dependencies remain optimal with respect to the best candidate, and our meta-algorithmic approach is flexible to incorporate multiple candidate algorithms and models. Finally, we show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds that depend on the gaps between the maximal values attainable by the candidates.

cs.LG↗