An official website of the United States government
Training and inference in Gaussian processes (GPs) require solving linear systems with n × n kernel matrices. To address the prohibitive O(n3) time complexity, recent work has employed fast iterative methods, like conjugate gradients (CG). However, as datasets increase in magnitude, the kernel matrices become increasingly ill-conditioned and still require O(n2) space without partitioning. Thus, while CG increases the size of datasets GPs can be trained on, modern datasets reach scales beyond its applicability. In this work, we propose an iterative method which only accesses subblocks of the kernel matrix, effectively enabling mini-batching. Our algorithm, based on alternating projection, has O(n) per-iteration time and space complexity, solving many of the practical challenges of scaling GPs to very large datasets. Theoretically, we prove the method enjoys linear convergence. Empirically, we demonstrate its fast convergence in practice and robustness to ill-conditioning. On large-scale benchmark datasets with up to four million data points, our approach accelerates GP training and in- ference by speed-up factors up to 27× and 72×, respectively, compared to CG.
more »
« less
Low-Precision Arithmetic for Fast Gaussian Processes
Low-precision arithmetic has had a transformative effect on the training of neural networks, reducing computation, memory and energy requirements. However, despite its promise, low-precision arithmetic has received little attention for Gaussian processes (GPs), largely because GPs require sophisticated linear algebra routines that are unstable in low-precision. We study the different failure modes that can occur when training GPs in half precision. To circumvent these failure modes, we propose a multi-faceted approach involving conjugate gradients with re-orthogonalization, mixed precision, and preconditioning. Our approach significantly improves the numerical stability and practical performance of conjugate gradients in low- precision over a wide range of settings, enabling GPs to train on 1.8 million data points in 10 hours on a single GPU, without any sparse approximations.
more »
« less
- Award ID(s):
- 1922658
- PAR ID:
- 10350918
- Date Published:
- Journal Name:
- UAI 2022.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Fixed-point decimal operations in databases with arbitrary-precision arithmetic refer to the ability to store and operate decimal fraction numbers with an arbitrary length of digits. This type of operation has become a requirement for many applications, including scientific databases, financial data processing, geometric data processing, and cryptography. However, the state-of-the-art fixed-point decimal technology either provides high performance for low-precision operations or supports arbitrary-precision arithmetic operations at low performance. In this paper, we present a design and implementation of a framework called UltraPrecise which supports arbitraryprecision arithmetic for databases on GPU, aiming to gain high performance for arbitrary-precision arithmetic operations. We build our framework based on the just-in-time compilation technique and optimize its performance via data representation design, PTX acceleration, and expression scheduling. UltraPrecise achieves comparable performance to other high-performance databases for low-precision arithmetic operations. For highprecision, we show that UltraPrecise consistently outperforms existing databases by two orders of magnitude, including workloads of RSA encryption and trigonometric function approximation.more » « less
-
While gliomas have become the most common cancerous brain tumors, manual diagnoses from 3D MRIs are time-consuming and possibly inconsistent when conducted by different radiotherapists, which leads to the pressing demand for automatic segmentation of brain tumors. State-of-the-art approaches employ FCNs to automatically segment the MRI scans. In particular, 3D U-Net has achieved notable performance and motivated a series of subsequent works. However, their significant size and heavy computation have impeded their actual deployment. Although there exists a body of literature on the compression of CNNs using low-precision representations, they either focus on storage reduction without computational improvement or cause severe performance degradation. In this article, we propose a CNN training algorithm that approximates weights and activations using non-negative integers along with trained affine mapping functions. Moreover, our approach allows the dot-product operations to be performed in an integer-arithmetic manner and defers the floating-point decoding and encoding phases until the end of layers. Experimental results on BraTS 2018 show that our trained affine mapping approach achieves near full-precision dice accuracy with 8-bit weights and activations. In addition, we achieve a dice accuracy within 0.005 and 0.01 of the full-precision counterparts when using 4-bit and 2-bit precisions, respectively.more » « less
-
Large language models trained for safety and harmlessness remain susceptible to adversarial misuse, as evidenced by the prevalence of "jailbreak" attacks on early releases of ChatGPT that elicit undesired behavior. Going beyond recognition of the issue, we investigate why such attacks succeed and how they can be created. We hypothesize two failure modes of safety training: competing objectives and mismatched generalization. Competing objectives arise when a model's capabilities and safety goals conflict, while mismatched generalization occurs when safety training fails to generalize to a domain for which capabilities exist. We use these failure modes to guide jailbreak design and then evaluate state-of-the-art models, including OpenAI's GPT-4 and Anthropic's Claude v1.3, against both existing and newly designed attacks. We find that vulnerabilities persist despite the extensive red-teaming and safety-training efforts behind these models. Notably, new attacks utilizing our failure modes succeed on every prompt in a collection of unsafe requests from the models' red-teaming evaluation sets and outperform existing ad hoc jailbreaks. Our analysis emphasizes the need for safety-capability parity -- that safety mechanisms should be as sophisticated as the underlying model -- and argues against the idea that scaling alone can resolve these safety failure modes.more » « less
-
Large language models trained for safety and harmlessness remain susceptible to adversarial misuse, as evidenced by the prevalence of "jailbreak" attacks on early releases of ChatGPT that elicit undesired behavior. Going beyond recognition of the issue, we investigate why such attacks succeed and how they can be created. We hypothesize two failure modes of safety training: competing objectives and mismatched generalization. Competing objectives arise when a model's capabilities and safety goals conflict, while mismatched generalization occurs when safety training fails to generalize to a domain for which capabilities exist. We use these failure modes to guide jailbreak design and then evaluate state-of-the-art models, including OpenAI's GPT-4 and Anthropic's Claude v1.3, against both existing and newly designed attacks. We find that vulnerabilities persist despite the extensive red-teaming and safety-training efforts behind these models. Notably, new attacks utilizing our failure modes succeed on every prompt in a collection of unsafe requests from the models' red-teaming evaluation sets and outperform existing ad hoc jailbreaks. Our analysis emphasizes the need for safety-capability parity -- that safety mechanisms should be as sophisticated as the underlying model -- and argues against the idea that scaling alone can resolve these safety failure modes.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
