4,939 research outputs found
Deterministic versus probabilistic quantum information masking
We investigate quantum information masking for arbitrary dimensional quantum
states. We show that mutually orthogonal quantum states can always be served
for deterministic masking of quantum information. We further construct a
probabilistic masking machine for linearly independent states. It is shown that
a set of d dimensional states, , , can be probabilistically masked by a general
unitary-reduction operation if they are linearly independent. The maximal
successful probability of probabilistic masking is analyzed and derived for the
case of two initial states.Comment: 5 pages, 1 figure
Basic Properties of Periodic Functions
In this article we present definitions, basic properties and some examples of periodic functions according to [5].Li Bo - Qingdao University of Science and Technology, ChinaLi Dailu - Qingdao University of Science and Technology, ChinaMen Yanhong - Qingdao University of Science and Technology, ChinaLiang Xiquan - Qingdao University of Science and Technology, ChinaGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Chuanzhang Chen. Mathematical Analysis. Higher Education Press, Beijing, 1978.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Peng Wang and Bo Li. Several differentiation formulas of special functions. Part V. Formalized Mathematics, 15(3):73-79, 2007, doi:10.2478/v10037-007-0009-4.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998
Norm Tweaking: High-performance Low-bit Quantization of Large Language Models
As the size of large language models (LLMs) continues to grow, model
compression without sacrificing accuracy has become a crucial challenge for
deployment. While some quantization methods, such as GPTQ, have made progress
in achieving acceptable 4-bit weight-only quantization, attempts at lower bit
quantization often result in severe performance degradation. In this paper, we
introduce a technique called norm tweaking, which can be used as a plugin in
current PTQ methods to achieve high precision while being cost-efficient. Our
approach is inspired by the observation that rectifying the quantized
activation distribution to match its float counterpart can readily restore
accuracy for LLMs. To achieve this, we carefully design a tweaking strategy
that includes calibration data generation and channel-wise distance constraint
to update the weights of normalization layers for better generalization. We
conduct extensive experiments on various datasets using several open-sourced
LLMs. Our method demonstrates significant improvements in both weight-only
quantization and joint quantization of weights and activations, surpassing
existing PTQ methods. On GLM-130B and OPT-66B, our method even achieves the
same level of accuracy at 2-bit quantization as their float ones. Our simple
and effective approach makes it more practical for real-world applications
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