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Expressive Power of Specification Languages
Formal Aspects of Computing, 1998Abstract. By abstracting away from a particular specification language and considering a ‘specification’ to be just a set of implementations, one can define a partial order on specification languages that reflects their expressive power. In addition, one can show that there is no universal specification language that can express all such ...
Ian J Hayes, Hayes Ian J
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The Expressive Power of Low-Rank Adaptation
International Conference on Learning Representations, 2023Low-Rank Adaptation (LoRA), a parameter-efficient fine-tuning method that leverages low-rank adaptation of weight matrices, has emerged as a prevalent technique for fine-tuning pre-trained models such as large language models and diffusion models ...
Yuchen Zeng, Kangwook Lee
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European Conference on Computer Vision, 2021
. We address the problem of uncertainty calibration and introduce a novel calibration method, Parametrized Temperature Scaling (PTS). Standard deep neural networks typically yield uncalibrated predictions, which can be transformed into calibrated ...
Christian Tomani +2 more
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. We address the problem of uncertainty calibration and introduce a novel calibration method, Parametrized Temperature Scaling (PTS). Standard deep neural networks typically yield uncalibrated predictions, which can be transformed into calibrated ...
Christian Tomani +2 more
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On the expressive power of CTL
Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158), 2003We show that the expressive power of the branching time logic CTL coincides with that of the class of bisimulation invariant properties expressible in so-called monadic path logic: monadic second order logic in which set quantification is restricted to paths. In order to prove this result, we first prove a new composition theorem for trees.
Faron Moller, Alexander Moshe Rabinovich
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On the Expressive Power of OKFDDs
Formal Methods in System Design, 1997Ordered Decision Diagrams (ODDs) as a means for the representation of Boolean functions are used in many applications in CAD. Depending on the decomposition type, various classes of ODDs have been defined, among them being the Ordered Binary Decision Diagrams (OBDDs), the Ordered Functional Decision Diagrams (OFDDs) and the Ordered Kronecker Functional
Bernd Becker 0001 +2 more
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On the Expressive Power of FO[ + ]
2010The characterization of the class of FO[+]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to bounded languages, this class coincides with the class of semilinear languages. We also study some closure properties of FO[+]-definable languages which, as a by-product, allow us to give an ...
Christian Choffrut +3 more
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A Little Depth Goes a Long Way: The Expressive Power of Log-Depth Transformers
Neural Information Processing SystemsRecent theoretical results show transformers cannot express sequential reasoning problems over long inputs, intuitively because their computational depth is bounded.
William Merrill, Ashish Sabharwal
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Exact Expressive Power of Transformers with Padding
Neural Information Processing SystemsChain of thought is a natural inference-time method for increasing the computational power of transformer-based large language models (LLMs), but comes at the cost of sequential decoding.
William Merrill, Ashish Sabharwal
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International Conference on Machine Learning
Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored.
Kevin Xu, Issei Sato
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Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored.
Kevin Xu, Issei Sato
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Understanding the Expressive Power and Mechanisms of Transformer for Sequence Modeling
Neural Information Processing SystemsWe conduct a systematic study of the approximation properties of Transformer for sequence modeling with long, sparse and complicated memory. We investigate the mechanisms through which different components of Transformer, such as the dot-product self ...
Mingze Wang, E. Weinan
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