137 research outputs found
Application of Interference Canceller in Bioelectricity Signal Disposing
AbstractBioelectricity signal is in strong interfering environment. When it is abstracted, filter is an important hinge. Adaptive interference canceller which based on LMS algorithm is excellent. It can adjust system parameter automatically. When signals are abstracted or disposed, it can play better performance. With this algorithm, this paper dispose ECG(Electrocardiograph)signal as an example in two aspect: canceling power line interference and canceling baseline shift. Both get well effect
Towards Revealing the Mystery behind Chain of Thought: a Theoretical Perspective
Recent studies have discovered that Chain-of-Thought prompting (CoT) can
dramatically improve the performance of Large Language Models (LLMs),
particularly when dealing with complex tasks involving mathematics or
reasoning. Despite the enormous empirical success, the underlying mechanisms
behind CoT and how it unlocks the potential of LLMs remain elusive. In this
paper, we take a first step towards theoretically answering these questions.
Specifically, we examine the capacity of LLMs with CoT in solving fundamental
mathematical and decision-making problems. We start by giving an impossibility
result showing that any bounded-depth Transformer cannot directly output
correct answers for basic arithmetic/equation tasks unless the model size grows
super-polynomially with respect to the input length. In contrast, we then prove
by construction that autoregressive Transformers of a constant size suffice to
solve both tasks by generating CoT derivations using a commonly-used math
language format. Moreover, we show LLMs with CoT are capable of solving a
general class of decision-making problems known as Dynamic Programming, thus
justifying its power in tackling complex real-world tasks. Finally, extensive
experiments on four tasks show that, while Transformers always fail to predict
the answers directly, they can consistently learn to generate correct solutions
step-by-step given sufficient CoT demonstrations.Comment: 33 page
Exact Shannon entropies for the multidimensional harmonic states
In this work we determine and discuss the entropic uncertainty measures of
Shannon type for all the discrete stationary states of the multidimensional
harmonic systems directly in terms of the states' hyperquantum numbers, the
dimensionality and the oscillator strength. We have found that these entropies
have a monotonically increasing behavior when both the dimensionality and the
population of the states are increasingComment: Accepted and Published in Physica
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