890 research outputs found
Note On Certain Inequalities for Neuman Means
In this paper, we give the explicit formulas for the Neuman means ,
, and , and present the best possible upper and lower
bounds for theses means in terms of the combinations of harmonic mean ,
arithmetic mean and contraharmonic mean .Comment: 9 page
Monotonicity of the Ratio of the Power and Second Seiffert Means with Applications
We present the necessary and sufficient condition for the monotonicity of the ratio of the power and second Seiffert means. As applications, we get the sharp upper and lower bounds for the second Seiffert mean in terms of the power mean
Preparation of FeO(OH) Modified with Polyethylene Glycol and Its Catalytic Activity on the Reduction of Nitrobenzene with Hydrazine Hydrate
Iron oxyhydroxide was prepared by dropping ammonia water to Fe(NO3)3.9H2O dispersed in polyethylene glycol (PEG) 1000. The catalyst was characterized by X-ray powder diffraction, Fourier transform infrared spectroscopy and laser particle size analyzer. The results showed the catalyst modified with polyethylene glycol was amorphous. The addition of PEG during the preparation make the particle size of the catalyst was smaller and more uniform. The catalytic performance was tested in the reduction of nitroarenes to corresponding amines with hydrazine hydrate, and the catalyst showed excellent activity and stability.
A HINT from Arithmetic: On Systematic Generalization of Perception, Syntax, and Semantics
Inspired by humans' remarkable ability to master arithmetic and generalize to
unseen problems, we present a new dataset, HINT, to study machines' capability
of learning generalizable concepts at three different levels: perception,
syntax, and semantics. In particular, concepts in HINT, including both digits
and operators, are required to learn in a weakly-supervised fashion: Only the
final results of handwriting expressions are provided as supervision. Learning
agents need to reckon how concepts are perceived from raw signals such as
images (i.e., perception), how multiple concepts are structurally combined to
form a valid expression (i.e., syntax), and how concepts are realized to afford
various reasoning tasks (i.e., semantics). With a focus on systematic
generalization, we carefully design a five-fold test set to evaluate both the
interpolation and the extrapolation of learned concepts. To tackle this
challenging problem, we propose a neural-symbolic system by integrating neural
networks with grammar parsing and program synthesis, learned by a novel
deduction--abduction strategy. In experiments, the proposed neural-symbolic
system demonstrates strong generalization capability and significantly
outperforms end-to-end neural methods like RNN and Transformer. The results
also indicate the significance of recursive priors for extrapolation on syntax
and semantics.Comment: Preliminary wor
Neural-Symbolic Recursive Machine for Systematic Generalization
Despite the tremendous success, existing machine learning models still fall
short of human-like systematic generalization -- learning compositional rules
from limited data and applying them to unseen combinations in various domains.
We propose Neural-Symbolic Recursive Machine (NSR) to tackle this deficiency.
The core representation of NSR is a Grounded Symbol System (GSS) with
combinatorial syntax and semantics, which entirely emerges from training data.
Akin to the neuroscience studies suggesting separate brain systems for
perceptual, syntactic, and semantic processing, NSR implements analogous
separate modules of neural perception, syntactic parsing, and semantic
reasoning, which are jointly learned by a deduction-abduction algorithm. We
prove that NSR is expressive enough to model various sequence-to-sequence
tasks. Superior systematic generalization is achieved via the inductive biases
of equivariance and recursiveness embedded in NSR. In experiments, NSR achieves
state-of-the-art performance in three benchmarks from different domains: SCAN
for semantic parsing, PCFG for string manipulation, and HINT for arithmetic
reasoning. Specifically, NSR achieves 100% generalization accuracy on SCAN and
PCFG and outperforms state-of-the-art models on HINT by about 23%. Our NSR
demonstrates stronger generalization than pure neural networks due to its
symbolic representation and inductive biases. NSR also demonstrates better
transferability than existing neural-symbolic approaches due to less
domain-specific knowledge required
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