progressive differentiation
Supplementary Material for Characterizing emergent representations in a space of candidate learning rules for deep networks
We apply singular value decomposition (SVD) to the dataset's input-output correlation matrix to extract the component of the input-output mapping for different hierarchical levels. To compute the strength of a network's input-output mapping for these hierarchical distinctions This author is now affiliated to University Medical Center Hamburg-Eppendorf, Hamburg, Germany. The task is to link each object's perceptual representation ( However, it seems critical to demonstrate that our framework is robust against a modification of this assumption about input structure. Here, we show that the conclusions presented in the main paper remain unchanged even if we relax the assumption of one-hot vectors (which are similar to grandmother-cell neurons: each object is represented by a dedicated single neuron). The differences in learning dynamics across different learning rules within the 2D space are robust against the shift from localist assumption to the current distributed assumption (Supp.
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6275d7071d005260ab9d0766d6df1145-AuthorFeedback.pdf
We agree O'Reilly's work is highly relevant and we should have We will also link to the repository containing code for replicating all results. We had investigated several alternatives like this before settling on our metric. We found this normalization would make the 2D-map visualization unintuitive. We will clarify these points in the paper. Second, however, it is well known that CHL [Eq.
Supplementary Material for Characterizing emergent representations in a space of candidate learning rules for deep networks
We apply singular value decomposition (SVD) to the dataset's input-output correlation matrix to extract the component of the input-output mapping for different hierarchical levels. To compute the strength of a network's input-output mapping for these hierarchical distinctions This author is now affiliated to University Medical Center Hamburg-Eppendorf, Hamburg, Germany. The task is to link each object's perceptual representation ( However, it seems critical to demonstrate that our framework is robust against a modification of this assumption about input structure. Here, we show that the conclusions presented in the main paper remain unchanged even if we relax the assumption of one-hot vectors (which are similar to grandmother-cell neurons: each object is represented by a dedicated single neuron). The differences in learning dynamics across different learning rules within the 2D space are robust against the shift from localist assumption to the current distributed assumption (Supp.
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The thermodynamic cost of fast thought
After more than sixty years, Shannon's research [1-3] continues to raise fundamental questions, such as the one formulated by Luce [4,5], which is still unanswered: "Why is information theory not very applicable to psychological problems, despite apparent similarities of concepts?" On this topic, Pinker [6], one of the foremost defenders of the computational theory of mind [6], has argued that thought is simply a type of computation, and that the gap between human cognition and computational models may be illusory. In this context, in his latest book, titled Thinking Fast and Slow [8], Kahneman [7,8] provides further theoretical interpretation by differentiating the two assumed systems of the cognitive functioning of the human mind. He calls them intuition (system 1) determined to be an associative (automatic, fast and perceptual) machine, and reasoning (system 2) required to be voluntary and to operate logical- deductively. In this paper, we propose an ansatz inspired by Ausubel's learning theory for investigating, from the constructivist perspective [9-12], information processing in the working memory of cognizers. Specifically, a thought experiment is performed utilizing the mind of a dual-natured creature known as Maxwell's demon: a tiny "man-machine" solely equipped with the characteristics of system 1, which prevents it from reasoning. The calculation presented here shows that [...]. This result indicates that when the system 2 is shut down, both an intelligent being, as well as a binary machine, incur the same energy cost per unit of information processed, which mathematically proves the computational attribute of the system 1, as Kahneman [7,8] theorized. This finding links information theory to human psychological features and opens a new path toward the conception of a multi-bit reasoning machine.
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