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Register a new userA remark on a paper of Krotov and Hopfield [arXiv:2008.06996]
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In their recent paper titled Large Associative Memory Problem in Neurobiology and Machine Learning [arXiv:2008.06996] the authors gave a biologically plausible microscopic theory from which one can recover many dense associative memory models discussed in the literature. We show that the layers of the recent MLP-mixer [arXiv:2105.01601] as well as the essentially equivalent model in [arXiv:2105.02723] are amongst them.
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We prove a sharp Lieb-Thirring type inequality for Jacobi matrices, thereby settling a conjecture of Hundertmark and Simon. An interesting feature of the proof is that it employs a technique originally used by Hundertmark-Laptev-Weidl concerning sums of singular values for compact operators.
The recent success of brain-inspired deep neural networks (DNNs) in solving complex, high-level visual tasks has led to rising expectations for their potential to match the human visual system. However, DNNs exhibit idiosyncrasies that suggest their visual representation and processing might be substantially different from human vision. One limitation of DNNs is that they are vulnerable to adversarial examples, input images on which subtle, carefully designed noises are added to fool a machine classifier. The robustness of the human visual system against adversarial examples is potentially of great importance as it could uncover a key mechanistic feature that machine vision is yet to incorporate. In this study, we compare the visual representations of white- and black-box adversarial examples in DNNs and humans by leveraging functional magnetic resonance imaging (fMRI). We find a small but significant difference in representation patterns for different (i.e. white- versus black- box) types of adversarial examples for both humans and DNNs. However, human performance on categorical judgment is not degraded by noise regardless of the type unlike DNN. These results suggest that adversarial examples may be differentially represented in the human visual system, but unable to affect the perceptual experience.
Neurodegenerative diseases and traumatic brain injuries (TBI) are among the main causes of cognitive dysfunction in humans. Both manifestations exhibit the extensive presence of focal axonal swellings (FAS). FAS compromises the information encoded in spike trains, thus leading to potentially severe functional deficits. Complicating our understanding of the impact of FAS is our inability to access small scale injuries with non-invasive methods, the overall complexity of neuronal pathologies, and our limited knowledge of how networks process biological signals. Building on Hopfields pioneering work, we extend a model for associative memory to account for FAS and its impact on memory encoding. We calibrate all FAS parameters from biophysical observations of their statistical distribution and size, providing a framework to simulate the effects of brain disorders on memory recall performance. A face recognition example is used to demonstrate and validate the functionality of the novel model. Our results link memory recall ability to observed FAS statistics, allowing for a description of different stages of brain disorders within neuronal networks. This provides a first theoretical model to bridge experimental observations of FAS in neurodegeneration and TBI with compromised memory recall, thus closing the large gap between theory and experiment on how biological signals are processed in damaged, high-dimensional functional networks. The work further lends new insight into positing diagnostic tools to measure cognitive deficits.
Scientific studies of consciousness rely on objects whose existence is assumed to be independent of any consciousness. On the contrary, we assume consciousness to be fundamental, and that one of the main features of consciousness is characterized as being other-dependent. We set up a framework which naturally subsumes this feature by defining a compact closed category where morphisms represent conscious processes. These morphisms are a composition of a set of generators, each being specified by their relations with other generators, and therefore co-dependent. The framework is general enough and fits well into a compositional model of consciousness. Interestingly, we also show how our proposal may become a step towards avoiding the hard problem of consciousness, and thereby address the combination problem of conscious experiences.
This comment is aimed to point out that the recent work due to Kim, et al. in which the clinical and experiential assessment of a brain network model suggests that asymmetry of synchronization suppression is the key mechanism of hysteresis has coupling with our theoretical hysteresis model of unconscious-conscious interconnection based on dynamics on m-adic trees.
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