Hebbian Descent: A Unified View on Log-Likelihood Learning.

This study discusses the negative impact of the derivative of the activation functions in the output layer of artificial neural networks, in particular in continual learning. We propose Hebbian descent as a theoretical framework to overcome this limitation, which is implemented through an alternative loss function for gradient descent we refer to as Hebbian descent loss. This loss is effectively the generalized log-likelihood loss and corresponds to an alternative weight update rule for the output layer wherein the derivative of the activation function is disregarded. We show how this update avoids vanishing error signals during backpropagation in saturated regions of the activation functions, which is particularly helpful in training shallow neural networks and deep neural networks where saturating activation functions are only used in the output layer. In combination with centering, Hebbian descent leads to better continual learning capabilities. It provides a unifying perspective on Hebbian learning, gradient descent, and generalized linear models, for all of which we discuss the advantages and disadvantages. Given activation functions with strictly positive derivative (as often the case in practice), Hebbian descent inherits the convergence properties of regular gradient descent. While established pairings of loss and output layer activation function (e.g., mean squared error with linear or cross-entropy with sigmoid/softmax) are subsumed by Hebbian descent, we provide general insights for designing arbitrary loss activation function combinations that benefit from Hebbian descent. For shallow networks, we show that Hebbian descent outperforms Hebbian learning, has a performance similar to regular gradient descent, and has a much better performance than all other tested update rules in continual learning. In combination with centering, Hebbian descent implements a forgetting mechanism that prevents catastrophic interference notably better than the other tested update rules. When training deep neural networks, our experimental results suggest that Hebbian descent has better or similar performance as gradient descent.

A neural network model for online one-shot storage of pattern sequences.

Based on the CRISP theory (Content Representation, Intrinsic Sequences, and Pattern completion), we present a computational model of the hippocampus that allows for online one-shot storage of pattern sequences without the need for a consolidation process. In our model, CA3 provides a pre-trained sequence that is hetero-associated with the input sequence, rather than storing a sequence in CA3. That is, plasticity on a short timescale only occurs in the incoming and outgoing connections of CA3, not in its recurrent connections. We use a single learning rule named Hebbian descent to train all plastic synapses in the network. A forgetting mechanism in the learning rule allows the network to continuously store new patterns while forgetting those stored earlier. We find that a single cue pattern can reliably trigger the retrieval of sequences, even when cues are noisy or missing information. Furthermore, pattern separation in subregion DG is necessary when sequences contain correlated patterns. Besides artificially generated input sequences, the model works with sequences of handwritten digits and natural images. Notably, our model is capable of improving itself without external input, in a process that can be referred to as 'replay' or 'offline-learning', which helps in improving the associations and consolidating the learned patterns.

tachAId-An interactive tool supporting the design of human-centered AI solutions.

In an era where Artificial Intelligence (AI) integration into business processes is crucial for maintaining competitiveness, there is a growing need for structured guidance on designing AI solutions that align with human needs. To this end, we present "technical assistance concerning human-centered AI development" (tachAId), an interactive advisory tool which comprehensively guides AI developers and decision makers in navigating the machine learning lifecycle with a focus on human-centered design. tachAId motivates and presents concrete technical advice to ensure human-centeredness across the phases of AI development. The tool's effectiveness is evaluated through a catalog of criteria for human-centered AI in the form of relevant challenges and goals, derived from existing methodologies and guidelines. Lastly, tachAId and one other comparable advisory tool were examined to determine their adherence to these criteria in order to provide an overview of the human-centered aspects covered by these tools and to allow interested parties to quickly assess whether the tools meet their needs.

A Tutorial on the Spectral Theory of Markov Chains.

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically. This tutorial provides an in-depth introduction to Markov chains and explores their connection to graphs and random walks. We use tools from linear algebra and graph theory to describe the transition matrices of different types of Markov chains, with a particular focus on exploring properties of the eigenvalues and eigenvectors corresponding to these matrices. The results presented are relevant to a number of methods in machine learning and data mining, which we describe at various stages. Rather than being a novel academic study in its own right, this text presents a collection of known results, together with some new concepts. Moreover, the tutorial focuses on offering intuition to readers rather than formal understanding and only assumes basic exposure to concepts from linear algebra and probability theory. It is therefore accessible to students and researchers from a wide variety of disciplines.

A map of spatial navigation for neuroscience.

Spatial navigation has received much attention from neuroscientists, leading to the identification of key brain areas and the discovery of numerous spatially selective cells. Despite this progress, our understanding of how the pieces fit together to drive behavior is generally lacking. We argue that this is partly caused by insufficient communication between behavioral and neuroscientific researchers. This has led the latter to under-appreciate the relevance and complexity of spatial behavior, and to focus too narrowly on characterizing neural representations of space-disconnected from the computations these representations are meant to enable. We therefore propose a taxonomy of navigation processes in mammals that can serve as a common framework for structuring and facilitating interdisciplinary research in the field. Using the taxonomy as a guide, we review behavioral and neural studies of spatial navigation. In doing so, we validate the taxonomy and showcase its usefulness in identifying potential issues with common experimental approaches, designing experiments that adequately target particular behaviors, correctly interpreting neural activity, and pointing to new avenues of research.

Modeling the function of episodic memory in spatial learning.

Episodic memory has been studied extensively in the past few decades, but so far little is understood about how it drives future behavior. Here we propose that episodic memory can facilitate learning in two fundamentally different modes: retrieval and replay, which is the reinstatement of hippocampal activity patterns during later sleep or awake quiescence. We study their properties by comparing three learning paradigms using computational modeling based on visually-driven reinforcement learning. Firstly, episodic memories are retrieved to learn from single experiences (one-shot learning); secondly, episodic memories are replayed to facilitate learning of statistical regularities (replay learning); and, thirdly, learning occurs online as experiences arise with no access to memories of past experiences (online learning). We found that episodic memory benefits spatial learning in a broad range of conditions, but the performance difference is meaningful only when the task is sufficiently complex and the number of learning trials is limited. Furthermore, the two modes of accessing episodic memory affect spatial learning differently. One-shot learning is typically faster than replay learning, but the latter may reach a better asymptotic performance. In the end, we also investigated the benefits of sequential replay and found that replaying stochastic sequences results in faster learning as compared to random replay when the number of replays is limited. Understanding how episodic memory drives future behavior is an important step toward elucidating the nature of episodic memory.

A Model of Semantic Completion in Generative Episodic Memory.

Many studies have suggested that episodic memory is a generative process, but most computational models adopt a storage view. In this article, we present a model of the generative aspects of episodic memory. It is based on the central hypothesis that the hippocampus stores and retrieves selected aspects of an episode as a memory trace, which is necessarily incomplete. At recall, the neocortex reasonably fills in the missing parts based on general semantic information in a process we call semantic completion. The model combines two neural network architectures known from machine learning, the vector-quantized variational autoencoder (VQ-VAE) and the pixel convolutional neural network (PixelCNN). As episodes, we use images of digits and fashion items (MNIST) augmented by different backgrounds representing context. The model is able to complete missing parts of a memory trace in a semantically plausible way up to the point where it can generate plausible images from scratch, and it generalizes well to images not trained on. Compression as well as semantic completion contribute to a strong reduction in memory requirements and robustness to noise. Finally, we also model an episodic memory experiment and can reproduce that semantically congruent contexts are always recalled better than incongruent ones, high attention levels improve memory accuracy in both cases, and contexts that are not remembered correctly are more often remembered semantically congruently than completely wrong. This model contributes to a deeper understanding of the interplay between episodic memory and semantic information in the generative process of recalling the past.

Context-dependent extinction learning emerging from raw sensory inputs: a reinforcement learning approach.

The context-dependence of extinction learning has been well studied and requires the hippocampus. However, the underlying neural mechanisms are still poorly understood. Using memory-driven reinforcement learning and deep neural networks, we developed a model that learns to navigate autonomously in biologically realistic virtual reality environments based on raw camera inputs alone. Neither is context represented explicitly in our model, nor is context change signaled. We find that memory-intact agents learn distinct context representations, and develop ABA renewal, whereas memory-impaired agents do not. These findings reproduce the behavior of control and hippocampal animals, respectively. We therefore propose that the role of the hippocampus in the context-dependence of extinction learning might stem from its function in episodic-like memory and not in context-representation per se. We conclude that context-dependence can emerge from raw visual inputs.

Improving sensory representations using episodic memory.

The medial temporal lobe (MTL) is well known to be essential for declarative memory. However, a growing body of research suggests that MTL structures might be involved in perceptual processes as well. Our previous modeling work suggests that sensory representations in cortex influence the accuracy of episodic memory retrieved from the MTL. We adopt that model here to show that, conversely, episodic memory can also influence the quality of sensory representations. We model the effect of episodic memory as (a) repeatedly replaying episodes from memory and (b) recombining episode fragments to form novel sequences that are more informative for learning sensory representations than the original episodes. We demonstrate that the performance in visual discrimination tasks is superior when episodic memory is present and that this difference is due to episodic memory driving the learning of a more optimized sensory representation. We conclude that the MTL can, even if it has only a purely mnemonic function, influence perceptual discrimination indirectly.

Storage fidelity for sequence memory in the hippocampal circuit.

Episodic memories have been suggested to be represented by neuronal sequences, which are stored and retrieved from the hippocampal circuit. A special difficulty is that realistic neuronal sequences are strongly correlated with each other since computational memory models generally perform poorly when correlated patterns are stored. Here, we study in a computational model under which conditions the hippocampal circuit can perform this function robustly. During memory encoding, CA3 sequences in our model are driven by intrinsic dynamics, entorhinal inputs, or a combination of both. These CA3 sequences are hetero-associated with the input sequences, so that the network can retrieve entire sequences based on a single cue pattern. We find that overall memory performance depends on two factors: the robustness of sequence retrieval from CA3 and the circuit's ability to perform pattern completion through the feedforward connectivity, including CA3, CA1 and EC. The two factors, in turn, depend on the relative contribution of the external inputs and recurrent drive on CA3 activity. In conclusion, memory performance in our network model critically depends on the network architecture and dynamics in CA3.

Slowness as a Proxy for Temporal Predictability: An Empirical Comparison.

The computational principles of slowness and predictability have been proposed to describe aspects of information processing in the visual system. From the perspective of slowness being a limited special case of predictability we investigate the relationship between these two principles empirically. On a collection of real-world data sets we compare the features extracted by slow feature analysis (SFA) to the features of three recently proposed methods for predictable feature extraction: forecastable component analysis, predictable feature analysis, and graph-based predictable feature analysis. Our experiments show that the predictability of the learned features is highly correlated, and, thus, SFA appears to effectively implement a method for extracting predictable features according to different measures of predictability.

The Interaction between Semantic Representation and Episodic Memory.

The experimental evidence on the interrelation between episodic memory and semantic memory is inconclusive. Are they independent systems, different aspects of a single system, or separate but strongly interacting systems? Here, we propose a computational role for the interaction between the semantic and episodic systems that might help resolve this debate. We hypothesize that episodic memories are represented as sequences of activation patterns. These patterns are the output of a semantic representational network that compresses the high-dimensional sensory input. We show quantitatively that the accuracy of episodic memory crucially depends on the quality of the semantic representation. We compare two types of semantic representations: appropriate representations, which means that the representation is used to store input sequences that are of the same type as those that it was trained on, and inappropriate representations, which means that stored inputs differ from the training data. Retrieval accuracy is higher for appropriate representations because the encoded sequences are less divergent than those encoded with inappropriate representations. Consistent with our model prediction, we found that human subjects remember some aspects of episodes significantly more accurately if they had previously been familiarized with the objects occurring in the episode, as compared to episodes involving unfamiliar objects. We thus conclude that the interaction with the semantic system plays an important role for episodic memory.

Experience-Dependency of Reliance on Local Visual and Idiothetic Cues for Spatial Representations Created in the Absence of Distal Information.

Spatial encoding in the hippocampus is based on a range of different input sources. To generate spatial representations, reliable sensory cues from the external environment are integrated with idiothetic cues, derived from self-movement, that enable path integration and directional perception. In this study, we examined to what extent idiothetic cues significantly contribute to spatial representations and navigation: we recorded place cells while rodents navigated towards two visually identical chambers in 180° orientation via two different paths in darkness and in the absence of reliable auditory or olfactory cues. Our goal was to generate a conflict between local visual and direction-specific information, and then to assess which strategy was prioritized in different learning phases. We observed that, in the absence of distal cues, place fields are initially controlled by local visual cues that override idiothetic cues, but that with multiple exposures to the paradigm, spaced at intervals of days, idiothetic cues become increasingly implemented in generating an accurate spatial representation. Taken together, these data support that, in the absence of distal cues, local visual cues are prioritized in the generation of context-specific spatial representations through place cells, whereby idiothetic cues are deemed unreliable. With cumulative exposures to the environments, the animal learns to attend to subtle idiothetic cues to resolve the conflict between visual and direction-specific information.

Correction: Gaussian-binary restricted Boltzmann machines for modeling natural image statistics.

[This corrects the article DOI: 10.1371/journal.pone.0171015.].

Gaussian-binary restricted Boltzmann machines for modeling natural image statistics.

We present a theoretical analysis of Gaussian-binary restricted Boltzmann machines (GRBMs) from the perspective of density models. The key aspect of this analysis is to show that GRBMs can be formulated as a constrained mixture of Gaussians, which gives a much better insight into the model's capabilities and limitations. We further show that GRBMs are capable of learning meaningful features without using a regularization term and that the results are comparable to those of independent component analysis. This is illustrated for both a two-dimensional blind source separation task and for modeling natural image patches. Our findings exemplify that reported difficulties in training GRBMs are due to the failure of the training algorithm rather than the model itself. Based on our analysis we derive a better training setup and show empirically that it leads to faster and more robust training of GRBMs. Finally, we compare different sampling algorithms for training GRBMs and show that Contrastive Divergence performs better than training methods that use a persistent Markov chain.

Modeling place field activity with hierarchical slow feature analysis.

What are the computational laws of hippocampal activity? In this paper we argue for the slowness principle as a fundamental processing paradigm behind hippocampal place cell firing. We present six different studies from the experimental literature, performed with real-life rats, that we replicated in computer simulations. Each of the chosen studies allows rodents to develop stable place fields and then examines a distinct property of the established spatial encoding: adaptation to cue relocation and removal; directional dependent firing in the linear track and open field; and morphing and scaling the environment itself. Simulations are based on a hierarchical Slow Feature Analysis (SFA) network topped by a principal component analysis (ICA) output layer. The slowness principle is shown to account for the main findings of the presented experimental studies. The SFA network generates its responses using raw visual input only, which adds to its biological plausibility but requires experiments performed in light conditions. Future iterations of the model will thus have to incorporate additional information, such as path integration and grid cell activity, in order to be able to also replicate studies that take place during darkness.

Memory storage fidelity in the hippocampal circuit: the role of subregions and input statistics.

In the last decades a standard model regarding the function of the hippocampus in memory formation has been established and tested computationally. It has been argued that the CA3 region works as an auto-associative memory and that its recurrent fibers are the actual storing place of the memories. Furthermore, to work properly CA3 requires memory patterns that are mutually uncorrelated. It has been suggested that the dentate gyrus orthogonalizes the patterns before storage, a process known as pattern separation. In this study we review the model when random input patterns are presented for storage and investigate whether it is capable of storing patterns of more realistic entorhinal grid cell input. Surprisingly, we find that an auto-associative CA3 net is redundant for random inputs up to moderate noise levels and is only beneficial at high noise levels. When grid cell input is presented, auto-association is even harmful for memory performance at all levels. Furthermore, we find that Hebbian learning in the dentate gyrus does not support its function as a pattern separator. These findings challenge the standard framework and support an alternative view where the simpler EC-CA1-EC network is sufficient for memory storage.

Spatial representations of place cells in darkness are supported by path integration and border information.

Effective spatial navigation is enabled by reliable reference cues that derive from sensory information from the external environment, as well as from internal sources such as the vestibular system. The integration of information from these sources enables dead reckoning in the form of path integration. Navigation in the dark is associated with the accumulation of errors in terms of perception of allocentric position and this may relate to error accumulation in path integration. We assessed this by recording from place cells in the dark under circumstances where spatial sensory cues were suppressed. Spatial information content, spatial coherence, place field size, and peak and infield firing rates decreased whereas sparsity increased following exploration in the dark compared to the light. Nonetheless it was observed that place field stability in darkness was sustained by border information in a subset of place cells. To examine the impact of encountering the environment's border on navigation, we analyzed the trajectory and spiking data gathered during navigation in the dark. Our data suggest that although error accumulation in path integration drives place field drift in darkness, under circumstances where border contact is possible, this information is integrated to enable retention of spatial representations.

Slow feature analysis on retinal waves leads to V1 complex cells.

The developing visual system of many mammalian species is partially structured and organized even before the onset of vision. Spontaneous neural activity, which spreads in waves across the retina, has been suggested to play a major role in these prenatal structuring processes. Recently, it has been shown that when employing an efficient coding strategy, such as sparse coding, these retinal activity patterns lead to basis functions that resemble optimal stimuli of simple cells in primary visual cortex (V1). Here we present the results of applying a coding strategy that optimizes for temporal slowness, namely Slow Feature Analysis (SFA), to a biologically plausible model of retinal waves. Previously, SFA has been successfully applied to model parts of the visual system, most notably in reproducing a rich set of complex-cell features by training SFA with quasi-natural image sequences. In the present work, we obtain SFA units that share a number of properties with cortical complex-cells by training on simulated retinal waves. The emergence of two distinct properties of the SFA units (phase invariance and orientation tuning) is thoroughly investigated via control experiments and mathematical analysis of the input-output functions found by SFA. The results support the idea that retinal waves share relevant temporal and spatial properties with natural visual input. Hence, retinal waves seem suitable training stimuli to learn invariances and thereby shape the developing early visual system such that it is best prepared for coding input from the natural world.

A computational model for preplay in the hippocampus.

The hippocampal network produces sequences of neural activity even when there is no time-varying external drive. In offline states, the temporal sequence in which place cells fire spikes correlates with the sequence of their place fields. Recent experiments found this correlation even between offline sequential activity (OSA) recorded before the animal ran in a novel environment and the place fields in that environment. This preplay phenomenon suggests that OSA is generated intrinsically in the hippocampal network, and not established by external sensory inputs. Previous studies showed that continuous attractor networks with asymmetric patterns of connectivity, or with slow, local negative feedback, can generate sequential activity. This mechanism could account for preplay if the network only represented a single spatial map, or chart. However, global remapping in the hippocampus implies that multiple charts are represented simultaneously in the hippocampal network and it remains unknown whether the network with multiple charts can account for preplay. Here we show that it can. Driven with random inputs, the model generates sequences in every chart. Place fields in a given chart and OSA generated by the network are highly correlated. We also find significant correlations, albeit less frequently, even when the OSA is correlated with a new chart in which place fields are randomly scattered. These correlations arise from random correlations between the orderings of place fields in the new chart and those in a pre-existing chart. Our results suggest two different accounts for preplay. Either an existing chart is re-used to represent a novel environment or a new chart is formed.