Time-courses of memory decay in vector-based and landmark-based systems of navigation in desert ants, Cataglyphis fortis

In foraging and homing, desert ants of the genus Cataglyphis employ two different systems of navigation: a vector-based or dead-reckoning mechanism, depending on angles steered and distances travelled, and a landmark-based piloting mechanism. In these systems the ants use either celestial or terrestrial visual information, respectively. In behavioural experiments we investigated how long these types of information are preserved in the ant's memory, i.e. how long the ants are able to orient properly in either way. To answer this question, ants were tested in specific dead-reckoning and piloting situations, whereby the two vector components, direction and distance, were examined separately. The ability to follow a particular vector course vanishes rapidly. Information about a given homing direction is lost from the 6th day on (the time constant of the exponential memory decay function is τ = 4.5 days). The homing distances show a significantly higher dispersion from the 4th day on (τ = 2.5 days). Having learned a constellation of landmarks positioned at the corners of an equidistant triangle all ants were oriented properly after 10 days in captivity, and 64% of the ants exhibited extremely precise orientation performances even when tested after 20 days. Thus, the memory decay functions have about the same short time-course for information on distance and direction, i.e. information used for dead-reckoning. In contrast, landmark-based information used in pinpointing the nest entrance is stored over the entire lifetime of a Cataglyphis forager. Accepted: 18 January 1997     

Transferring learning from external to internal weights in echo-state networks with sparse connectivity

Modifying weights within a recurrent network to improve performance on a task has proven to be difficult. Echo-state networks in which modification is restricted to the weights of connections onto network outputs provide an easier alternative, but at the expense of modifying the typically sparse architecture of the network by including feedback from the output back into the network. We derive methods for using the values of the output weights from a trained echo-state network to set recurrent weights within the network. The result of this "transfer of learning" is a recurrent network that performs the task without requiring the output feedback present in the original network. We also discuss a hybrid version in which online learning is applied to both output and recurrent weights. Both approaches provide efficient ways of training recurrent networks to perform complex tasks. Through an analysis of the conditions required to make transfer of learning work, we define the concept of a "self-sensing" network state, and we compare and contrast this with compressed sensing.     

When Does Previewing the Landscape Affect Pigeon Homing?

The importance of visual landmarks during homing in pigeons (Columba livia) remains a contentious issue. Three experiments which explore the role of visual landmarks at release sites are reported here. The effects of releasing homing pigeons after a 5-minute period in either a clear or an opaque sided release box were investigated. In the clear sided box pigeons were able to observe local surroundings at a release site, but this view was obstructed in the opaque sided box. In experiment 1 pigeons were released from familiar locations close to home (between 2 and 5.6 km): being unable to view landmarks prior to release significantly slowed homing speeds. In experiment 2 pigeons were released at familiar locations further from home (between 8.4 and 10 km): being unable to view landmarks prior to release did not significantly affect homing speeds. In experiment 3 pigeons were trained to home from distant release sites but were tested at closer, unfamiliar sites located on the likely homing routes used by the pigeons in training. No significant difference in homing speeds were observed when pigeons were released from either the clear or opaque sided box. The significance of these results for understanding the role of visual landmarks within a pigeon's familiar area is discussed.     

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.     

Hebbian learning in parallel and modular memories

Many cognitive and sensorimotor functions in the brain involve parallel and modular memory subsystems that are adapted by activity-dependent Hebbian synaptic plasticity. This is in contrast to the multilayer perceptron model of supervised learning where sensory information is presumed to be integrated by a common pool of hidden units through backpropagation learning. Here we show that Hebbian learning in parallel and modular memories is more advantageous than backpropagation learning in lumped memories in two respects: it is computationally much more efficient and structurally much simpler to implement with biological neurons. Accordingly, we propose a more biologically relevant neural network model, called a tree-like perceptron, which is a simple modification of the multilayer perceptron model to account for the general neural architecture, neuronal specificity, and synaptic learning rule in the brain. The model features a parallel and modular architecture in which adaptation of the input-to-hidden connection follows either a Hebbian or anti-Hebbian rule depending on whether the hidden units are excitatory or inhibitory, respectively. The proposed parallel and modular architecture and implicit interplay between the types of synaptic plasticity and neuronal specificity are exhibited by some neocortical and cerebellar systems. Received: 13 October 1996 / Accepted in revised form: 16 October 1997     

Neural network programming in bioprocess variable estimation and state prediction.

A neural network program with efficient learning ability for bioprocess variable estimation and state prediction was developed. A 3 layer, feed-forward neural network architecture was used, and the program was written in Quick C ver 2.5 for an IBM compatible computer with a 80486/33 MHz processor. A back propagation training algorithm was used based on learning by pattern and momentum in a combination as used to adjust the connection of weights of the neurons in adjacent layers. The delta rule was applied in a gradient descent search technique to minimize a cost function equal to the mean square difference between the target and the network output. A non-linear, sigmoidal logistic transfer function was used in squashing the weighted sum of the inputs of each neuron to a limited range output. A good neural network prediction model was obtained by training with a sequence of past time course data of a typical bioprocess. The well trained neural network estimated accurately and rapidly the state variables with or without noise even under varying process dynamics.     

Learning multiple routes in homing pigeons

The aerial lifestyle of central-place foraging birds allows wide-ranging movements, raising fundamental questions about their remarkable navigation and memory systems. For example, we know that pigeons (Columba livia), long-standing models for avian navigation, rely on individually distinct routes when homing from familiar sites. But it remains unknown how they cope with the task of learning several routes in parallel. Here, we examined how learning multiple routes influences homing in pigeons. We subjected groups of pigeons to different training protocols, defined by the sequence in which they were repeatedly released from three different sites, either sequentially, in rotation or randomly. We observed that pigeons from all groups successfully developed and applied memories of the different release sites (RSs), irrespective of the training protocol, and that learning several routes in parallel did not impair their capacity to quickly improve their homing efficiency over multiple releases. Our data also indicated that they coped with increasing RS uncertainty by adjusting both their initial behaviour upon release and subsequent homing efficiency. The results of our study broaden our understanding of avian route following and open new possibilities for studying learning and memory in free-flying animals.     

Can the antCataglyphis cursor (Hymenoptera: Formicidae) encode global landmark-landmark relationships in addition to isolated landmark-goal relationships?

The antCataglyphis cursor was tested for its landmark-based homing in a laboratory setting. Workers were induced to go down a tube at the center of an arena to forage. On the periphery of the arena were four different black shapes serving as the only distinguishing visual landmarks, i.e., a cross, a circle, a triangle, and a square. The purpose was to show that the spatial memory of ants represents something of the overall arrangement of landmarks. When first released into the arena, the ants were not oriented toward home in their navigation. After 2 days of free access in the usual landmark setup, the ants learned to orient rapidly significantly goalward. When landmarks were all removed, they did not orient in any direction significantly. When the landmarks were rotated by 90°, their compass positions were changed but their relative positions maintained, and the ants rotated their heading by a similar amount. This rotated homing direction implies that the array of landmarks was used as the only source of directional determination. When the landmark nearest their home was absent, but the other three were in their usual places, the ants were slightly homeward oriented at one-quarter of the way, but not at one-half of the way when the other landmarks were behind them. When the landmarks were randomly permuted, both their compass positions and their overall spatial relationships were altered, and the ants were not significantly oriented in any direction. These results indicate that spatial memory in the antC. cursor encodes global landmark-landmark relations. Thus, ants can abstract certain topological properties of their environment.     

A recurrent network for landmark-based navigation

A new type of network is proposed that can be applied to landmark navigation. It solves the guidance task, that is, it finds a nonvisually marked location using knowledge concerning its spatial relation to other, visible landmarks. The path to the searched location is not disturbed if a landmark is not visible for some time. The network can also describe findings obtained by experiments with insects and rodents, where the position of the landmarks has been changed after training. In this net, recognition does not occur by searching for a match between a pattern seen and the same pattern being stored but by searching for a match between a pattern seen with a prediction calculated from different data. A simple extension allows a unique match of the landmarks seen with the items stored in memory. With this extension a recognition of the individual landmark is not necessary. A specific output unit of the network can be interpreted in such a way as to show properties of place cells found in vertebrates and the function of the network proposed here as to determine the input to a place cell. The model can explain the observation that a given place cell can also be active when the animal moves in a different environment. An extension is discussed of how the network could be exploited for recognition-triggered response that allows animals to follow fixed routes.     

Stable panoramic views facilitate snap-shot like memories for spatial reorientation in homing pigeons

Following spatial disorientation, animals can reorient themselves by relying on geometric cues (metric and sense) specified both by the macroscopic surface layout of an enclosed space and prominent visual landmarks in arrays. Whether spatial reorientation in arrays of landmarks is based on explicit representation of the geometric cues is a matter of debate. Here we trained homing pigeons (Columba livia) to locate a food-reward in a rectangular array of four identical or differently coloured pipes provided with four openings, only one of which allowed the birds to have access to the reward. Pigeons were trained either with a stable or a variable position of the opening on pipes, so that they could view the array either from the same or a variable perspective. Explicit mapping of configural geometry would predict successful reorientation irrespective of access condition. In contrast, we found that a stable view of the array facilitated spatial learning in homing pigeons, likely through the formation of snapshot-like memories.     

Convergence analysis of cascade error projection--an efficient learning algorithm for hardware implementation

In this paper, we present a mathematical foundation, including a convergence analysis, for cascading architecture neural network. Our analysis also shows that the convergence of the cascade architecture neural network is assured because it satisfies Liapunov criteria, in an added hidden unit domain rather than in the time domain. From this analysis, a mathematical foundation for the cascade correlation learning algorithm can be found. Furthermore, it becomes apparent that the cascade correlation scheme is a special case from mathematical analysis in which an efficient hardware learning algorithm called Cascade Error Projection(CEP) is proposed. The CEP provides efficient learning in hardware and it is faster to train, because part of the weights are deterministically obtained, and the learning of the remaining weights from the inputs to the hidden unit is performed as a single-layer perceptron learning with previously determined weights kept frozen. In addition, one can start out with zero weight values (rather than random finite weight values) when the learning of each layer is commenced. Further, unlike cascade correlation algorithm (where a pool of candidate hidden units is added), only a single hidden unit is added at a time. Therefore, the simplicity in hardware implementation is also achieved. Finally, 5- to 8-bit parity and chaotic time series prediction problems are investigated; the simulation results demonstrate that 4-bit or more weight quantization is sufficient for learning neural network using CEP. In addition, it is demonstrated that this technique is able to compensate for less bit weight resolution by incorporating additional hidden units. However, generation result may suffer somewhat with lower bit weight quantization.     

Connectionistic models of boolean category representation

Several distinct connectionistic/neural representations capable of computing arbitrary Boolean functions are described and discussed in terms of possible tradeoffs between time, space, and expressive clarity. It is suggested that the ability of a threshold logic unit (TLU) to represent prototypical groupings has significant advantages for representing real world categories. Upper and lower bounds on the number of nodes needed for Boolean completeness are demonstrated. The necessary number of nodes is shown to increase exponentially with the number of input features, the exact rate of increase depending on the representation scheme. In addition, in non-recurrent networks, connection weights are shown to increase exponentially with a linear reduction in the number of nodes below approximately 2^d. This result suggests that optimum memory efficiency may require unacceptable learning time. Finally, two possible extensions to deal with non-Boolean values are considered.     

A hybrid neural network of addressable and content-addressable memory

We investigate the memory structure and retrieval of the brain and propose a hybrid neural network of addressable and content-addressable memory which is a special database model and can memorize and retrieve any piece of information (a binary pattern) both addressably and content-addressably. The architecture of this hybrid neural network is hierarchical and takes the form of a tree of slabs which consist of binary neurons with the same array. Simplex memory neural networks are considered as the slabs of basic memory units, being distributed on the terminal vertexes of the tree. It is shown by theoretical analysis that the hybrid neural network is able to be constructed with Hebbian and competitive learning rules, and some other important characteristics of its learning and memory behavior are also consistent with those of the brain. Moreover, we demonstrate the hybrid neural network on a set of ten binary numeral patters     

A neuromorphic architecture for object recognition and motion anticipation using burst-STDP

In this work we investigate the possibilities offered by a minimal framework of artificial spiking neurons to be deployed in silico. Here we introduce a hierarchical network architecture of spiking neurons which learns to recognize moving objects in a visual environment and determine the correct motor output for each object. These tasks are learned through both supervised and unsupervised spike timing dependent plasticity (STDP). STDP is responsible for the strengthening (or weakening) of synapses in relation to pre- and post-synaptic spike times and has been described as a Hebbian paradigm taking place both in vitro and in vivo. We utilize a variation of STDP learning, called burst-STDP, which is based on the notion that, since spikes are expensive in terms of energy consumption, then strong bursting activity carries more information than single (sparse) spikes. Furthermore, this learning algorithm takes advantage of homeostatic renormalization, which has been hypothesized to promote memory consolidation during NREM sleep. Using this learning rule, we design a spiking neural network architecture capable of object recognition, motion detection, attention towards important objects, and motor control outputs. We demonstrate the abilities of our design in a simple environment with distractor objects, multiple objects moving concurrently, and in the presence of noise. Most importantly, we show how this neural network is capable of performing these tasks using a simple leaky-integrate-and-fire (LIF) neuron model with binary synapses, making it fully compatible with state-of-the-art digital neuromorphic hardware designs. As such, the building blocks and learning rules presented in this paper appear promising for scalable fully neuromorphic systems to be implemented in hardware chips.     

A new neural network architecture with associative memory, pruning and order-sensitive learning

A new paradigm of neural network architecture is proposed that works as associative memory along with capabilities of pruning and order-sensitive learning. The network has a composite structure wherein each node of the network is a Hopfield network by itself. The Hopfield network employs an order-sensitive learning technique and converges to user-specified stable states without having any spurious states. This is based on geometrical structure of the network and of the energy function. The network is so designed that it allows pruning in binary order as it progressively carries out associative memory retrieval. The capacity of the network is 2n, where n is the number of basic nodes in the network. The capabilities of the network are demonstrated by experimenting on three different application areas, namely a Library Database, a Protein Structure Database and Natural Language Understanding.     

Avoiding catastrophic forgetting by coupling two reverberating neural networks

Gradient descent learning procedures are most often used in neural network modeling. When these algorithms (e.g., backpropagation) are applied to sequential learning tasks a major drawback, termed catastrophic forgetting (or catastrophic interference), generally arises: when a network having already learned a first set of items is next trained on a second set of items, the newly learned information may completely destroy the information previously learned. To avoid this implausible failure, we propose a two-network architecture in which new items are learned by a first network concurrently with internal pseudo-items originating from a second network. As it is demonstrated that these pseudo-items reflect the structure of items previously learned by the first network, the model thus implements a refreshing mechanism using the old information. The crucial point is that this refreshing mechanism is based on reverberating neural networks which need only random stimulations to operate. The model thus provides a means to dramatically reduce retroactive interference while conserving the essentially distributed nature of information and proposes an original but plausible means to ‘copy and paste’ a distributed memory from one place in the brain to another.     

Are binary synapses superior to graded weight representations in stochastic attractor networks?

Synaptic plasticity is an underlying mechanism of learning and memory in neural systems, but it is controversial whether synaptic efficacy is modulated in a graded or binary manner. It has been argued that binary synaptic weights would be less susceptible to noise than graded weights, which has impelled some theoretical neuroscientists to shift from the use of graded to binary weights in their models. We compare retrieval performance of models using both binary and graded weight representations through numerical simulations of stochastic attractor networks. We also investigate stochastic attractor models using multiple discrete levels of weight states, and then investigate the optimal threshold for dilution of binary weight representations. Our results show that a binary weight representation is not less susceptible to noise than a graded weight representation in stochastic attractor models, and we find that the load capacities with an increasing number of weight states rapidly reach the load capacity with graded weights. The optimal threshold for dilution of binary weight representations under stochastic conditions occurs when approximately 50% of the smallest weights are set to zero.     

Conditions for landmark-based navigation in the house mouse, Mus musculus

I investigated whether mice, after learning to home by relying on visual extra-arena landmarks, still required instantaneous access to such cues for successful navigation. Two groups of lactating mice were trained to retrieve their pups from the centre of a circular arena back to their peripheral nest. On test trials, mice from one group were allowed to view distal visual cues while moving from the nest towards the centre, and mice from the other group were allowed to view distal visual cues when homing from the centre towards the nest. The results indicate that viewing the visual cues when homing is necessary for landmark-based navigation.     

Unilateral Lateral Entorhinal Inactivation Impairs Memory Expression in Trace Eyeblink Conditioning

Memory in trace eyeblink conditioning is mediated by an inter-connected network that involves the hippocampus (HPC), several neocortical regions, and the cerebellum. This network reorganizes after learning as the center of the network shifts from the HPC to the medial prefrontal cortex (mPFC). Despite the network reorganization, the lateral entorhinal cortex (LEC) plays a stable role in expressing recently acquired HPC-dependent memory as well as remotely acquired mPFC-dependent memory. Entorhinal involvement in recent memory expression may be attributed to its previously proposed interactions with the HPC. In contrast, it remains unknown how the LEC participates in memory expression after the network disengages from the HPC. The present study tested the possibility that the LEC and mPFC functionally interact during remote memory expression by examining the impact of pharmacological inactivation of the LEC in one hemisphere and the mPFC in the contralateral hemisphere on memory expression in rats. Memory expression one day and one month after learning was significantly impaired after LEC-mPFC inactivation; however, the degree of impairment was comparable to that after unilateral LEC inactivation. Unilateral mPFC inactivation had no effect on recent or remote memory expression. These results suggest that the integrity of the LEC in both hemispheres is necessary for memory expression. Functional interactions between the LEC and mPFC should therefore be tested with an alternative design.