Frontiers in Computational Neuroscience

Neuroscience-inspired neural networks bridge biology and technology, offering powerful tools to model brain function while enabling adaptive, efficient control in robotics. In this work, we present a neuroscience-inspired synaptic learning rule based on the synchronization of synaptic inputs to single excitatory neurons within a feedforward spiking neural network. The model consists of three excitatory layers and two feedback inhibitory layers, with initially low connection probabilities and weak synaptic weights assigned to the excitatory neurons. Under an unsupervised learning paradigm, stimulus patterns were presented to the network, allowing synaptic weights and connectivity to evolve dynamically across training trials. We investigated how these dynamics depended on feedback inhibition intensity and identified conditions under which the network achieved stable activity. Furthermore, we evaluated the models pattern separation efficacy and its relationship to network dynamics. The results highlight the critical role of feedback inhibition in both stabilizing the network and enhancing pattern separation. In particular, results show balanced synchronization between excitatory and inhibitory populations maximizes separation efficacy. Beyond providing a novel computational framework for understanding information processing in neural systems, this model also offers insights into cognitive disorders associated with impaired inhibition and pattern separation, such as autism and schizophrenia. Finally, we embedded the trained network within a simulated agent navigating a two-dimensional environment, where it was tasked with identifying a trained stimulus as an obstacle and avoiding it. The model offers a framework for advancing cognitive robotics by enabling novel approaches that mimic natural intelligence and support the learning of complex environmental patterns.

Orientation preference maps (OPMs) in the primary visual cortex of primates organize orientation-tuned neurons into columnar structures, forming pinwheel-like patterns. However, lower-level animals like rodents typically exhibit a lack of OPMs, with neurons either randomly distributed or aggregated in small clusters. This distinction prompts an inquiry into whether more structured cortical columns correlate with improved visual computational or coding efficiency. To explore this, we propose a novel self-evolving spiking neural network (SESNN). To the best of our knowledge, the SESNN is the first spiking network, incorporating mechanisms of neural plasticity in forming neural connections without explicit objective functions. We reveal that the emergence of pinwheel structures is primarily driven by sparse coding constraints and local synaptic plasticity as fundamental mechanisms. Second, for higher mammals with expansive iso-orientation domains (IODs), the firing responses in pinwheel structures primarily emanate from pinwheel centers (PCs) and progressively extend toward the periphery, encompassing adjacent IODs. Third, the size and organization of these IODs across species are significantly influenced by the receptive fields ability to process overlapping visual information. Lastly, PCs within large IODs demonstrate enhanced robustness and population sparseness in detecting a variety of orientation features. These results indicate that the spatial pinwheel structure facilitates highly efficient and reliable coding performance.

Equilibrium propagation (EP) is a biologically plausible alternative to backpropagation that has demonstrated competitive performance across a range of machine learning tasks. Recent work has extended EP to spiking neural networks (SNNs), leveraging leaky integrate-and-fire (LIF) neurons and spike-based plasticity rules to improve biological realism while maintaining strong performance. In this work, we propose an EP-based SNN framework that combines LIF neural dynamics with a predictive learning rule, replacing conventional spike-timing-dependent plasticity (STDP) with a learning rule more directly aligned with predictive coding principles. We evaluate the proposed model on multiple image classification benchmarks, including MNIST, KMNIST, and Fashion-MNIST, and compare its performance with a BP-trained LIF SNN baseline. Our results show that the proposed EP-based LIF model (EP+LIF) achieves competitive accuracy across datasets, with performance approaching that of the BP-trained counterpart (BP+LIF) while relying on a biologically motivated local learning rule. In addition, analysis of hidden-layer spiking activity reveals that EP+LIF produces more persistent hidden-state activity, whereas BP+LIF yields sparser spiking representations. These results demonstrate that predictive learning can support effective EP-based training in LIF spiking networks, while also highlighting differences in activity patterns that motivate future work on activity regulation and sparse spiking dynamics.

Neurons in visual and vestibular information integration areas of macaque brain such as medial superior temporal (MSTd) and ventral intraparietal (VIP) have been classified into congruent neurons and opposite neurons, which prefer congruent inputs and opposite inputs from the two sensory modalities, respectively. In this work, we propose a mechanistic spiking neural model that can account for the emergence of congruent and opposite neurons and their interactions in a neural circuit for multi-sensory integration. The spiking neural circuit model is adopted from an established model for the circuits of the primary visual cortex with little changes in parameters. The network can learn, based on the basic Hebbian learning principle, the correct topological organization and behaviors of the congruent and opposite neurons that have been proposed to play a role in multi-sensory integration. This work explore the constraints and the conditions that lead to the development of a proposed neural circuit for cue integration. It also demonstrates that such neural circuit might indeed be a canonical circuit shared by computations in many cortical areas.

Although there is a plethora of modelling literature dedicated to the object recognition processes of the ventral ("what") pathway of primate visual systems, modelling studies on the motion sensitive regions like the Medial superior temporal area (MST) of the dorsal ("where") pathway are relatively scarce. Neurons in the MST area of the macaque monkey respond selectively to different types of optic flow sequences such as radial and rotational flows. We present three models that are designed to simulate the computation of optic flow performed by the MST neurons in primates. The first two models are each composed of 3 stages: the first stage comprises the Direction Selective Mosaic Network (DSMN), the second stage comprises the Cell Plane Network (CPNW) or the Hebbian Network (HBNW) and the third stage comprises the optic flow network (OF). The three stages roughly correspond to V1-MT-MST areas respectively in the primate motion pathway. Both these models are trained stage by stage using a biologically plausible variation of Hebbian learning. On the other hand, model-3 consists of the Velocity Selective Mosaic Network (VSMN) followed by a convolutional neural network (CNN) which is trained using supervised backpropagation algorithm. We created various dot configurations that can move in translational, radial, and rotational trajectories to make training and test set. The simulation results show that, while neurons in model-1 and model-2 could account for MSTd cell properties found neurobiologically, model-3 neuron responses are consistent with the idea of functional hierarchy in the macaque motion pathway. These results also suggest that the deep learning models could offer a computationally elegant and biologically plausible solution to simulate the development of cortical responses of the primate motion pathway.

Human cognition is characterized by a wide range of capabilities including goal-oriented selective attention, distractor suppression, decision making, response inhibition, and working memory. Much research has focused on studying these individual components of cognition in isolation, whereas in several translational applications for cognitive impairment, multiple cognitive functions are altered in a given individual. Hence it is important to study multiple cognitive abilities in the same subject or, in computational terms, model them using a single model. To this end, we propose a unified, reinforcement learning-based agent model comprising of systems for representation, memory, value computation and exploration. We successfully modelled the aforementioned cognitive tasks and show how individual performance can be mapped to model meta-parameters. This model has the potential to serve as a proxy for cognitively impaired conditions, and can be used as a clinical testbench on which therapeutic interventions can be simulated first before delivering to human subjects.

The primary visual cortex (V1) of high-level animals exhibits a complex organization of neuronal orientation preferences, characterized by pinwheel structure topology, yet the functional role of those complex patterns in natural image representation remains largely unexplored. Our study first establishes a new self-evolving spiking neural network (SESNN) model, designed to mimic the functional topological structure of orientation selectivity within V1. We observe the emergence of a particularly new "spread-out" firing patterns from center to the surround of the pinwheel structures in response to natural visual stimuli in pinwheel structures, propagating from pinwheel centers and spreading to iso-orientation domains--a pattern not found in salt- and-pepper organizations. To investigate this phenomenon, we propose a novel deep recurrent U-Net architecture to reconstruct images from V1s spiking activity across time steps and assess the encoded information entropy of different firing patterns via the models predicted uncertainty, offering a spatiotemporal analysis of V1s functional structures. Our findings reveal a trade-off between visual acuity and coding time: the "spread-out" pattern enhances the representation of complex visual details at the cost of increased response latency, while salt-and-pepper organizations, lacking such domains, prioritize rapid processing at the expense of reduced visual acuity. Additionally, we demonstrate that this trade-off is modulated by the size of iso-orientation domains, with larger domains--supported by denser neuronal populations--substantially improving both visual acuity, coding efficiency, and robustness, features diminished in smaller domains and salt-and-pepper arrangements. Our research provides a foundational understanding of the principles underlying efficient visual information representation and suggests novel strategies for advancing the robustness and performance of image recognition algorithms in artificial intelligence.

The basal ganglia (BG) is part of a basic feedback circuit, regulating cortical function, such as voluntary movement control, via their influence on thalamocortical projections. BG disorders, namely Parkinsons disease (PD), characterized by the loss of neurons in the substantia nigra, involve the progressive loss of motor functions. At the present, PD is incurable. Converging evidence suggests the onset of PD-specific pathology prior to the appearance of classical motor signs. This latent phase of neurodegeneration in PD is of particular relevance in developing more effective therapies by intervening at the earliest stages of disease. Therefore, a key challenge in PD research is to identify and validate markers for the preclinical and prodromal stage of the illness. We propose a mechanistic neurocomputational model of the BG at mesoscopic scale to investigate the behavior of the simulated neural system after several degrees of lesion of the substantia nigra, with the aim of possibly evaluating which is the smallest lesion compromising motor learning. In other words, we developed a working framework for the analysis of theoretical early-stage PD. While simulations in healthy conditions confirm the key role of dopamine in learning, in pathological conditions networks predict that there may exist abnormalities of motor learning process for physiological alterations in the BG which do not yet involve the presence of symptoms typical of the clinical diagnosis. Our model may account for the discovery of markers for an early diagnosis of the disease and give directions for developing novel noninvasive support systems.

The brain performs visual object recognition using much shallower hierarchical stages than artificial deep neural networks employ. However, the mechanism underlying this cost-efficient function is elusive. Here, we show that cortical long-range connectivity(LRC) may enable this parsimonious organization of circuits for balancing cost and performance. Using model network simulations based on data in tree shrews, we found that sparse LRCs, when added to local connections, organize a small-world network that dramatically enhances object recognition of shallow feedforward networks. We found that optimization of the ratio between LRCs and local connections maximizes the small-worldness and task performance of the network, by minimizing the total length of wiring needed for integration of the global information. We also found that the effect of LRCs varies by network size, which explains the existence of species-specific LRCs in mammalian visual cortex of various sizes. Our results demonstrate a biological strategy to achieve cost-efficient brain circuits. HighlightsO_LILong-range connections (LRCs) enhance the object recognition of shallow networks C_LIO_LISparse LRCs added to dense local connections organize a small-world type network C_LIO_LISmall-worldness of networks modulates the balance between performance and wiring cost C_LIO_LIDistinct LRCs in various species are due to the size-dependent effect of LRCs C_LI Significance statementThe hierarchical depth of the visual pathway in the brain is constrained by biological factors, whereas artificial deep neural networks consist of super-deep structures (i.e., as deep as computational power allows). Here, we show that long-range horizontal connections (LRCs) observed in mammalian visual cortex may enable shallow biological networks to perform cognitive tasks that require deeper artificial structures, by implementing cost-efficient organization of circuitry. Using model simulations based on anatomical data, we found that sparse LRCs, when added to dense local circuits, organize "small-world" type networks and that this dramatically enhances image classification performance by integrating both local and global components of visual stimulus. Our findings show a biological strategy of brain circuitry to balance sensory performance and wiring cost in the networks. One sentence summaryCortical long-range connections organize a small-world type network to achieve cost-efficient functional circuits under biological constraints

While artificial machine learning systems achieve superhuman performance in specific tasks such as language processing, image and video recognition, they do so use extremely large datasets and huge amounts of power. On the other hand, the brain remains superior in several cognitively challenging tasks while operating with the energy of a small lightbulb. We use a biologically constrained spiking neural network model to explore how the neural tissue achieves such high efficiency and assess its learning capacity on discrimination tasks. We found that synaptic turnover, a form of structural plasticity, which is the ability of the brain to form and eliminate synapses continuously, increases both the speed and the performance of our network on all tasks tested. Moreover, it allows accurate learning using a smaller number of examples. Importantly, these improvements are most significant under conditions of resource scarcity, such as when the number of trainable parameters is halved and when the task difficulty is increased. Our findings provide new insights into the mechanisms that underlie efficient learning in the brain and can inspire the development of more efficient and flexible machine learning algorithms.

We present a deep network-based model of the associative memory functions of the hippocampus. The proposed network architecture has two key modules: 1) an autoencoder module which represents the forward and backward projections of the cortico-hippocampal projections and 2) a module that computes familiarity of the stimulus and implements hill-climbing over the familiarity which represents the dynamics of the loops within the hippocampus. The proposed network is used in two simulation studies. In the first part of the study, the network is used to simulate image pattern completion by autoassociation under normal conditions. In the second part of the study, the proposed network is extended to a heteroassociative memory and is used to simulate picture naming task in normal and Alzheimers disease (AD) conditions. The network is trained on pictures and names of digits from 0 - 9. The encoder layer of the network is partly damaged to simulate AD conditions. As in case of AD patients, under moderate damage condition, the network recalls superordinate words ("odd" instead of "nine"). Under severe damage conditions, the network shows a null response ("I dont know"). Neurobiological plausibility of the model is extensively discussed.

Sensorimotor adaptation enables us to adjust our goal-oriented movements in response to external perturbations. These phenomena have been studied experimentally and computationally at the level of human and animals reaching movements, and have clear links to the cerebellum as evidenced by cerebellar lesions and neurodegeneration. Yet, despite our macroscopic understanding of the high-level computational mechanisms it is unclear how these are mapped and are implemented in the neural substrates of the cerebellum at a cellular-computational level. We present here a novel spiking neural circuit model of the sensorimotor system including a cerebellum which control physiological muscle models to reproduce behaviour experiments. Our cerebellar model is composed of spiking neuron populations reflecting cells in the cerebellar cortex and deep cerebellar nuclei, which generate motor correction to change behaviour in response to perturbations. The model proposes two learning mechanisms for adaptation: predictive learning and memory formation, which are implemented with synaptic updating rules. Our model is tested in a force-field sensorimotor adaptation task and successfully reproduce several phenomena arising from human adaptation, including well-known learning curves, aftereffects, savings and other multi-rate learning effects. This reveals the capability of our model to learn from perturbations and generate motor corrections while providing a bottom-up view for the neural basis of adaptation. Thus, it also shows the potential to predict how patients with specific types of cerebellar damage will perform in behavioural experiments. We explore this by in silico experiments where we selectively incapacitate selected cerebellar circuits of the model which generate and reproduce defined motor learning deficits. Author summaryA rich body of work in human motor neuroscience developed high-level computational theories of sensorimotor control, learning and adaptation. But there is a gap in understanding how this may be implemented and learn on the level of neurons, synapses and spikes. Conversely, studies of patients with cerebellar lesions or neurological disease highlight the essential role the cerebellum plays in our ability to perform motor learning. Yet, how these anatomical and molecular defects play out in terms of human movement have to date not been linked to a model that spans multiple level of biological organisation from neural circuits to reproducing human motor experiments. To address this gap, we present a spiking neuron of the sensorimotor system focused on the cerebellum, with which we can on the one side reproduce the high-level behaviour learning phenomena observed in healthy subjects, as well as quantitatively predicting the putative effects on human movement trajectories of cerebellar lesions implemented at the cellular level.

Continuous persist activity of the competitive network is related to many functions, such as working memory, oculomotor integrator and decision making. Many competition models with mutual inhibition structures achieve activity maintenance via positive feedback, which requires meticulous fine tuning of the network parameters strictly. Negative derivative feedback, according to recent research, might represent a novel mechanism for sustaining neural activity that is more resistant to multiple neural perturbations than positive feedback. Many classic models with only mutual inhibition structure are not capable of providing negative derivative feedback because double-inhibition acts as a positive feedback loop, and lack of negative feedback loop that is indispensable for negative derivative feedback. Here in the proposal, we aim to derive a new competition network with negative derivative feedback. The network is made up of two symmetric pairs of EI populations that the four population are completely connected. We conclude that the negative derivative occurs in two circumstances, in which one the activity of the two sides is synchronous but push-pull-like in the other, as well as the switch of two conditions in mathematical analysis and numerical simulation.

Spiking Neural Networks (SNNs) have the potential to replicate the brains computational efficacy by explicitly incorporating action potentials or "spikes", which is not a feature of most artificial neural networks. However, training SNNs is difficult due to the non-differentiable nature of the most common spiking models: integrate-and-fire neurons. This study investigates if some of the difficulty in training SNNs arises from the use of integrate-and-fire neurons, rather than smoother alternatives, like conductance-based neurons. To that end, we considered networks of Morris-Lecar (ML) neurons, a conductance-based neuron model which is differentiable. Networks were built using kinetic synaptic models that smoothly link presynaptic voltage dynamics directly to postsynaptic conductance changes, ensuring that all components remain fully differentiable. Switching to biophysically detailed models of synapses and neurons enabled direct end-to-end training through Backpropagation Through Time (BPTT). Biophysically detailed networks were successfully trained on image classification, regression, and time series prediction tasks. These results demonstrate the feasibility of employing biophysically detailed differentiable point neuron models to create SNNs that function as more accurate paradigms for the study of neural computations and learning. Further, this work confirms that some aspects of the difficulty in translating gradient-based learning algorithms from machine learning may arise from model choice, rather than SNNs being intrinsically difficult to train. 1. Author summaryThe brains information-processing efficiency arises in part from neurons communicating via discrete spikes. Spiking Neural Networks (SNNs) mimic this process at the neuronal level but have been difficult to train as most machine learning algorithms are not directly applicable. Most SNNs use integrate-and-fire neurons, a modelling framework that simplifies spikes into non-differentiable, abrupt voltage changes, which makes them difficult to train with powerful, standard AI training methods that use derivatives to compute gradients (e.g. Backprop). In our work, we asked if this difficulty could be overcome by considering end-to-end differentiable spiking neural networks. We used completely differentiable SNNs using the Morris-Lecar neuron, a biophysically detailed neuron model that produces smooth spikes, along with differentiable kinetic synapses. With the entire network being mathematically differentiable, we found that we could train it directly using standard backpropagation through time on different tasks (regression, classification, and chaotic time series prediction). This work demonstrates that the use of integrate-and-fire models may be limiting applications of machine learning algorithms towards understanding how learning functions in the brain.

In this paper we introduce a novel Salience Affected Artificial Neural Network (SANN) that models the way neuromodulators such as dopamine and noradrenaline affect neural dynamics in the human brain by being distributed diffusely through neocortical regions. This allows one-time learning to take place through strengthening entire patterns of activation at one go. We present a model that accepts a salience signal, and returns a reverse salience signal. We demonstrate that we can tag an image with salience with only a single training iteration, and that the same image will then produces the highest reverse salience signal during classification. We explore the effects of salience on learning via its effect on the activation functions of each node, as well as on the strength of weights in the network. We demonstrate that a salience signal improves classification accuracy of the specific image that was tagged with salience, as well as all images in the same class, while penalizing images in other classes. Results are validated using 5-fold validation testing on MNIST and Fashion MNIST datasets. This research serves as a proof of concept, and could be the first step towards introducing salience tagging into Deep Learning Networks and robotics.

Normal functioning of the brain relies on a continual and efficient delivery of energy by a vast network of cerebral blood vessels. The bidirectional coupling between neurons and blood vessels consists of vasodilatory energy demand signals from neurons to blood vessels, and the retrograde flow of energy substrates from the vessels to neurons, which fuel neural firing, growth and other housekeeping activities in the neurons. Recent works indicate that, in addition to the functional coupling observed in the adult brain, the interdependence between the neural and vascular networks begins at the embryonic stage, and continues into subsequent developmental stages. The proposed Vascular Arborization Model (VAM) captures the effect of neural cytoarchitecture and neural activity on vascular arborization. The VAM describes three important stages of vascular tree growth: (i) The prenatal growth phase, where the vascular arborization depends on the cytoarchitecture of neurons and non-neural cells, (ii) the post-natal growth phase during which the further arborization of the vasculature depends on neural activity in addition to neural cytoarchitecture, and (iii) the settling phase, where the fully grown vascular tree repositions its vascular branch points or nodes to ensure minimum path length and wire length. The vasculature growth depicted by VAM captures structural characteristics like vascular volume density, radii, mean distance to proximal neurons in the cortex. VAM-grown vasculature agrees with the experimental observation that the neural densities do not covary with the vascular density along the depth of the cortex but predicts a high correlation between neural areal density and microvascular density when compared over a global scale (across animals and regions). To explore the influence of neural activity on vascular arborization, the VAM was used to grow the vasculature in neonatal rat whisker barrel cortex under two conditions: (i) Control, where the whiskers were intact and (ii) Lesioned, where one row of whiskers was cauterized. The model captures a significant reduction in vascular branch density in lesioned animals compared to control animals, concurring with experimental observation.

This research report introduces ElegansNet, a neural network that mimics real-world neuronal network circuitry, with the goal of better understanding the interplay between connectome topology and deep learning systems. The proposed approach utilizes the powerful representational capabilities of living beings neuronal circuitry to design and generate improved deep learning systems with a topology similar to natural networks. The Caenorhabditis elegans connectome is used as a reference due to its completeness, reasonable size, and functional neuron classes annotations. It is demonstrated that the connectome of simple organisms exhibits specific functional relationships between neurons, and once transformed into learnable tensor networks and integrated into modern architectures, it offers bio-plausible structures that efficiently solve complex tasks. The performance of the models is demonstrated against randomly wired networks and compared to artificial networks ranked on global benchmarks. In the first case, ElegansNet outperforms randomly wired networks. Interestingly, ElegansNet models show slightly similar performance with only those based on the Watts-Strogatz small-world property. When compared to state-of-the-art artificial neural networks, such as transformers or attention-based autoencoders, ElegansNet outperforms well-known deep learning and traditional models in both supervised image classification tasks and unsupervised hand-written digits reconstruction, achieving top-1 accuracy of 99.99% on Cifar10 and 99.84% on MNIST Unsup on the validation sets.

Faces contain both identity and personality trait information. Previous studies have found that convolutional neural networks trained for face identity recognition spontaneously generate personality trait information. However, the successful classification of different personality traits does not necessarily mean that convolutional neural networks adopt brain-like representation mechanisms to achieve the same computational goals. Our study found that convolutional neural network with visual experience in face identity recognition (VGG-face) exhibited brain-like neural representations of personality traits, including coupling effects and confusion effects, while convolutional neural networks with the same network architecture but lacked visual experience for face identity recognition (VGG-16 and VGG-untrained) did not exhibit brain-like effects. In addition, compared to the VGG-16 and the VGG-untrained, the VGG-face exhibited higher similarity in neural representations with the human brain across all individual personality traits. In summary, these findings revealed the necessity of visual experience in face identity recognition for developing face personality traits judgment.

Recurrent neural networks (RNNs) have proven to be highly successful in emulating human-like cognitive functions such as working memory. In recent years, RNNs are evolving to incorporate more biophysical realism to produce more plausible predictions on how cognitive tasks are solved in real neural circuits. However, there are major challenges in constructing and training networks with the complex and nonlinear properties of real neurons. A major component of the success of RNNs is that they share the same mathematical base as deep neural networks, permitting highly efficient optimization of model parameters using standard deep learning techniques. To do so, they use abstract representations of neurons which fail to capture the impact of cell-level biophysical and morphologic properties that may benefit network-level function. Expanding task-trained RNNs with biophysical properties such as dendrites and active ionic currents poses substantial challenges, as it moves these models away from the validated training regimes known to be highly effective for RNNs. To address this gap, we developed a biophysically detailed reservoir computing (BRC) framework with the goal of extracting mechanistic insights from biophysical neural models, and propose that these insights can be used to guide model choices that will work for specific categories of cognitive tasks. The BRC network was constructed with synaptically coupled excitatory and inhibitory cells, in which the excitatory cells include multicompartment biophysically active dendrites; motivated by empirical studies suggesting dendrites have desirable computational benefits (e.g. pattern classification and coincidence detection). We trained the BRC network to do a simplified working memory task where it had to maintain the representation of an extrinsic "cue" input. We studied the impact of extrinsic input time constants (fast AMPA vs slow NMDA) and location (dendrite vs soma) on the ability of a network to solve the task. Our results revealed that cue inputs through NMDA receptors are particularly efficient for solving the working memory task. Further, the properties of NMDA receptors are uniquely suited for cue inputs delivered at the dendrite, as networks trained with dendritic AMPA cue inputs failed to solve the task. Detailed examination of the cell and network dynamics that solve the task reveals distinct local network configurations and computing principles for the different types of extrinsic input. Overall, much like the body of mechanistic insights that have underpinned the success of training RNNs, this study lays the groundwork for applying the BRC framework to train biophysically detailed neural models to solve complex human-like cognitive tasks.

We present a model of a tonotopic map known as the Oscillatory Tonotopic Self-Organizing Map (OTSOM). It is a 2-dimensional, self-organizing array of Hopf oscillators, capable of performing a Fourier-like decomposition of the input signal. While the rows in the map encode the input phase, the columns encode frequency. Although Hopf oscillators exhibit resonance to a sinusoidal signal when there is a frequency match, there is no obvious way to also achieve phase tuning. We propose a simple method by which a pair of Hopf oscillators, unilaterally coupled through a coupling scheme termed as modified power coupling, can exhibit tuning to the phase offset of sinusoidal forcing input. The training of OTSOM is performed in 2 stages: while the frequency tuning is adapted in stage 1, phase tuning is adapted in stage 2. Earlier tonotopic map models have modeled frequency as an abstract parameter unconnected to any oscillation. By contrast, in OTSOM, frequency tuning emerges as a natural outcome of an underlying resonant process. The OTSOM model can be regarded as an approximation of the tonotopic map found in the primary auditory cortices of mammals, particularly exemplified in the studies of echolocating bats.