Chris Eliasmith

Karim Habashy, Chris Eliasmith

Vector Symbolic Algebras (VSAs) enable robust neurosymbolic reasoning by encoding symbolic information into high-dimensional distributed representations. For continuous domains, Spatial Semantic Pointers (SSPs) extend this framework by mapping variables onto continuous toroidal manifolds. However, standard approaches like Flow Matching assume a flat Euclidean geometry, which fails to account for the geometric constraints imposed on valid SSP states. We demonstrate that this assumption fails for SSPs: Euclidean linear interpolants ``cut through" the manifold's interior, destroying the phase and magnitude structure required for accurate decoding. To resolve this, we employ Geodesic Flow Matching, adapting Riemannian transport dynamics to strictly restrict the denoising flow to the SSP toroidal manifold. We validate this approach in a Spiking Neural SLAM system, showing that manifold-aware cleanup stabilizes path integration against drift. The method achieves a 72\% reduction in tracking error and enables a 40\% increase in neural efficiency compared to competitive baselines. Code is available at https://github.com/kremHabashy/CleanupSSP .

Narsimha Chilkuri, Chris Eliasmith

In this report we consider the following problem: Given a trained model that is partially faulty, can we correct its behaviour without having to train the model from scratch? In other words, can we ``debug" neural networks similar to how we address bugs in our mathematical models and standard computer code. We base our approach on the hypothesis that debugging can be treated as a two-task continual learning problem. In particular, we employ a modified version of a continual learning algorithm called Orthogonal Gradient Descent (OGD) to demonstrate, via two simple experiments on the MNIST dataset, that we can in-fact \textit{unlearn} the undesirable behaviour while retaining the general performance of the model, and we can additionally \textit{relearn} the appropriate behaviour, both without having to train the model from scratch.

Isaac Joffe, Chris Eliasmith

The Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) is a generative, few-shot fluid intelligence benchmark. Although humans effortlessly solve ARC-AGI, it remains extremely difficult for even the most advanced artificial intelligence systems. Inspired by methods for modelling human intelligence spanning neuroscience to psychology, we propose a cognitively plausible ARC-AGI solver. Our solver integrates System 1 intuitions with System 2 reasoning in an efficient and interpretable process using neurosymbolic methods based on Vector Symbolic Algebras (VSAs). Our solver works by object-centric program synthesis, leveraging VSAs to represent abstract objects, guide solution search, and enable sample-efficient neural learning. Preliminary results indicate success, with our solver scoring 10.8% on ARC-AGI-1-Train and 3.0% on ARC-AGI-1-Eval. Additionally, our solver performs well on simpler benchmarks, scoring 94.5% on Sort-of-ARC and 83.1% on 1D-ARC -- the latter outperforming GPT-4 at a tiny fraction of the computational cost. Importantly, our approach is unique; we believe we are the first to apply VSAs to ARC-AGI and have developed the most cognitively plausible ARC-AGI solver yet. Our code is available at: https://github.com/ijoffe/ARC-VSA-2025.

Varun Dhanraj, Chris Eliasmith

Large language models (LLMs) continue to face challenges in reliably solving reasoning tasks, particularly those that require precise rule following, as often found in mathematical reasoning. This paper introduces a novel neurosymbolic method that improves LLM reasoning by encoding hidden states into neurosymbolic vectors, enabling problem-solving within a neurosymbolic vector space. The results are decoded and merged with the original hidden state, significantly boosting the model's performance on numerical reasoning tasks. By offloading computation through neurosymbolic representations, this method enhances efficiency, reliability, and interpretability. Experimental results demonstrate an average of 88.6% lower cross-entropy loss and 15.4 times more problems correctly solved on a suite of mathematical reasoning tasks compared to chain-of-thought prompting and supervised fine-tuning (LoRA), without degrading performance on other tasks. We make our code available at: https://github.com/vdhanraj/Neurosymbolic-LLM.

Narsimha Chilkuri, Eric Hunsberger, Aaron Voelker et al.

Recent studies have demonstrated that the performance of transformers on the task of language modeling obeys a power-law relationship with model size over six orders of magnitude. While transformers exhibit impressive scaling, their performance hinges on processing large amounts of data, and their computational and memory requirements grow quadratically with sequence length. Motivated by these considerations, we construct a Legendre Memory Unit based model that introduces a general prior for sequence processing and exhibits an $O(n)$ and $O(n \ln n)$ (or better) dependency for memory and computation respectively. Over three orders of magnitude, we show that our new architecture attains the same accuracy as transformers with 10x fewer tokens. We also show that for the same amount of training our model improves the loss over transformers about as much as transformers improve over LSTMs. Additionally, we demonstrate that adding global self-attention complements our architecture and the augmented model improves performance even further.

Kinjal Patel, Eric Hunsberger, Sean Batir et al.

We seek to investigate the scalability of neuromorphic computing for computer vision, with the objective of replicating non-neuromorphic performance on computer vision tasks while reducing power consumption. We convert the deep Artificial Neural Network (ANN) architecture U-Net to a Spiking Neural Network (SNN) architecture using the Nengo framework. Both rate-based and spike-based models are trained and optimized for benchmarking performance and power, using a modified version of the ISBI 2D EM Segmentation dataset consisting of microscope images of cells. We propose a partitioning method to optimize inter-chip communication to improve speed and energy efficiency when deploying multi-chip networks on the Loihi neuromorphic chip. We explore the advantages of regularizing firing rates of Loihi neurons for converting ANN to SNN with minimum accuracy loss and optimized energy consumption. We propose a percentile based regularization loss function to limit the spiking rate of the neuron between a desired range. The SNN is converted directly from the corresponding ANN, and demonstrates similar semantic segmentation as the ANN using the same number of neurons and weights. However, the neuromorphic implementation on the Intel Loihi neuromorphic chip is over 2x more energy-efficient than conventional hardware (CPU, GPU) when running online (one image at a time). These power improvements are achieved without sacrificing the task performance accuracy of the network, and when all weights (Loihi, CPU, and GPU networks) are quantized to 8 bits.

Narsimha Chilkuri, Chris Eliasmith

Recently, a new recurrent neural network (RNN) named the Legendre Memory Unit (LMU) was proposed and shown to achieve state-of-the-art performance on several benchmark datasets. Here we leverage the linear time-invariant (LTI) memory component of the LMU to construct a simplified variant that can be parallelized during training (and yet executed as an RNN during inference), thus overcoming a well known limitation of training RNNs on GPUs. We show that this reformulation that aids parallelizing, which can be applied generally to any deep network whose recurrent components are linear, makes training up to 200 times faster. Second, to validate its utility, we compare its performance against the original LMU and a variety of published LSTM and transformer networks on seven benchmarks, ranging from psMNIST to sentiment analysis to machine translation. We demonstrate that our models exhibit superior performance on all datasets, often using fewer parameters. For instance, our LMU sets a new state-of-the-art result on psMNIST, and uses half the parameters while outperforming DistilBERT and LSTM models on IMDB sentiment analysis.

Yexin Yan, Terrence C. Stewart, Xuan Choo et al.

We implemented two neural network based benchmark tasks on a prototype chip of the second-generation SpiNNaker (SpiNNaker 2) neuromorphic system: keyword spotting and adaptive robotic control. Keyword spotting is commonly used in smart speakers to listen for wake words, and adaptive control is used in robotic applications to adapt to unknown dynamics in an online fashion. We highlight the benefit of a multiply accumulate (MAC) array in the SpiNNaker 2 prototype which is ordinarily used in rate-based machine learning networks when employed in a neuromorphic, spiking context. In addition, the same benchmark tasks have been implemented on the Loihi neuromorphic chip, giving a side-by-side comparison regarding power consumption and computation time. While Loihi shows better efficiency when less complicated vector-matrix multiplication is involved, with the MAC array, the SpiNNaker 2 prototype shows better efficiency when high dimensional vector-matrix multiplication is involved.

Peter Blouw, Gurshaant Malik, Benjamin Morcos et al.

Keyword spotting (KWS) provides a critical user interface for many mobile and edge applications, including phones, wearables, and cars. As KWS systems are typically 'always on', maximizing both accuracy and power efficiency are central to their utility. In this work we use hardware aware training (HAT) to build new KWS neural networks based on the Legendre Memory Unit (LMU) that achieve state-of-the-art (SotA) accuracy and low parameter counts. This allows the neural network to run efficiently on standard hardware (212$μ$W). We also characterize the power requirements of custom designed accelerator hardware that achieves SotA power efficiency of 8.79$μ$W, beating general purpose low power hardware (a microcontroller) by 24x and special purpose ASICs by 16x.

Travis DeWolf, Pawel Jaworski, Chris Eliasmith

In this paper we demonstrate how the Nengo neural modeling and simulation libraries enable users to quickly develop robotic perception and action neural networks for simulation on neuromorphic hardware using familiar tools, such as Keras and Python. We identify four primary challenges in building robust, embedded neurorobotic systems: 1) developing infrastructure for interfacing with the environment and sensors; 2) processing task specific sensory signals; 3) generating robust, explainable control signals; and 4) compiling neural networks to run on target hardware. Nengo helps to address these challenges by: 1) providing the NengoInterfaces library, which defines a simple but powerful API for users to interact with simulations and hardware; 2) providing the NengoDL library, which lets users use the Keras and TensorFlow API to develop Nengo models; 3) implementing the Neural Engineering Framework, which provides white-box methods for implementing known functions and circuits; and 4) providing multiple backend libraries, such as NengoLoihi, that enable users to compile the same model to different hardware. We present two examples using Nengo to develop neural networks that run on CPUs, GPUs, and Intel's neuromorphic chip, Loihi, to demonstrate this workflow. The first example is an end-to-end spiking neural network that controls a rover simulated in Mujoco. The network integrates a deep convolutional network that processes visual input from mounted cameras to track a target, and a control system implementing steering and drive functions to guide the rover to the target. The second example augments a force-based operational space controller with neural adaptive control to improve performance during a reaching task using a real-world Kinova Jaco2 robotic arm. Code and details are provided with the intent of enabling other researchers to build their own neurorobotic systems.

Aaron R. Voelker, Daniel Rasmussen, Chris Eliasmith

The machine learning community has become increasingly interested in the energy efficiency of neural networks. The Spiking Neural Network (SNN) is a promising approach to energy-efficient computing, since its activation levels are quantized into temporally sparse, one-bit values (i.e., "spike" events), which additionally converts the sum over weight-activity products into a simple addition of weights (one weight for each spike). However, the goal of maintaining state-of-the-art (SotA) accuracy when converting a non-spiking network into an SNN has remained an elusive challenge, primarily due to spikes having only a single bit of precision. Adopting tools from signal processing, we cast neural activation functions as quantizers with temporally-diffused error, and then train networks while smoothly interpolating between the non-spiking and spiking regimes. We apply this technique to the Legendre Memory Unit (LMU) to obtain the first known example of a hybrid SNN outperforming SotA recurrent architectures -- including the LSTM, GRU, and NRU -- in accuracy, while reducing activities to at most 3.74 bits on average with 1.26 significant bits multiplying each weight. We discuss how these methods can significantly improve the energy efficiency of neural networks.

Andreas Stöckel, Chris Eliasmith

Nonlinear interactions in the dendritic tree play a key role in neural computation. Nevertheless, modeling frameworks aimed at the construction of large-scale, functional spiking neural networks, such as the Neural Engineering Framework, tend to assume a linear superposition of post-synaptic currents. In this paper, we present a series of extensions to the Neural Engineering Framework that facilitate the construction of networks incorporating Dale's principle and nonlinear conductance-based synapses. We apply these extensions to a two-compartment LIF neuron that can be seen as a simple model of passive dendritic computation. We show that it is possible to incorporate neuron models with input-dependent nonlinearities into the Neural Engineering Framework without compromising high-level function and that nonlinear post-synaptic currents can be systematically exploited to compute a wide variety of multivariate, bandlimited functions, including the Euclidean norm, controlled shunting, and non-negative multiplication. By avoiding an additional source of spike noise, the function-approximation accuracy of a single layer of two-compartment LIF neurons is on a par with or even surpasses that of two-layer spiking neural networks up to a certain target function bandwidth.

Peter Blouw, Xuan Choo, Eric Hunsberger et al.

Using Intel's Loihi neuromorphic research chip and ABR's Nengo Deep Learning toolkit, we analyze the inference speed, dynamic power consumption, and energy cost per inference of a two-layer neural network keyword spotter trained to recognize a single phrase. We perform comparative analyses of this keyword spotter running on more conventional hardware devices including a CPU, a GPU, Nvidia's Jetson TX1, and the Movidius Neural Compute Stick. Our results indicate that for this inference application, Loihi outperforms all of these alternatives on an energy cost per inference basis while maintaining equivalent inference accuracy. Furthermore, an analysis of tradeoffs between network size, inference speed, and energy cost indicates that Loihi's comparative advantage over other low-power computing devices improves for larger networks.

Andreas Stöckel, Aaron R. Voelker, Chris Eliasmith

The mathematical model underlying the Neural Engineering Framework (NEF) expresses neuronal input as a linear combination of synaptic currents. However, in biology, synapses are not perfect current sources and are thus nonlinear. Detailed synapse models are based on channel conductances instead of currents, which require independent handling of excitatory and inhibitory synapses. This, in particular, significantly affects the influence of inhibitory signals on the neuronal dynamics. In this technical report we first summarize the relevant portions of the NEF and conductance-based synapse models. We then discuss a naïve translation between populations of LIF neurons with current- and conductance-based synapses based on an estimation of an average membrane potential. Experiments show that this simple approach works relatively well for feed-forward communication channels, yet performance degrades for NEF networks describing more complex dynamics, such as integration.

Aaron R. Voelker, Chris Eliasmith

We review our current software tools and theoretical methods for applying the Neural Engineering Framework to state-of-the-art neuromorphic hardware. These methods can be used to implement linear and nonlinear dynamical systems that exploit axonal transmission time-delays, and to fully account for nonideal mixed-analog-digital synapses that exhibit higher-order dynamics with heterogeneous time-constants. This summarizes earlier versions of these methods that have been discussed in a more biological context (Voelker & Eliasmith, 2017) or regarding a specific neuromorphic architecture (Voelker et al., 2017).

Eric Hunsberger, Chris Eliasmith

We describe a method to train spiking deep networks that can be run using leaky integrate-and-fire (LIF) neurons, achieving state-of-the-art results for spiking LIF networks on five datasets, including the large ImageNet ILSVRC-2012 benchmark. Our method for transforming deep artificial neural networks into spiking networks is scalable and works with a wide range of neural nonlinearities. We achieve these results by softening the neural response function, such that its derivative remains bounded, and by training the network with noise to provide robustness against the variability introduced by spikes. Our analysis shows that implementations of these networks on neuromorphic hardware will be many times more power-efficient than the equivalent non-spiking networks on traditional hardware.

Chris Eliasmith, Jan Gosmann, Xuan Choo

We describe a large-scale functional brain model that includes detailed, conductance-based, compartmental models of individual neurons. We call the model BioSpaun, to indicate the increased biological plausibility of these neurons, and because it is a direct extension of the Spaun model \cite{Eliasmith2012b}. We demonstrate that including these detailed compartmental models does not adversely affect performance across a variety of tasks, including digit recognition, serial working memory, and counting. We then explore the effects of applying TTX, a sodium channel blocking drug, to the model. We characterize the behavioral changes that result from this molecular level intervention. We believe this is the first demonstration of a large-scale brain model that clearly links low-level molecular interventions and high-level behavior.

Eric Hunsberger, Chris Eliasmith

We train spiking deep networks using leaky integrate-and-fire (LIF) neurons, and achieve state-of-the-art results for spiking networks on the CIFAR-10 and MNIST datasets. This demonstrates that biologically-plausible spiking LIF neurons can be integrated into deep networks can perform as well as other spiking models (e.g. integrate-and-fire). We achieved this result by softening the LIF response function, such that its derivative remains bounded, and by training the network with noise to provide robustness against the variability introduced by spikes. Our method is general and could be applied to other neuron types, including those used on modern neuromorphic hardware. Our work brings more biological realism into modern image classification models, with the hope that these models can inform how the brain performs this difficult task. It also provides new methods for training deep networks to run on neuromorphic hardware, with the aim of fast, power-efficient image classification for robotics applications.