Reinforcement learning (RL) is rapidly reaching and surpassing human-level control capabilities. However, state-of-the-art RL algorithms often require timesteps and reaction times significantly faster than human capabilities, which is impractical in real-world settings and typically necessitates specialized hardware. We introduce Sequence Reinforcement Learning (SRL), an RL algorithm designed to produce a sequence of actions for a given input state, enabling effective control at lower decision frequencies. SRL addresses the challenges of learning action sequences by employing both a model and an actor-critic architecture operating at different temporal scales. We propose a "temporal recall" mechanism, where the critic uses the model to estimate intermediate states between primitive actions, providing a learning signal for each individual action within the sequence. Once training is complete, the actor can generate action sequences independently of the model, achieving model-free control at a slower frequency. We evaluate SRL on a suite of continuous control tasks, demonstrating that it achieves performance comparable to state-of-the-art algorithms while significantly reducing actor sample complexity. To better assess performance across varying decision frequencies, we introduce the Frequency-Averaged Score (FAS) metric. Our results show that SRL significantly outperforms traditional RL algorithms in terms of FAS, making it particularly suitable for applications requiring variable decision frequencies. Furthermore, we compare SRL with model-based online planning, showing that SRL achieves comparable FAS while leveraging the same model during training that online planners use for planning.

Neural networks are known to be universal computers for Boolean functions. Recent advancements in hardware have significantly reduced matrix multiplication times, making neural network simulation both fast and efficient. Consequently, functions defined by complex Boolean networks are increasingly viable candidates for simulation through their neural network representation. Prior research has introduced a general method for deriving neural network representations of Boolean networks. However, the resulting neural networks are often suboptimal in terms of the number of neurons and connections, leading to slower simulation performance. Optimizing them while preserving functional equivalence --lossless optimization-- is an NP-hard problem, and current methods only provide lossy solutions. In this paper, we present a deterministic algorithm to optimize such neural networks in terms of neurons and connections while preserving functional equivalence. Moreover, to accelerate the compression of the neural network, we introduce an objective-aware algorithm that exploits representations that are shared among subproblems of the overall optimization. We demonstrate experimentally that we are able to reduce connections and neurons by up to 70% and 60%, respectively, in comparison to state-of-the-art. We also find that our objective-aware algorithm results in consistent speedups in optimization time, achieving up to 34.3x and 5.9x speedup relative to naive and caching solutions, respectively. Our methods are of practical relevance to applications such as high-throughput circuit simulation and placing neurosymbolic systems on the same hardware architecture.

The energy paradigm, exemplified by Hopfield networks, offers a principled framework for memory in neural systems by interpreting dynamics as descent on an energy surface. While powerful for static associative memories, it falls short in modeling sequential memory, where transitions between memories are essential. We introduce the Exponential Dynamic Energy Network (EDEN), a novel architecture that extends the energy paradigm to temporal domains by evolving the energy function over multiple timescales. EDEN combines a static high-capacity energy network with a slow, asymmetrically interacting modulatory population, enabling robust and controlled memory transitions. We formally derive short-timescale energy functions that govern local dynamics and use them to analytically compute memory escape times, revealing a phase transition between static and dynamic regimes. The analysis of capacity, defined as the number of memories that can be stored with minimal error rate as a function of the dimensions of the state space (number of feature neurons), for EDEN shows that it achieves exponential sequence memory capacity $\mathcal{O}(\gamma^N)$, outperforming the linear capacity $\mathcal{O}(N)$ of conventional models. Furthermore, EDEN's dynamics resemble the activity of time and ramping cells observed in the human brain during episodic memory tasks, grounding its biological relevance. By unifying static and sequential memory within a dynamic energy framework, EDEN offers a scalable and interpretable model for high-capacity temporal memory in both artificial and biological systems.

Recent work has revealed that state space models (SSMs), while efficient for long-sequence processing, are fundamentally limited in their ability to represent formal languages—particularly due to time-invariant and real-valued recurrence structures. In this work, we draw inspiration from adaptive and structured dynamics observed in biological neural systems and introduce the Adaptive Unitary State Space Model (AUSSM): a novel class of SSMs that leverages skew-symmetric, input-dependent recurrence to achieve unitary evolution and high expressive power. Using algebraic automata theory, we prove that AUSSM can perform modulo counting and simulate solvable group automata at precision logarithmically bounded in the input length, enabling SSMs to model a broad class of regular languages out of reach for other SSM architectures. To overcome the practical inefficiencies of adaptive recurrence, we develop a separable convolution formulation and a CUDA implementation that enables scalable parallel training. Empirically, we show that AUSSM and its hybrid variant—interleaved with Mamba—outperform prior SSMs on formal algorithmic tasks such as parity and modular arithmetic, and achieve competent performance on real-world long time-series classification benchmarks. Our results demonstrate that adaptive unitary recurrence provides a powerful and efficient inductive bias for both symbolic and continuous sequence modeling. The code is available at https://github.com/arjunkaruvally/AUSSM

Traveling waves are a fundamental phenomenon in the brain, playing a crucial role in short-term information storage. In this study, we leverage the concept of traveling wave dynamics within a neural lattice to formulate a theoretical model of neural working memory in Recurrent Neural Networks (RNNs), study its properties, and its real world implications in AI. The proposed model diverges from traditional approaches, which assume information storage in static, register-like locations updated by interference. Instead, the model stores data as waves that is updated by the wave's boundary conditions. We rigorously examine the model's capabilities in representing and learning state histories, which are vital for learning history-dependent dynamical systems. The findings reveal that the model reliably stores external information and enhances the learning process by addressing the diminishing gradient problem of RNNs. To understand the model's real-world applicability, we explore two cases: linear boundary condition and non-linear, self-attention-driven boundary condition. The experiments reveal that the linear scenario is effectively *learned* by RNNs through backpropagation when modeling history-dependent dynamical systems. Conversely, the non-linear scenario parallels an attention-only transformer. Collectively, our findings suggest the broader relevance of traveling waves in AI and its potential in advancing neural network architectures.

The current reinforcement learning framework focuses exclusively on performance, often at the expense of efficiency. In contrast, biological control achieves remarkable performance while also optimizing computational energy expenditure and decision frequency. We propose a decision-bounded Markov decision process (DB-MDP) that constrains the number of decisions and computational energy available to agents in reinforcement learning environments. Our experiments demonstrate that existing reinforcement learning algorithms struggle within this framework, leading to either failure or suboptimal performance. To address this, we introduce a biologically inspired, temporally layered architecture (TLA), enabling agents to manage computational costs through two layers with distinct timescales and energy requirements. TLA achieves optimal performance in decision-bounded environments and in continuous control environments, matching state-of-the-art performance while using a fraction of the computing cost. Compared to current reinforcement learning algorithms that solely prioritize performance, our approach significantly lowers computational energy expenditure while maintaining performance. These findings establish a benchmark and pave the way for future research on energy and time-aware control.

We propose a new learning framework, signal propagation (sigprop), for propagating a learning signal and updating neural network parameters via a forward pass, as an alternative to backpropagation (BP). In sigprop, there is only the forward path for inference and learning. So, there are no structural or computational constraints necessary for learning to take place, beyond the inference model itself, such as feedback connectivity, weight transport, or a backward pass, which exist under BP-based approaches. That is, sigprop enables global supervised learning with only a forward path. This is ideal for parallel training of layers or modules. In biology, this explains how neurons without feedback connections can still receive a global learning signal. In hardware, this provides an approach for global supervised learning without backward connectivity. Sigprop by construction has compatibility with models of learning in the brain and in hardware than BP, including alternative approaches relaxing learning constraints. We also demonstrate that sigprop is more efficient in time and memory than they are. To further explain the behavior of sigprop, we provide evidence that sigprop provides useful learning signals in context to BP. To further support relevance to biological and hardware learning, we use sigprop to train continuous time neural networks with the Hebbian updates and train spiking neural networks (SNNs) with only the voltage or with biologically and hardware-compatible surrogate functions.

The state-of-the-art memory model is the General Associative Memory Model, a generalization of the classical Hopfield network. Like its ancestor, the general associative memory has a well-defined state-dependant energy surface, and its memories correlate with its fixed points. This is unlike human memories, which are commonly sequential rather than separated fixed points. In this paper, we introduce a class of General Sequential Episodic Memory Models (GSEMM) that, in the adiabatic limit, exhibit a dynamic energy surface, leading to a series of meta-stable states capable of encoding memory sequences. A multiple-timescale architecture enables the dynamic nature of the energy surface with newly introduced asymmetric synapses and signal propagation delays. We demonstrate its dense capacity under polynomial activation functions. GSEMM combines separate memories, short and long sequential episodic memories, under a unified theoretical framework, demonstrating how energy-based memory modeling can provide richer, human-like episodes.

Register Transfer Level (RTL) simulation and verification of Digital Circuits are extremely important and costly tasks in the Integrated Circuits industry. While some simulators have incorporated the exploitation of parallelism in the structure of Digital Circuits to run on multi-core CPUs, the maximum throughput they achieve quickly reaches a plateau, as described by Amdahl’s Law. Recent research from Nvidia has obtained much higher throughput in simulations using GPUs, highlighting the potential of these devices for Digital Circuit simulation. However, they were required to incorporate sophisticated algorithms to support GPU simulation. In addition, the unbalanced structure of real-life Digital Circuits provides difficulties for processing on multi-threaded devices. In this paper, we present a Digital Circuit compiler that utilizes Neural Networks to exploit the various parallelisms in RTL simulation, making use of PyTorch, a widely-used Neural Network framework that facilitate their simulation on GPUs. By using properties of Boolean Functions, we developed a novel algorithm that converts any Digital Circuit into a Neural Network, and optimization techniques that help in pushing the thread computational capability to the limit. The results show three orders of magnitude higher throughput than Verilator RTL simulator, an improvement of one order of magnitude compared to the state-of-the-art GPU techniques from Nvidia. We believe that the use of Neural Networks not only provides a significant improvement in simulation and verification tasks in the Integrated Circuits industry, but also opens a line of research for simulators at the logic and physical gate level.

Technology-mediated dance experiences, as a medium of entertainment, are a key element in both traditional and virtual reality-based gaming platforms. These platforms predominantly depend on unobtrusive and continuous human pose estimation as a means of capturing input. Current solutions primarily employ RGB or RGB-Depth cameras for dance gaming applications; however, the former is hindered by low-light conditions due to motion blur and reduced sensitivity, while the latter exhibits excessive power consumption, diminished frame rates, and restricted operational distance. Boasting ultra-low latency, energy efficiency, and a wide dynamic range, neuromorphic cameras present a viable solution to surmount these limitations. Here, we introduce YeLan, a neuromorphic camera-driven, three-dimensional, high-frequency human pose estimation (HPE) system capable of withstanding low-light environments and dynamic backgrounds. We have compiled the first-ever neuromorphic camera dance HPE dataset and devised a fully adaptable motion-to-event, physics-conscious simulator. YeLan surpasses baseline models under strenuous conditions and exhibits resilience against varying clothing types, background motion, viewing angles, occlusions, and lighting fluctuations.

Digital circuits are the basic structure of most of today's electronic devices. Simulation plays a critical role in the iterative development of such circuits as a consequence of the time and financial expenses that accompany fabrication. There are existing tools that achieve simulation by modeling circuits with Hardware Description Languages (HDL). However, with recent advances in neural networks (NN) and hardware accelerators for NN simulation, a niche of digital circuit simulation via NNs has opened up. Here, we introduce C2NN (Circuit to Neural Network), a novel method that converts (or transpiles) any digital circuit expressed in a HDL into a NN for simulation. The conversion to a NN representation not only affords the benefits of parallelization, the use of GPUs for simulation, and optimizations such as pruning, but it also provides a methodology for achieving equivalent digital circuit computation in neuromorphic hardware. We describe the transpilation process of C2NN and verify its correctness on small- and large-scale digital circuits. We also found that the simulation time of the transpiled circuits is competitive with one of the fastest digital circuit simulators.

Previous works have proved that recurrent neural networks (RNNs) are Turing-complete. However, in the proofs, the RNNs allow for neurons with unbounded precision, which is neither practical in implementation nor biologically plausible. To remove this assumption, we propose a dynamically growing memory module made of neurons of fixed precision. The memory module dynamically recruits new neurons when more memories are needed, and releases them when memories become irrelevant. We prove that a 54-neuron bounded-precision RNN with growing memory modules can simulate a Universal Turing Machine, with time complexity linear in the simulated machine's time and independent of the memory size. The result is extendable to various other stack-augmented RNNs. Furthermore, we analyze the Turing completeness of both unbounded-precision and bounded-precision RNNs, revisiting and extending the theoretical foundations of RNNs.

Replay is the reactivation of one or more neural patterns that are similar to the activation patterns experienced during past waking experiences. Replay was first observed in biological neural networks during sleep, and it is now thought to play a critical role in memory formation, retrieval, and consolidation. Replay-like mechanisms have been incorporated in deep artificial neural networks that learn over time to avoid catastrophic forgetting of previous knowledge. Replay algorithms have been successfully used in a wide range of deep learning methods within supervised, unsupervised, and reinforcement learning paradigms. In this letter, we provide the first comprehensive comparison between replay in the mammalian brain and replay in artificial neural networks. We identify multiple aspects of biological replay that are missing in deep learning systems and hypothesize how they could be used to improve artificial neural networks.

A longstanding problem for Deep Neural Networks (DNNs) is understanding their puzzling ability to generalize well. We approach this problem through the unconventional angle of \emph{cognitive abstraction mechanisms}, drawing inspiration from recent neuroscience work, allowing us to define the Cognitive Neural Activation metric (CNA) for DNNs, which is the correlation between information complexity (entropy) of given input and the concentration of higher activation values in deeper layers of the network. The CNA is highly predictive of generalization ability, outperforming norm-and-sharpness-based generalization metrics on an extensive evaluation of close to 200 network instances comprising a breadth of dataset-architecture combinations, especially in cases where additive noise is present and/or training labels are corrupted. These strong empirical results show the usefulness of the CNA as a generalization metric and encourage further research on the connection between information complexity and representations in the deeper layers of networks in order to better understand the generalization capabilities of DNNs.

Spiking neural networks (SNNs) are a promising candidate for biologically-inspired and energy efficient computation. However, their simulation is restrictively time consuming, and creates a bottleneck in developing competitive training methods with potential deployment on neuromorphic hardware platforms, even on simple tasks. To address this issue, we provide an implementation of mini-batch processing applied to clock-based SNN simulation, leading to drastically increased data throughput. To our knowledge, this is the first general-purpose implementation of mini-batch processing in a spiking neural networks simulator, which works with arbitrary neuron and synapse models. We demonstrate nearly constant-time scaling with batch size on a simulation setup (up to GPU memory limits), and showcase the effectiveness of large batch sizes in two SNN application domains, resulting in ≈880X and ≈24X reductions in wall-clock time respectively. Different parameter reduction techniques are shown to produce different learning outcomes in a simulation of networks trained with spike-timing-dependent plasticity. Machine learning practitioners and biological modelers alike may benefit from the drastically reduced simulation time and increased iteration speed this method enables.

Sparsity learning aims to decrease the computational and memory costs of large deep neural networks (DNNs) via pruning neural connections while simultaneously retaining high accuracy. A large body of work has developed sparsity learning approaches, with recent large-scale experiments showing that two main methods, magnitude pruning and Variational Dropout (VD), achieve similar state-of-the-art results for classification tasks. We propose Adaptive Neural Connections (ANC), a method for explicitly parameterizing fine-grained neuron-to-neuron connections via adjacency matrices at each layer that are learned through backpropagation. Explicitly parameterizing neuron-to-neuron connections confers two primary advantages: 1. Sparsity can be explicitly optimized for via norm-based regularization on the adjacency matrices; and 2. When combined with VD (which we term, ANC-VD), the adjacencies can be interpreted as learned weight importance parameters, which we hypothesize leads to improved convergence for VD. Experiments with ResNet18 show that architectures augmented with ANC outperform their vanilla counterparts.

Embodiment is a key feature of biological intelligence, and energy-awareness can be viewed as the ultimate expression of situated intelligence. Energy constraint is often ignored, or it has just secondary role in typical cutting-edge AI approaches. For example, Deep Learning Networks often require huge amount of data/time/energy/resources, which may not be readily available in various practical scenarios. We outline a simple computational model of spiking neural activity lined link astrocytes responsible for energy management in brains. We analyze oscillatory neural dynamics and its modulation by astrocytes mediating energy constrains. We indicate the potential benefits of the proposed design to be implemented on neuromorphic computational platforms.

We present a system comprising a hybridization of self-organized map (SOM) properties with spiking neural networks (SNNs) that retain many of the features of SOMs. Networks are trained in an unsupervised manner to learn a self-organized lattice of filters via excitatory-inhibitory interactions among populations of neurons. We develop and test various inhibition strategies, such as growing with inter-neuron distance and two distinct levels of inhibition. The quality of the unsupervised learning algorithm is evaluated using examples with known labels. Several biologically-inspired classification tools are proposed and compared, including population-level confidence rating, and n-grams using spike motif algorithm. Using the optimal choice of parameters, our approach produces improvements over state-of-art spiking neural networks.

Spiking neural networks are motivated from principles of neural systems and may possess unexplored advantages in the context of machine learning. A class of convolutional spiking neural networks is introduced, trained to detect image features with an unsupervised, competitive learning mechanism. Image features can be shared within subpopulations of neurons, or each may evolve independently to capture different features in different regions of input space. We analyze the time and memory requirements of learning with and operating such networks. The MNIST dataset is used as an experimental testbed, and comparisons are made between the performance and convergence speed of a baseline spiking neural network.

The human brain is an energy hungry organ. How that brain manages its energy consumption in maintaining its health and executing sensori-motor and cognitive functions is an important but overlooked research area in contemporary cognitive neuroscience. It is argued here that the principal method whereby the human brain manages its energy utilization is through maintaining a relatively elevated level of activity in what can be referred to as “resting state networks” (RSN). The elevated energy consumption in the human brain's varied RSNs is driven and maintained by a physiological mechanism we call the Frame-Formation Energy Cycle (FFEC). Running the FFEC cycle is metabolically expensive and therefore offers a mechanism to explain the increased energy consumption in human-brain RSNs as compared to regions not involved in such networks.

We design and implement a small neural network, comprised of 52 fixed precision neurons - computationally equivalent to a bounded memory Universal Turing Machine; this design is an order of magnitude smaller than the smallest known universal neural nets. The network is the core of a practical universal neural computer; all neurons have fixed precision and a small set of simple weights. External memory will be used, or additional neurons dynamically recruited for more memory intensive calculations or input.

We study the computational capabilities of a biologically inspired neural model where the synaptic weights, the connectivity pattern, and the number of neurons can evolve over time rather than stay static. Our study focuses on the mere concept of plasticity of the model so that the nature of the updates is assumed to be not constrained. In this context, we show that the so-called plastic recurrent neural networks (RNNs) are capable of the precise super-Turing computational power--as the static analog neural networks--irrespective of whether their synaptic weights are modeled by rational or real numbers, and moreover, irrespective of whether their patterns of plasticity are restricted to bi-valued updates or expressed by any other more general form of updating. Consequently, the incorporation of only bi-valued plastic capabilities in a basic model of RNNs suffices to break the Turing barrier and achieve the super-Turing level of computation. The consideration of more general mechanisms of architectural plasticity or of real synaptic weights does not further increase the capabilities of the networks. These results support the claim that the general mechanism of plasticity is crucially involved in the computational and dynamical capabilities of biological neural networks. They further show that the super-Turing level of computation reflects in a suitable way the capabilities of brain-like models of computation.

The paper addresses a relation between logical reasoning and probability and presents probability-generated aggregators. The obtained aggregators implement probability distributions for specification of generator functions; as it was proven in the paper, such implementation is always possible. In the paper, the relation between neutral element of the probabilistic uninorm and parameters of the underlying probability distribution is demonstrated, and a method for specification of the probabilistic uninorm, and thus—of the probability distribution using t-norm and t-conorm—is constructed. In addition, the obtained probabilistic uninorm and probabilistic absorbing norm or nullnorm are briefly considered as algebraic operations on the open unit interval. In is demonstrated, that, in general, the obtained algebra is nondistributive and depends on the distributions, which are used for generating probabilistic uninorm and absorbing norm. The obtained results bridge several gaps between fuzzy and probabilistic logics and provide a basis both for theoretical studies in the field and for practical techniques of digital/analog schemes synthesis and analysis.

In classical computation, rational- and real-weighted recurrent neural networks were shown to be respectively equivalent to and strictly more powerful than the standard Turing machine model. Here, we study the computational power of recurrent neural networks in a more biologically oriented computational framework, capturing the aspects of sequential interactivity and persistence of memory. In this context, we prove that so-called interactive rational- and real-weighted neural networks show the same computational powers as interactive Turing machines and interactive Turing machines with advice, respectively. A mathematical characterization of each of these computational powers is also provided. It follows from these results that interactive real-weighted neural networks can perform uncountably many more translations of information than interactive Turing machines, making them capable of super-Turing capabilities.

The computational power of recurrent neural networks is intimately related to the nature of their synaptic weights. In particular, neural networks with static rational weights are known to be Turing equivalent, and recurrent networks with static real weights were proved to be super-Turing. Here, we study the computational power of a more biologically-oriented model where the synaptic weights can evolve rather than stay static. We prove that such evolving networks gain a super-Turing computational power, equivalent to that of static real-weighted networks, regardless of whether their synaptic weights are rational or real. These results suggest that evolution might play a crucial role in the computational capabilities of neural networks.

We use emotional communication within a predator-prey game to evaluate the tradeoff between socio-emotional behavior at individual- and species- scales. In this predator-prey game, individual predators and prey use emotion in their decision making, and communicate their emotional state with neighboring conspecifics. The model of emotion is based upon the somatic marker hypothesis. In comparing individual utility and population dynamics we find emotion is capable of both supporting species and individual gain. We suggest this type of dynamic may provide a mechanism for the emergence of altruistic behavior within a species under individual and/or group selection.

As man-made systems become more complex and autonomous, there is a growing need for novel engineering methods that offer self-construction, adaptation to the environment, and self-repair. In a step towards developing such methods, we demonstrate how a simple model multicellular organism can assemble itself by replication from a single cell and finally express a fundamental behavior: foraging. Previous studies have employed evolutionary approaches to this problem. Instead, we aim at explicit design of self-constructing and -repairing systems by hierarchical specification of elementary intracellular mechanisms via a kind of genetic code. The interplay between individual cells and the gradually increasing self-created complexity of the local structure that surrounds them causes the serial unfolding of the final functional organism. The developed structure continuously feeds back to the development process, and so the system is also capable of self-repair.

Abstract When a client interacts with an expert, e.g., a doctor, it falls upon the expert to ask questions that steer the process towards fulfilling the client's needs. This is most efficient given that the expert has more knowledge and a broader view of possible illnesses and treatments. On the other hand, when faced with an information retrieval (IR) task, most IR systems leave to the client the task of coming up with queries. We propose an information retrieval framework that assumes the responsibility of leading the users to the information, thus increasing efficiency and satisfaction.

In classical large information retrieval systems, the system responds to a user initiated query with a list of results ranked by relevance. The users may further refine their query as needed. This process may result in a lengthy correspondence without conclusion. We propose an alternative active learning approach, where the sys(cid:173) tem responds to the initial user's query by successively probing the user for distinctions at multiple levels of abstraction. The system's initiated queries are optimized for speedy recovery and the user is permitted to respond with multiple selections or may reject the query. The information is in each case unambiguously incorporated by the system and the subsequent queries are adjusted to minimize the need for further exchange. The system's initiated queries are subject to resource constraints pertaining to the amount of infor(cid:173) mation that can be presented to the user per iteration.

We present a novel kernel method for data clustering using a description of the data by support vectors. The kernel reflects a projection of the data points from data space to a high dimensional feature space. Cluster boundaries are defined as spheres in feature space, which represent complex geometric shapes in data space. We utilize this geometric representation of the data to construct a simple clustering algorithm.

We present a novel method for clustering using the support vector ma(cid:173) chine approach. Data points are mapped to a high dimensional feature space, where support vectors are used to define a sphere enclosing them. The boundary of the sphere forms in data space a set of closed contours containing the data. Data points enclosed by each contour are defined as a cluster. As the width parameter of the Gaussian kernel is decreased, these contours fit the data more tightly and splitting of contours occurs. The algorithm works by separating clusters according to valleys in the un(cid:173) derlying probability distribution, and thus clusters can take on arbitrary geometrical shapes. As in other SV algorithms, outliers can be dealt with by introducing a soft margin constant leading to smoother cluster bound(cid:173) aries. The structure of the data is explored by varying the two parame(cid:173) ters. We investigate the dependence of our method on these parameters and apply it to several data sets.

This article introduces a method for clustering irregularly shaped data arrangements using high-order neurons. Complex analytical shapes are modeled by replacing the classic synaptic weight of the neuron by high-order tensors in homogeneous coordinates. In the first- and second-order cases, this neuron corresponds to a classic neuron and to an ellipsoidalmetric neuron. We show how high-order shapes can be formulated to follow the maximum-correlation activation principle and permit simple local Hebbian learning. We also demonstrate decomposition of spatial arrangements of data clusters, including very close and partially overlapping clusters, which are difficult to distinguish using classic neurons. Superior results are obtained for the Iris data.

This article studies the computational power of various discontinuous real computational models that are based on the classical analog recurrent neural network (ARNN). This ARNN consists of finite number of neurons; each neuron computes a polynomial net function and a sigmoid-like continuous activation function. We introduce arithmetic networks as ARNN augmented with a few simple discontinuous (e.g., threshold or zero test) neurons. We argue that even with weights restricted to polynomial time computable reals, arithmetic networks are able to compute arbitrarily complex recursive functions. We identify many types of neural networks that are at least as powerful as arithmetic nets, some of which are not in fact discontinuous, but they boost other arithmetic operations in the net function (e.g., neurons that can use divisions and polynomial net functions inside sigmoid-like continuous activation functions). These arithmetic networks are equivalent to the Blum-Shub-Smale model, when the latter is restricted to a bounded number of registers. With respect to implementation on digital computers, we show that arithmetic networks with rational weights can be simulated with exponential precision, but even with polynomial-time computable real weights, arithmetic networks are not subject to any fixed precision bounds. This is in contrast with the ARNN that are known to demand precision that is linear in the computation time. When nontrivial periodic functions (e.g., fractional part, sine, tangent) are added to arithmetic networks, the resulting networks are computationally equivalent to a massively parallel machine. Thus, these highly discontinuous networks can solve the presumably intractable class of PSPACE-complete problems in polynomial time.

Attractor systems are useful in neurodynamics, mainly in the modeling of associative memory. This paper presents a complexity theory for continuous phase space dynamical systems with discrete or continuous time update, which evolve to attractors. In our framework we associate complexity classes with different types of attractors. Fixed points belong to the class BPP/sub d/, while chaotic attractors are in NP/sub d/. The BPP=NP question of classical complexity theory is translated into a question in the realm of chaotic dynamical systems. This theory enables an algorithmic analysis of attractor networks and flows for the solution of various problem such as linear programming. We exemplify our approach with an analysis of the Hopfield network.

The computational power of recurrent neural networks is shown to depend ultimately on the complexity of the real constants (weights) of the network. The complexity, or information contents, of the weights is measured by a variant of resource-bounded Kolmogorov (1965) complexity, taking into account the time required for constructing the numbers. In particular, we reveal a full and proper hierarchy of nonuniform complexity classes associated with networks having weights of increasing Kolmogorov complexity.

We formally define the Multiprocessor Document Allocation Problem (MDAP) and prove it to be computationally intractable (NP complete). Once it is shown that MDAP is NP complete, we describe a document allocation algorithm based on genetic algorithms. This algorithm assumes that the documents are clustered using any one of the many clustering techniques. We later show that our allocation algorithm probabilistically converges to a good solution. For a behavioral evaluation, we present sample experimental results.

Recently, fully connected recurrent neural networks have been proven to be computationally rich-at least as powerful as Turing machines. This work focuses on another network which is popular in control applications and has been found to be very effective at learning a variety of problems. These networks are based upon Nonlinear AutoRegressive models with eXogenous Inputs (NARX models), and are therefore called NARX networks. As opposed to other recurrent networks, NARX networks have a limited feedback which comes only from the output neuron rather than from hidden states. They are formalized by y(t)=Psi(u(t-n(u)), ..., u(t-1), u(t), y(t-n(y)), ..., y(t-1)) where u(t) and y(t) represent input and output of the network at time t, n(u) and n(y) are the input and output order, and the function Psi is the mapping performed by a Multilayer Perceptron. We constructively prove that the NARX networks with a finite number of parameters are computationally as strong as fully connected recurrent networks and thus Turing machines. We conclude that in theory one can use the NARX models, rather than conventional recurrent networks without any computational loss even though their feedback is limited. Furthermore, these results raise the issue of what amount of feedback or recurrence is necessary for any network to be Turing equivalent and what restrictions on feedback limit computational power.

This article studies finite size networks that consist of interconnections of synchronously evolving processors. Each processor updates its state by applying an activation function to a linear combination of the previous states of all units. We prove that any function for which the left and right limits exist and are different can be applied to the neurons to yield a network which is at least as strong computationally as a finite automaton. We conclude that if this is the power required, one may choose any of the aforementioned neurons, according to the hardware available or the learning software preferred for the particular application.

Selecting a "best subset" of input variables is a critical issue in forecasting. This is especially true when the number of available input series is large, and an exhaustive search through all combinations of variables is computationally infeasible. Inclusion of irrelevant variables not only doesn't help prediction, but can reduce forecasting accuracy through added noise or systematic bias. We demonstrate a technique called "sensitivity-based pruning" (SBP) that removes irrelevant input variables from a nonlinear forecasting or regression model. The technique makes use of a saliency measure computed for each input variable and uses estimates of prediction risk for determining the number of input variables to prune. We present preliminary results of the SBP technique applied to neural network predictors of a key business cycle measure, the US Index of Industrial Production.

Deals with computational issues of loading a fixed-architecture neural network with a set of positive and negative examples. This is the first result on the hardness of loading a simple three-node architecture which does not consist of the binary-threshold neurons, but rather utilizes a particular continuous activation function, commonly used in the neural-network literature. The authors observe that the loading problem is polynomial-time if the input dimension is constant. Otherwise, however, any possible learning algorithm based on particular fixed architectures faces severe computational barriers. Similar theorems have already been proved by Megiddo and by Blum and Rivest, to the case of binary-threshold networks only. The authors' theoretical results lend further suggestion to the use of incremental (architecture-changing) techniques for training networks rather than fixed architectures. Furthermore, they imply hardness of learnability in the probably approximately correct sense as well.

This paper deals with learnability of concept classes defined by neural networks, showing the hardness of PAC-learning (in the complexity, not merely information-theoretic sense) for networks with a particular class of activation. The obstruction lies not with the VC dimension, which is known to grow slowly; instead, the result follows the fact that the loading problem is NP-complete. (The complexity scales badly with input dimension; the loading problem is polynomial-time if the input dimension is constant.) Similar and well-known theorems had already been proved by Megiddo and by Blum and Rivest, for binary-threshold networks. It turns out the general problem for continuous sigmoidal-type functions, as used in practical applications involving steepest descent, is not NP-hard—there are “sigmoidals” for which the problem is in fact trivial—so it is an open question to determine what properties of the activation function cause difficulties. Ours is the first result on the hardness of loading networks which do not consist of binary neurons; we employ a piecewise-linear activation function that has been used in the neural network literature. Our theoretical results lend further justification to the use of incremental (architecture-changing) techniques for training networks.

On top of FUELCON and NEL, two extant, successful projects in, respectively, expert systems for engineering, and neural networks, we have defined and designed a new phase, meant to greatly increase the significance, for AI, of the combined project with respect to the already recognized merits of the two seed-projects. The NEL symbolic-to-neural conversion schema and language is resorted to in NEURALIZER, a component meant to automatically revise a ruleset, iteration after iteration, within the operation cycle of FUELCON, a generator of families of configurations of fuel assemblies for reloading the core of nuclear reactors.

We investigate the power of recurrent neural networks that apply the standard sigmoid activation function: a(z) = [2/(1 + e-”)] -1. We show that in the noiseless model, there exists a universal architecture that can be used to compute any recursive function. As a result, basic convergence questions concerning these architectures are shown to be undecidi~ble even for fixed-size networks. This is the first result of its kind for the standard sigmoid activation function; previous techniques only applied to linearized and truncated versions of this function. The significance of our result, besides the proving technique itself, lies in the popularity of the sigmoidal function both in applications of artificial neural networks and in models of biological neural networks. Our techniques can be applied to a much more general class of “sigmoid-like” activation functions, suggesting that Turing universality is a relatively common property of recurrent neural network models.

This paper deals with finite networks which consist of interconnections of synchronously evolving processors. Each processor updates its state by applying a “sigmoidal” scalar nonlinearity to a linear combination of the previous states of all units. We prove that one may simulate all Turing Machines by rational nets. In particular, one can do this in linear time, and there is a net made up of about 1,000 processors which computes a universal partial-recursive function. Products (high order nets) are not required, contrary to what had been stated in the literature. Furthermore, we assert a similar theorem about non-deterministic Turing Machines. Consequences for undecidability and complexity issues about nets are discussed too.

Abstract. Information retrieval is the selection of documents that are potentially relevant to a user’s information need. Given the vast volume of data stored in modern information retrieval systems, searching the document database requires vast computational resources. To meet these computational demands, various researchers have developed parallel information retrieval systems. As efficient exploitation of parallelism demands fast access to the documents, data organization and placement significantly affect the total processing time. We describe and evaluate a data placement strategy for distributed memory, distributed 1/0 multicomputers. Initially, a formal description of the Multiprocessor Document Allocation Problem (MDAP) and a proof that MDAP is NP Complete are presented. A document allocation