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Weight Agnostic Neural Networks

Adam Gaier, David Ha

arXiv:1906.04358v2cs.LGcs.NEstat.ML

TL;DR

The paper asks whether neural-network architectures can encode task solutions without learning individual weights. It searches topologies using one shared sampled weight across rollouts, finding weight-agnostic architectures for reinforcement learning and approximately 92% MNIST accuracy without explicit weight training.

  • Problem

    The paper investigates whether architectures alone can encode solutions, addressing the usual reliance on selecting an architecture and then learning its weight parameters.

  • Method

    The method evolves network topologies while assigning every connection one shared weight sampled across rollouts, ranking candidates by performance and complexity.

  • Results

    The search finds minimal architectures that perform several reinforcement-learning tasks without weight training and achieves approximately 92% MNIST test accuracy with random weights.

  • Takeaways & Limitations

    The results suggest that useful inductive biases can be encoded in architecture, while a single shared weight remains easy to tune without gradient-based methods.

  • Takeaways & Limitations

    The approach does not match convolutional-network performance, and its future scope includes exploring recurrent connections and broader task capabilities.

Abstract

from arXiv · show

Not all neural network architectures are created equal, some perform much better than others for certain tasks. But how important are the weight parameters of a neural network compared to its architecture? In this work, we question to what extent neural network architectures alone, without learning any weight parameters, can encode solutions for a given task. We propose a search method for neural network architectures that can already perform a task without any explicit weight training. To evaluate these networks, we populate the connections with a single shared weight parameter sampled from a uniform random distribution, and measure the expected performance. We demonstrate that our method can find minimal neural network architectures that can perform several reinforcement learning tasks without weight training. On a supervised learning domain, we find network architectures that achieve much higher than chance accuracy on MNIST using random weights. Interactive version of this paper at https://weightagnostic.github.io/

1 Introduction

The paper asks whether neural-network architectures can encode task solutions with little or no learned weight information. It proposes searching for architectures that perform across shared weight values and reports strong results on control tasks and MNIST.

  • The work is inspired by precocial animals, whose young possess useful abilities from birth, unlike artificial agents typically trained through architecture selection followed by weight learning.
  • The proposed approach searches for architectures by assigning one shared weight parameter to every connection and evaluating performance across many values.
  • ∼92% test accuracy on MNIST was achieved without explicit weight training using a discovered architecture.
  • The method is designed to find architectures with strong inductive biases that can perform continuous-control tasks using random weight parameters.

2 Related Work

The related work situates this approach among studies of inductive biases, topology search, random-weight networks, biological connectivity, information-theoretic simplicity, and pruning. Its distinction is searching for minimal architectures that encode solutions rather than optimizing or compressing weights in predefined networks.

  • The method builds on NEAT-style topology search but ignores simultaneous weight optimization, focusing instead on network structure.
  • Unlike Bayesian approaches that sample individual weights from distributions, this work applies weight-sharing across the entire network and samples one fixed-distribution weight.
  • Algorithmic information theory and MDL motivate preferring simpler models, while this paper searches for minimal architectures that can represent task solutions.
  • Pruning begins with a full trained network and removes connections, whereas this approach starts without connections and adds complexity without an upper bound imposed by a parent network.
  • The work also relates architecture graphs to biological connectomes and aims to learn network graphs that encode skills for artificial agents.

3 Weight Agnostic Neural Network Search

Weight Agnostic Neural Network Search evolves topologies while replacing weight training with evaluation under shared sampled weights. It ranks networks by performance and simplicity, then mutates promising structures to discover compact architectures whose behavior is encoded largely by topology.

  • NAS seeks architectures that outperform after training, whereas this method seeks architectures whose solutions are innate to their structure.
  • Replacing weight training with random weight sampling makes task performance a product of network topology, although exhaustive sampling is infeasible in high-dimensional weight spaces.
  • Weight-sharing reduces the number of weight values to one, making systematic sampling efficient enough to approximate network performance in a few trials.
  • The search repeatedly initializes minimal topologies, evaluates rollouts with different shared weights, ranks networks by performance and complexity, and probabilistically mutates selected networks.
  • Topology mutations insert nodes, add connections, or change hidden-node activation functions while preserving feed-forward structure.
  • Networks are evaluated using shared weights [−2, −1, −0.5, +0.5, +1, +2], with mean performance computed from cumulative rewards across rollouts.
  • The ranking treats performance and connection count as multiple objectives, preferring simpler networks when performance is similar and sometimes ranking complexity probabilistically.

4 Experimental Results

The experiments test whether weight-agnostic architectures can solve continuous-control and MNIST classification tasks with shared or random weights. The discovered networks encode useful behaviors in their topologies, remain trainable, and can be remarkably compact.

  • Continuous Control: WANNs are evaluated on CartPoleSwingUp, BipedalWalker-v2, and CarRacing-v0 using random, shared, tuned, and individually tuned weights.Performance is measured as cumulative reward averaged over 100 random trials.
  • Continuous Control: Random shared weights still produce useful behaviors, unlike conventional fixed-topology networks that require extensive tuning.The architectures encode relationships between inputs and outputs; consistency, especially sign consistency, matters more than precise weight magnitude.
  • Continuous Control: By generation 32, CartPoleSwingUp networks encode centering and swing-up relationships; by generation 128, added complexity refines balancing.Later balancing is less reliable under variable weights, but reliable centering and swing-up help the system recover and try again.
  • Continuous Control: The BipedalWalker controller solves the task with 210 connections, compared with 2804 connections in the SOTA baseline.It uses only 17 of 25 possible inputs, ignoring many LIDAR sensors and knee-speed signals.
  • Continuous Control: The CarRacing controller uses a sparsely connected two-layer network and one shared weight, achieving a comparable score to a baseline with additional recurrent and representation inputs.The WANN operates on the VAE latent space alone and uses a feed-forward controller.
  • Classification: On MNIST, a single-weight WANN matches a gradient-trained single-layer neural network with thousands of weights, while multiple weight values form a more accurate ensemble than random sampling.The architecture remains compatible with weight training for further accuracy improvements, and different weight values produce distinct classifiers.

5 Discussion and Future Work

The paper searches for simple neural architectures whose inductive biases encode useful behavior before weight training, connecting architecture, evolution, learning, and neuroscience. It also identifies open directions, including broader task reuse and discovering new building blocks.

  • The method searches for simple architectures with strong inductive biases by optimizing performance across shared-weight values rather than training individual weights.
  • Weight-tolerant architectures may support rapid fine-tuning in few-shot or continual learning settings, where agents acquire, transfer, and refine skills.
  • A future WANN could pursue intrinsic motivation in an open-ended environment to accumulate many skills that later become easy to fine-tune.
  • The approach relates to pruning and supermask methods that identify subnetworks performing well with randomly initialized weights.
  • Gradient-based training confines exploration to architectures it can optimize, limiting models with discrete components or adaptive computation mechanisms.
  • Because the discovered networks do not match CNN performance, future progress may require discovering new building blocks rather than only rearranging existing structures.
  • The work is motivated by biological behavior that is partly innate rather than entirely learned, aiming to connect neuroscience and machine learning.

A.1 Code Release

The authors release a general-purpose implementation and the experiment code and discovered networks through the interactive article.

  • The released NumPy implementation of NEAT supports MPI and OpenAI Gym environments.
  • Experiment code and the best networks from each run are referenced in the interactive article.

A.2 “Have you also thought about trying ... ?”

This section marks topics the authors attempted but did not explore in sufficient depth.

  • The authors identify several attempted topics as insufficiently explored in depth.

A.2.1 Searching for network architecture using a single weight rather than range of weights.

Using a single fixed weight can accelerate search and improve its endpoint, but produces brittle behavior when that value changes slightly. Training across a range yields greater weight tolerance.

  • A fixed shared weight such as 0.7 made search faster and improved the final result, but changing it to 0.6 caused complete task failure.
  • Training across a wide range of weight parameters enabled networks to perform outside the training values, with the best values also lying outside that set.

A.2.2 Searching for network architecture using random weights for each connection.

Using the same random value for every connection unexpectedly produced functioning policies, prompting the authors to reconsider the role of shared weights.

  • A bug assigned one random value to every connection instead of different random values.The result appeared promising because poles balanced and walkers walked, but the apparent success was initially attributed to a coding error.
  • This unexpected result led the authors to approach the problem through Minimal Description Length and Algorithmic Information Theory.

A.2.3 Adding noise to the single weight values.

Adding Gaussian noise around a shared weight value produced little change in limited swing-up experiments, except at very high noise levels.

  • Limited swing-up experiments found no large performance difference after adding Gaussian noise around each shared weight value.The experiments varied weights around a set mean at each rollout.
  • Very high noise levels caused poor performance.
  • The authors expected noise to improve topology robustness but recognized that noisier evaluations could require more rollouts.

A.2.4 Using backpropagation to fine-tune weights of a WANN.

The paper examines fine-tuning and evaluation choices for WANNs, including activation diversity, MNIST preprocessing, repeated evaluations, baselines, and population-based weight optimization.

  • Fine-tuning individual WANN weights with JAX improved MNIST performance, but CMA-ES and population-based REINFORCE found better solutions.The authors suggest the activations produced by WANN search may create harder optimization landscapes for gradient-based methods than standard ReLU networks.
  • WANNs encode input relationships, with symmetry and repetition supporting more compact networks alongside ReLU or sigmoid activations.
  • The authors’ intuition is that activation variety is important, although they are not confident that only linear activations would suffice.
  • MNIST images were reduced from 28x28 to 16x16, deskewed, normalized to [0,1], and classified using 256 inputs and 10 outputs.Evaluations used 1000 randomly selected training samples and a reward based on softmax cross entropy.
  • Each task used nine WANN searches, with candidate networks repeatedly reevaluated before retaining a new best network.The reevaluation count was 96 or 64, depending on the available processors.
  • Champion networks were reevaluated thirty times at each weight in the series [−2, −1.5, −1, −0.5, 0.5, 1, 1.5, 2].
  • Individual weights were fine-tuned with population-based REINFORCE for 3000 generations, using task-specific population sizes and rollout counts.Swing Up Cartpole and Bipedal Walker used populations of 384 and 16 rollouts per agent; Car Racing used 64 and 4 rollouts.
  • MNIST optimization used negative cross entropy on the training set, while baselines included a 71-parameter Swing Up controller, an estool Bipedal Walker model, and an 867-parameter Car Racing controller.The Bipedal Walker and Car Racing baselines were described as state-of-the-art at the time of writing.
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