growing-neural-network-breadth-depth-time

name	growing-neural-network-breadth-depth-time
description	Differentiable cost framework for jointly optimizing neural network breadth, depth, and time - reveals resource trade-offs and human reaction time correlation
trigger_words	["neural network architecture","resource constraints","breadth depth time","recurrent network","computational graphs","reaction time","task complexity"]
activation_keywords	["architecture growth","resource optimization","breadth depth","recurrent convolutional network","human reaction time","finite lattice","computational resource"]
version	1.0.0
last_updated	2026-06-19T00:00:00.000Z
paper_source	arXiv:2605.25174
authors	Eivinas Butkus, Kedar Garzón Gupta, Nikolaus Kriegeskorte
submitted	2026-05-24T00:00:00.000Z

Growing a Neural Network in Breadth, Depth, and Time

Background

Spatial and temporal resource constraints are critical for both biological and artificial intelligent systems. This paper defines differentiable cost terms for three key dimensions of neural computation:

1. Breadth - Number of parallel units/layers
2. Depth - Number of sequential processing stages
3. Time - Number of recurrent processing steps

Core Innovation

Define a recurrent convolutional neural network as a finite subset of an infinite lattice, then optimize resource costs jointly with task errors via backpropagation.

Key Framework Features

• Differentiable cost functions for all three dimensions
• Joint optimization (accuracy + resource constraints)
• Emergent architecture based on task demands
• Direct comparison with human behavior

Methodology

Network Architecture

Conceptualized as finite subset of infinite lattice:

• Each position has breadth, depth, and temporal extent
• Recurrent connections enable time dimension
• Convolutional structure for spatial processing

Cost Terms

# Conceptual form
total_loss = task_error + λ_b * breadth_cost + λ_d * depth_cost + λ_t * time_cost

# Where:
# breadth_cost = number of parallel units activated
# depth_cost = number of sequential layers used  
# time_cost = number of recurrent steps taken

Training Process

1. Initialize with minimal architecture
2. Apply different pressures via λ coefficients
3. Networks grow organically to meet task demands
4. All three dimensions trade-off against each other

Key Findings

1. Resource Trade-offs

• All three resources can be traded off against each other
• To achieve same accuracy: can use:
  • More breadth, less depth
  • More depth, less time
  • More time, less breadth
• Task complexity determines growth in all dimensions

2. Adaptive Behavior