Lossy communication constrains iterated learning

TL;DR

The paper investigates how small, quantitative changes in social communication capacity shape iterated learning across generations using an information-theoretic framework. By modeling transmission as rate-limited posterior passing and applying rate-distortion theory with Blahut-Arimoto optimization, it reveals non-linear, regime-dependent effects where modest increases in channel rate can trigger large gains in cumulative knowledge, while very low or very high rates have distinct, predictable impacts. A variant of Fano's inequality is derived to connect local communication constraints with global learning progress, highlighting the balance between informative observations and information transfer. These results suggest that gradual improvements in communication could underlie the human cultural ratchet without requiring abrupt cognitive innovations, with implications for understanding cultural evolution and designing communication systems that harness incremental capacity gains.

Abstract

Humans' distinctive role in the world can largely be attributed to our capacity for iterated learning, a process by which knowledge is expanded and refined over generations. A range of theories seek to explain why humans are so adept at iterated learning, many positing substantial evolutionary discontinuities in communication or cognition. Is it necessary to posit large differences in abilities between humans and other species, or could small differences in communication ability produce large differences in what a species can learn over generations? We investigate this question through a formal model based on information theory. We manipulate how much information individual learners can send each other and observe the effect on iterated learning performance. Incremental changes to the channel rate can lead to dramatic, non-linear changes to the eventual performance of the population. We complement this model with a theoretical result that describes how individual lossy communications constrain the global performance of iterated learning. Our results demonstrate that incremental, quantitative changes to communication abilities could be sufficient to explain large differences in what can be learned over many generations.

Figures (8)

• Figure 1: A: Illustration of our iterated learning setup. Learners (yellow circles) observe samples from a true distribution and form posterior beliefs, represented as Dirichlet distributions (top). After observing a fixed number of samples, a learner passes its belief to the next over a rate-limited channel. The next learner starts learning using the received distribution as a prior. B: Illustration of an example channel for a simplified Beta-Bernoulli learning task, where each row corresponds to a transmitted posterior belief and each column represents a received prior. Cells are colored by probability. Example transmitted (green) and received (orange) Beta distributions for a single cell are shown above. C: Illustration of the rate-distortion tradeoff. As the maximum acceptable distortion increases, the necessary rate decreases. Each point along this curve corresponds to a different channel.
• Figure 2: Accuracy of chains of learners' beliefs by generation and channel rate. Left: Scores achieved by learners in each generation of our model by communication rate. Right: Performance at generation 20 by channel rate for communication between individuals. Grey line denotes the expected score of an individual learner starting with a uniform prior and making one observation.
• Figure 3: Visualization of channels in a simplified Beta-Bernoulli learning task for three different rate limits. Each row corresponds to a pair of transmitted parameters and each column corresponds to a pair of received parameters. Cells are colored according to the probability that the channel assigns to the received parameters given the source parameters (yellow=0, purple=1). A channel with a rate of 0 maps every pair of source parameters to the received parameters that minimize expected distortion over all parameters. A channel with a high rate looks diagonal, with every pair of parameters being mapped to itself with high probability.
• Figure 4: Performance by generation and performance at last generation by rate for the model variant with exponentially decreasing source probability
• Figure 5: Performance by generation and performance at last generation by rate for the model variant with two observations per agent rather than one

Theorems & Definitions (4)

• Theorem 1
• proof
• Theorem 1
• proof