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Landmark universal function approximation results for neural networks with trained weights and biases provided the impetus for the ubiquitous use of neural networks as learning models in neuroscience and Artificial Intelligence (AI). Recent work has extended these results to networks in which a smaller subset of weights (e.g., output weights) are tuned, leaving other parameters random. However, it remains an open question whether universal approximation holds when only biases are learned, despite evidence from neuroscience and AI that biases significantly shape neural responses. The current paper answers this question. We provide theoretical and numerical evidence demonstrating that feedforward neural networks with fixed random weights can approximate any continuous function on compact sets. We further show an analogous result for the approximation of dynamical systems with recurrent neural networks. Our findings are relevant to neuroscience, where they demonstrate the potential for behaviourally relevant changes in dynamics without modifying synaptic weights, as well as for AI, where they shed light on recent fine-tuning methods for large language models, like bias and prefix-based approaches.
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This content will become publicly available on March 1, 2026
NSF Workshop Report: Exploring Measurements and Interpretations of Intelligent Behaviors Across Animal Model Systems
ABSTRACT Defining intelligence is a challenging and fraught task, but one that neuroscientists are repeatedly confronted with. A central goal of neuroscience is to understand how phenomena like intelligent behaviors emerge from nervous systems. This requires some determination of what defines intelligence and how to measure it. The challenge is multifaceted. For instance, as we begin to describe and understand the brain in increasingly specific physical terms (e.g., anatomy, cell types, activity patterns), we amplify an ever‐growing divide in how we connect measurable properties of the brain to less tangible concepts like intelligence. As our appreciation for evolutionary diversity in neuroscience grows, we are further confronted with whether there can be a unifying theory of intelligence. The National Science Foundation (NSF) NeuroNex consortium recently gathered experts from multiple animal model systems to discuss intelligence across species. We summarize here the different perspectives offered by the consortium, with the goal of promoting thought and debate of this ancient question from a modern perspective, and asking whether defining intelligence is a useful exercise in neuroscience or an ill‐posed and distracting question. We present data from the vantage points of humans, macaques, ferrets, crows, octopuses, bees, and flies, highlighting some of the noteworthy capabilities of each species within the context of each species’ ecological niche and how these may be challenged by climate change. We also include a remarkable example of convergent evolution between primates and crows in the circuit and molecular basis for working memory in these highly divergent animal species.
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- Award ID(s):
- 2015276
- PAR ID:
- 10616356
- Publisher / Repository:
- na
- Date Published:
- Journal Name:
- Journal of Comparative Neurology
- Volume:
- 533
- Issue:
- 3
- ISSN:
- 0021-9967
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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