# The Ups and Downs of Backprop Weights

arXiv: https://arxiv.org/abs/2609.22554 · HTML: https://mlsanity.com/paper/2609.22554/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 51 references that are in the map.
- First posted on arXiv 18 Sep 2026.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Machine Unlearning](https://mlsanity.com/paper/1912.03817/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [How Auto-Encoders Could Provide Credit Assignment in Deep Networks via Target Propagation](https://mlsanity.com/paper/1407.7906/) (2014)
- [A Closer Look at the Limitations of Instruction Tuning](https://mlsanity.com/paper/2402.05119/) (2024)
- [Credit Assignment in Neural Networks through Deep Feedback Control](https://mlsanity.com/paper/2106.07887/) (2021)
- [Neural-guided, Bidirectional Program Search for Abstraction and Reasoning](https://mlsanity.com/paper/2110.11536/) (2021)
- [Questioning Representational Optimism in Deep Learning: The Fractured Entangled Representation Hypothesis](https://mlsanity.com/paper/2505.11581/) (2025)
- [Adaptive Intelligence: leveraging insights from adaptive behavior in animals to build flexible AI systems](https://mlsanity.com/paper/2411.15234/) (2024)
- [Continual Learning through Control Minimization](https://mlsanity.com/paper/2602.04542/) (2026)
- [Learning Compositional Latent Structure with Vector Networks](https://mlsanity.com/paper/2605.28007/) (2026)

## Abstract (arXiv)

Backpropagation (BP) has driven the remarkable success of modern deep learning by enabling large hierarchical networks to learn complex functions end-to-end. Yet it does not by itself determine how parameters should be organized so that functional components can be reused and adapted selectively. For example, object recognition and motion prediction may depend on overlapping parameter sets, making them difficult to isolate or modify independently. We call this condition weight entanglement. Modern architectures dynamically select which parts of a network process each sample: nonlinearities gate units, attention selects interactions, and Mixture-of-Experts architectures route inputs to modules. Yet such selection does not ensure that the same functional component remains linked to an identifiable parameter set across samples. We propose weight operators: parameterized modules that implement reusable functional components and can be composed at inference to form the function required by each sample. Learning proceeds in two stages: the model first infers the required operator composition, then updates only the selected operators' parameter sets. Vector Networks (VNs) provide one implementation. They couple operator selection to local error-driven updates within each layer and show that learned operators can be reused in combinations absent from training while updates remain restricted to the selected parameter sets. This provides a basis for testing functional parameter identifiability: whether an operator remains linked to the same functional component during learning. We argue that functional parameter identifiability may provide an organizing principle for models that systematically reuse and recombine learned functions while adapting only the components that need to change.