We thank the reviewers for their time and helpful feedback. Below we respond to their comments in turn. 'permutation invariance in write values' Y es, we process the values in parallel and then take the sum over the batch We will make this clearer in the updated manuscript. We agree this discussion would be useful. 'Error bars for the plots in Figure 2.' We will conduct multiple runs and include error bars in Figure 2. 'Add titles to each subgraph in Figure 5.' Indeed, we should have done this.

UPDATED I think the authors for their rebuttal comments. All my concerns have been addressed (modulo seeing the extra results / error bars) so I am raising my score to 8. The idea of parameterising the memory as a neural network, and using ideas from metalearning to quickly train it to produce a specified output for new sequences, is very interesting and novel. The paper is overall well written, and I believe should be reproducable by those familiar with metalearning approaches. The justification for the model is interesting - essentially instead of writing some values to a fixed size memory, and then reads being limited to a convex combination of the written values, using a neural network allows potential benefits with compression, as well as generalisation, with constant space. Obviously the key issue with this is whether the memory function can be easily modified in one shot so that a new set of keys and values will be'read' approximately correctly.

Language-based agentic systems have shown great promise in recent years, transitioning from solving small-scale research problems to being deployed in challenging real-world tasks. However, optimizing these systems often requires substantial manual labor. Recent studies have demonstrated that these systems can be represented as computational graphs, enabling automatic optimization. Despite these advancements, most current efforts in Graph-based Agentic System Optimization (GASO) fail to properly assign feedback to the system's components given feedback on the system's output. To address this challenge, we formalize the concept of semantic backpropagation with semantic gradients -- a generalization that aligns several key optimization techniques, including reverse-mode automatic differentiation and the more recent TextGrad by exploiting the relationship among nodes with a common successor. This serves as a method for computing directional information about how changes to each component of an agentic system might improve the system's output. To use these gradients, we propose a method called semantic gradient descent which enables us to solve GASO effectively. Our results on both BIG-Bench Hard and GSM8K show that our approach outperforms existing state-of-the-art methods for solving GASO problems. A detailed ablation study on the LIAR dataset demonstrates the parsimonious nature of our method. A full copy of our implementation is publicly available at https://github.com/HishamAlyahya/semantic_backprop

With high forward gain, a negative feedback system has the ability to perform the inverse of a linear or non linear function that is in the feedback path. This property of negative feedback systems has been widely used in analog circuits to construct precise closed-loop functions. This paper describes how the property of a negative feedback system to perform inverse of a function can be used for training neural networks. This method does not require that the cost or activation functions be differentiable. Hence, it is able to learn a class of non-differentiable functions as well where a gradient descent-based method fails. We also show that gradient descent emerges as a special case of the proposed method. We have applied this method to the MNIST dataset and obtained results that shows the method is viable for neural network training. This method, to the best of our knowledge, is novel in machine learning.