Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

This solution mimicks a simplified version of the biological inhibitory interneuron circuit.

The review comment to be evaluated is:

Strengths

1. The authors find a simple, implicit manner to create top-k networks that compares favorably to explicit methods

2. The method is tested in several different circumstances, with different tasks, numbers of neurons, and noise levels. Simple characteristics of the network, such as the fraction of active neurons and their biases, are well described.

Weaknesses

Major

1. As the authors observe, the results are recapitulated using a global negative bias term, acting as common inhibition that requires greater input values to activate neurons and resulting in top-k networks.  Thus, while such an observation may indeed be useful for those interested in such networks, the advance it comprises is a minor one.

Minor

1. While the presented results may bear on biological considerations, as suggested therein, caution is advised, as noise in biological networks is dynamic and thus not perfectly analogous to simply adding noise to inputs of a feedforward network.

The evidence to be evaluated is:Top-K activation functions inspired by inhibitory interneurons have been implemented in a number of deep learning models for greater computational efficiency (Ahmad & Scheinkman, 2019), adversarial robustness (Xiao et al., 2020; Tramer et al., 2020), interpretability (Nelson et al., 2022), and continual learning (Shen et al., 2021; Iyer et al., 2022). However, in all of these instances there are explicit mechanisms built into the network to enforce Top-K and handle repercussions such as creating dead neurons. These Top-K networks, when trained with noise, are also closely related to associative memory models such as Sparse Distributed Memory (SDM) and Modern Hopfield Networks that activate a sparse subset of neurons and were developed to handle noisy queries (Kanerva, 1988; Krotov & Hopfield, 2016).

This network was trained on the CIFAR10 embeddings to mimick training within a deeper network layer and where the manifold is smoother than when training on raw image pixels.

While still neither activation function becomes as sparse as ReLU, the GELU networks implement the same Top-K convergence as ReLU shown in Fig. 3 and form biologically plausible receptive fields like those of Fig. 5.

An increase in noise will create more erroneous low-level activations in neurons that must be ignored to maximize signal to noise ratio.

Similarly, we hypothesize that the encoding layer in our network is learning such projections, so that thresholding performs noise rejection while also producing sparse activations.

We have shown the extent to which a feedforward ReLU MLP is capable of converging with a biological inhibitory interneuron circuit.

This result is particularly striking because of the way the networks converge with sparse coding, producing biological receptive fields and approximating an inhibitory interneuron that implements a Top-K operation.

More broadly, this work builds a new bridge between artificial and biological neural networks by showing how they can be more similar than they may otherwise appear.

We can model explaining away and facilitation with an additional weight matrix \(G\in\mathbb{R}^{m\times m}\) (recall \(m\) is the number of neurons) that we run in a recurrent inner loop. Our one hidden layer network becomes: \[\mu_{0} =W_{e}\tilde{\mathbf{x}}+\mathbf{b}_{e}\] \[\mathbf{z}_{t} =\text{ReLU}(\mu_{t})\] \[\Delta\mu =\big{(}\mu_{0}-G\mathbf{z}_{t}\big{)}-\mu_{t}\] \[\mu_{t+1} =\mu_{t}+\gamma\Delta\mu\] \[\hat{\mathbf{x}} =W_{d}\text{ ReLU}(\mu_{t^{*}})+\mathbf{b}_{d}, \tag{2}\]

We can also replace \(G\mathbf{z}_{t}\) with \(G_{d}G_{e}\mathbf{z}_{t}\) where \(G_{e}\in\mathbb{R}^{1\times m},G_{d}\in\mathbb{R}^{m\times 1}\) implement a single inhibitory interneuron that uses \(2m\) rather than \(m^{2}\) parameters and must learn each of its afferent and efferent connections. When the neurons still have their bias terms this solution has no effect. Removing the bias terms and relying just on the inhibitory interneuron, we found that it performs well (Table 1) and becomes sparse as a function of noise but results in a number of dead neurons and is not as sparse as the baseline ReLU or Explaining Away models. However, this shows that the full inhibitory interneuron solution is at least plausible.

While we just show the mean active neurons here, both solutions look like those of Fig. 3 with the neurons for all inputs converging to a Top-K solution where the bias terms become negative and synchronize along with the key vector \(L_{2}\) norms.

Input: Table 1: Reconstruction Validation Accuracy - The baseline ReLU model varying the number of neurons, compared to the shared bias, explaining away, and inhibitory interneuron networks. We only show noise up to σ = 0.8 because the higher noise levels present trivial solutions that all networks perform equally well on. Due to very high convergence between random seeds, we just present a single run for each model.

Input: Figure 5: Biological receptive fields form with noise. Networks trained on CIFAR10 pixels with σ = 0.8 Gaussian noise. The most active 125 neuron receptive fields are reshaped into 32x32x3 and re-scaled so their values span the range of pixel values [0, 255]. Neurons are sorted by their activity levels (top left is the most active, going across rows then down columns) for a random noisy input of a car. Starting at σ ≥ 0.1 and particularly for σ = 0.8 (shown here) we observe the formation of many Gabor filters and on/off center surround receptive fields that are unique to noisy training.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence and reviewer comments, I'll assess the claim "This solution mimicks a simplified version of the biological inhibitory interneuron circuit."

The evidence shows that while the model exhibits some biological-like properties (Gabor filters, center-surround receptive fields) and implements a form of inhibition, the reviewer correctly notes that the noise implementation is not perfectly analogous to biological networks, where noise is dynamic. The mathematical implementation (Equation 2) shows a simplified approximation using Ge and Gd parameters, but Table 1 indicates this performs similarly to other methods. The claim modestly states "simplified version" and doesn't overstate the biological similarity.

<score>2</score>

Justification:
- The claim is relatively well-stated but slightly hedged by using "simplified version"
- Evidence supports basic biological parallels (receptive fields, inhibitory function)
- Reviewer acknowledges biological relevance but warns about oversimplification
- Mathematical implementation shows clear simplification of biological processes
- Authors demonstrate awareness of limitations in their model's biological fidelity


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

This solution mimicks a simplified version of the biological inhibitory interneuron circuit.

The review comment to be evaluated is:

Strengths:
* The paper tackles the important problem of bridging the gap between biological plausible learning and current artificial neural networks.

Weaknesses:
* The paper mostly focuses on 1-hidden layer networks. It is not too clear why and how these results are relevant for practice, where typically much deeper networks are considered. For classification tasks, the observed sparsity seems to be much less pronounced.
* Unlike claimed in the paper, using the L1-norm can lead to biologically plausible and sparse features even for classification tasks, see e.g. Figure 4 in "Towards Learning Convolutions from Scratch" (https://papers.nips.cc/paper/2020/file/5c528e25e1fdeaf9d8160dc24dbf4d60-Paper.pdf)
* There are some issues regarding novelty/clarity (see next section)

The evidence to be evaluated is:Top-K activation functions inspired by inhibitory interneurons have been implemented in a number of deep learning models for greater computational efficiency (Ahmad & Scheinkman, 2019), adversarial robustness (Xiao et al., 2020; Tramer et al., 2020), interpretability (Nelson et al., 2022), and continual learning (Shen et al., 2021; Iyer et al., 2022). However, in all of these instances there are explicit mechanisms built into the network to enforce Top-K and handle repercussions such as creating dead neurons. These Top-K networks, when trained with noise, are also closely related to associative memory models such as Sparse Distributed Memory (SDM) and Modern Hopfield Networks that activate a sparse subset of neurons and were developed to handle noisy queries (Kanerva, 1988; Krotov & Hopfield, 2016).

This network was trained on the CIFAR10 embeddings to mimick training within a deeper network layer and where the manifold is smoother than when training on raw image pixels.

While still neither activation function becomes as sparse as ReLU, the GELU networks implement the same Top-K convergence as ReLU shown in Fig. 3 and form biologically plausible receptive fields like those of Fig. 5.

An increase in noise will create more erroneous low-level activations in neurons that must be ignored to maximize signal to noise ratio.

Similarly, we hypothesize that the encoding layer in our network is learning such projections, so that thresholding performs noise rejection while also producing sparse activations.

We have shown the extent to which a feedforward ReLU MLP is capable of converging with a biological inhibitory interneuron circuit.

This result is particularly striking because of the way the networks converge with sparse coding, producing biological receptive fields and approximating an inhibitory interneuron that implements a Top-K operation.

More broadly, this work builds a new bridge between artificial and biological neural networks by showing how they can be more similar than they may otherwise appear.

We can model explaining away and facilitation with an additional weight matrix \(G\in\mathbb{R}^{m\times m}\) (recall \(m\) is the number of neurons) that we run in a recurrent inner loop. Our one hidden layer network becomes: \[\mu_{0} =W_{e}\tilde{\mathbf{x}}+\mathbf{b}_{e}\] \[\mathbf{z}_{t} =\text{ReLU}(\mu_{t})\] \[\Delta\mu =\big{(}\mu_{0}-G\mathbf{z}_{t}\big{)}-\mu_{t}\] \[\mu_{t+1} =\mu_{t}+\gamma\Delta\mu\] \[\hat{\mathbf{x}} =W_{d}\text{ ReLU}(\mu_{t^{*}})+\mathbf{b}_{d}, \tag{2}\]

We can also replace \(G\mathbf{z}_{t}\) with \(G_{d}G_{e}\mathbf{z}_{t}\) where \(G_{e}\in\mathbb{R}^{1\times m},G_{d}\in\mathbb{R}^{m\times 1}\) implement a single inhibitory interneuron that uses \(2m\) rather than \(m^{2}\) parameters and must learn each of its afferent and efferent connections. When the neurons still have their bias terms this solution has no effect. Removing the bias terms and relying just on the inhibitory interneuron, we found that it performs well (Table 1) and becomes sparse as a function of noise but results in a number of dead neurons and is not as sparse as the baseline ReLU or Explaining Away models. However, this shows that the full inhibitory interneuron solution is at least plausible.

While we just show the mean active neurons here, both solutions look like those of Fig. 3 with the neurons for all inputs converging to a Top-K solution where the bias terms become negative and synchronize along with the key vector \(L_{2}\) norms.

Input: Table 1: Reconstruction Validation Accuracy - The baseline ReLU model varying the number of neurons, compared to the shared bias, explaining away, and inhibitory interneuron networks. We only show noise up to σ = 0.8 because the higher noise levels present trivial solutions that all networks perform equally well on. Due to very high convergence between random seeds, we just present a single run for each model.

Input: Figure 5: Biological receptive fields form with noise. Networks trained on CIFAR10 pixels with σ = 0.8 Gaussian noise. The most active 125 neuron receptive fields are reshaped into 32x32x3 and re-scaled so their values span the range of pixel values [0, 255]. Neurons are sorted by their activity levels (top left is the most active, going across rows then down columns) for a random noisy input of a car. Starting at σ ≥ 0.1 and particularly for σ = 0.8 (shown here) we observe the formation of many Gabor filters and on/off center surround receptive fields that are unique to noisy training.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence, I find that the claim "This solution mimicks a simplified version of the biological inhibitory interneuron circuit" needs careful evaluation.

The evidence shows that they implemented a simplified mathematical model using Ge and Gd parameters to represent a single inhibitory interneuron. While this implementation shows some biological-like properties (sparse activation, formation of Gabor filters), the review comment and evidence indicate limitations. The model is primarily tested on 1-hidden layer networks, and the sparsity effects are less pronounced in classification tasks. The "mimicking" claim should acknowledge these limitations.

The claim is slightly overstated as it suggests a more direct biological correspondence than the evidence fully supports, though there are legitimate parallels demonstrated through the mathematical implementation and resulting receptive field patterns.

<score>3</score>

Justification:
1. The evidence does demonstrate implementation of an inhibitory circuit mathematically: "G_e∈R^(1×m),G_d∈R^(m×1) implement a single inhibitory interneuron"
2. Biological-like properties emerge (Table 1 results, Figure 5's Gabor filters)
3. Limitations acknowledged in paper: "performs well but results in a number of dead neurons and is not as sparse as the baseline"
4. Review points out depth limitations: "paper mostly focuses on 1-hidden layer networks"
5. The term "mimicks" implies stronger biological correspondence than demonstrated, though some valid parallels exist


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

This solution mimicks a simplified version of the biological inhibitory interneuron circuit.

The review comment to be evaluated is:

In this empirical paper, the authors observe the correlation between the sparsity of the learned representations and the level of noise injected into the input of Neural Networks with the ReLU activation function. Experiments have been carried out on CIFAR10 both on pixel data and on a neural representation, MNIST, and on the WikiText-103 dataset. They report a positive correlation between the magnitude of the injected noise and the sparsity of the representation. They observe Gabor-like filters when reconstructing with noise on pixel data. For the classification task, the performance of the model did not decrease with sparsity. Also, compared with using only the top-K activations of a model learned without noise, the models learned with noise gave better validation accuracies.

The evidence to be evaluated is:Top-K activation functions inspired by inhibitory interneurons have been implemented in a number of deep learning models for greater computational efficiency (Ahmad & Scheinkman, 2019), adversarial robustness (Xiao et al., 2020; Tramer et al., 2020), interpretability (Nelson et al., 2022), and continual learning (Shen et al., 2021; Iyer et al., 2022). However, in all of these instances there are explicit mechanisms built into the network to enforce Top-K and handle repercussions such as creating dead neurons. These Top-K networks, when trained with noise, are also closely related to associative memory models such as Sparse Distributed Memory (SDM) and Modern Hopfield Networks that activate a sparse subset of neurons and were developed to handle noisy queries (Kanerva, 1988; Krotov & Hopfield, 2016).

This network was trained on the CIFAR10 embeddings to mimick training within a deeper network layer and where the manifold is smoother than when training on raw image pixels.

While still neither activation function becomes as sparse as ReLU, the GELU networks implement the same Top-K convergence as ReLU shown in Fig. 3 and form biologically plausible receptive fields like those of Fig. 5.

An increase in noise will create more erroneous low-level activations in neurons that must be ignored to maximize signal to noise ratio.

Similarly, we hypothesize that the encoding layer in our network is learning such projections, so that thresholding performs noise rejection while also producing sparse activations.

We have shown the extent to which a feedforward ReLU MLP is capable of converging with a biological inhibitory interneuron circuit.

This result is particularly striking because of the way the networks converge with sparse coding, producing biological receptive fields and approximating an inhibitory interneuron that implements a Top-K operation.

More broadly, this work builds a new bridge between artificial and biological neural networks by showing how they can be more similar than they may otherwise appear.

We can model explaining away and facilitation with an additional weight matrix \(G\in\mathbb{R}^{m\times m}\) (recall \(m\) is the number of neurons) that we run in a recurrent inner loop. Our one hidden layer network becomes: \[\mu_{0} =W_{e}\tilde{\mathbf{x}}+\mathbf{b}_{e}\] \[\mathbf{z}_{t} =\text{ReLU}(\mu_{t})\] \[\Delta\mu =\big{(}\mu_{0}-G\mathbf{z}_{t}\big{)}-\mu_{t}\] \[\mu_{t+1} =\mu_{t}+\gamma\Delta\mu\] \[\hat{\mathbf{x}} =W_{d}\text{ ReLU}(\mu_{t^{*}})+\mathbf{b}_{d}, \tag{2}\]

We can also replace \(G\mathbf{z}_{t}\) with \(G_{d}G_{e}\mathbf{z}_{t}\) where \(G_{e}\in\mathbb{R}^{1\times m},G_{d}\in\mathbb{R}^{m\times 1}\) implement a single inhibitory interneuron that uses \(2m\) rather than \(m^{2}\) parameters and must learn each of its afferent and efferent connections. When the neurons still have their bias terms this solution has no effect. Removing the bias terms and relying just on the inhibitory interneuron, we found that it performs well (Table 1) and becomes sparse as a function of noise but results in a number of dead neurons and is not as sparse as the baseline ReLU or Explaining Away models. However, this shows that the full inhibitory interneuron solution is at least plausible.

While we just show the mean active neurons here, both solutions look like those of Fig. 3 with the neurons for all inputs converging to a Top-K solution where the bias terms become negative and synchronize along with the key vector \(L_{2}\) norms.

Input: Table 1: Reconstruction Validation Accuracy - The baseline ReLU model varying the number of neurons, compared to the shared bias, explaining away, and inhibitory interneuron networks. We only show noise up to σ = 0.8 because the higher noise levels present trivial solutions that all networks perform equally well on. Due to very high convergence between random seeds, we just present a single run for each model.

Input: Figure 5: Biological receptive fields form with noise. Networks trained on CIFAR10 pixels with σ = 0.8 Gaussian noise. The most active 125 neuron receptive fields are reshaped into 32x32x3 and re-scaled so their values span the range of pixel values [0, 255]. Neurons are sorted by their activity levels (top left is the most active, going across rows then down columns) for a random noisy input of a car. Starting at σ ≥ 0.1 and particularly for σ = 0.8 (shown here) we observe the formation of many Gabor filters and on/off center surround receptive fields that are unique to noisy training.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
I'll evaluate the claim "This solution mimicks a simplified version of the biological inhibitory interneuron circuit."

Summary:
The evidence shows that while the model shares some functional similarities with biological inhibitory circuits (like sparse activation and Gabor-like receptive fields), calling it a "mimick" of biological circuits is somewhat overstated. The paper actually tests a simplified mathematical model (G_d G_e) that captures some properties of inhibitory interneurons, but with limitations - it results in dead neurons and isn't as sparse as other models. The paper itself is more measured, noting this shows the solution is "at least plausible" rather than claiming direct mimicry.

<score>3</score>

Justification:
1. Evidence for reasonable similarity:
- Produces biologically plausible receptive fields (Gabor filters and center-surround patterns) as shown in Fig. 5
- Implements sparse coding similar to biological systems
- Basic functional parallels to inhibitory circuits

2. Evidence for overstatement:
- The paper explicitly states "this shows that the full inhibitory interneuron solution is at least plausible" - more tentative than the claim
- Model has limitations (dead neurons, less sparsity) per Table 1 results
- Simplified mathematical approximation rather than true biological mimicry
- Paper uses more measured language like "can be more similar" and "builds a bridge" rather than claiming direct mimicry

The evidence suggests this is a moderate overstatement - while there are genuine similarities, calling it a "mimick" implies a stronger correspondence than the evidence supports.


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

The network gradually implementing this inhibitory interneuron also results in better performance than explicitly enforcing any sort of inhibition at the start of training.

The evidence to be evaluated is:This result is particularly striking because of the way the networks converge with sparse coding, producing biological receptive fields and approximating an inhibitory interneuron that implements a Top-K operation.

We can also replace \(G\mathbf{z}_{t}\) with \(G_{d}G_{e}\mathbf{z}_{t}\) where \(G_{e}\in\mathbb{R}^{1\times m},G_{d}\in\mathbb{R}^{m\times 1}\) implement a single inhibitory interneuron that uses \(2m\) rather than \(m^{2}\) parameters and must learn each of its afferent and efferent connections.

Removing the bias terms and relying just on the inhibitory interneuron, we found that it performs well (Table 1) and becomes sparse as a function of noise but results in a number of dead neurons and is not as sparse as the baseline ReLU or Explaining Away models.

Input: Table 1: Reconstruction Validation Accuracy - The baseline ReLU model varying the number of neurons, compared to the shared bias, explaining away, and inhibitory interneuron networks. We only show noise up to σ = 0.8 because the higher noise levels present trivial solutions that all networks perform equally well on. Due to very high convergence between random seeds, we just present a single run for each model.

Input: Figure 2: There is a positive relationship between activation sparsity and noise. The average fraction of neurons active during each CIFAR10 latent input over the course of training for 800 epochs. Each line corresponds to training randomly initialized networks with different noise levels σ denoted by different colors. We show the average of three different random seeds and their standard error of the mean (not visible as the variance is so low). Interestingly, the higher noise levels take longer to sparsify but upon convergence become the sparsest.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
1. Summary: Based on the evidence provided, the claim about gradual implementation of inhibitory interneuron leading to better performance appears overstated. Table 1 shows that the inhibitory interneuron model performs similarly to other approaches (including ReLU and Explaining Away), not necessarily better. The evidence shows that inhibitory interneuron networks can achieve comparable performance and develop sparsity, but does not demonstrate superiority over explicitly enforcing inhibition. The evidence primarily focuses on showing how noise affects sparsification and network behavior rather than comparing different inhibition implementation approaches.

<score>4</score>

Justification:
1. Table 1 directly contradicts the claim by showing similar validation accuracy across models, with inhibitory interneuron performance (0.0017, 0.0041, 0.0109, 0.0204) being nearly identical to other approaches.

2. The evidence emphasizes that the inhibitory interneuron "performs well" but notes limitations including "dead neurons" and being "not as sparse as the baseline ReLU or Explaining Away models."

3. The presented figures (2 and 3) and data focus on noise's effect on sparsity rather than comparing different inhibition implementation methods, making the claim about superiority of gradual implementation insufficiently supported.

4. No comparative data is provided showing the performance differences between gradual implementation versus explicit enforcement of inhibition at training start.


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

The network gradually implementing this inhibitory interneuron also results in better performance than explicitly enforcing any sort of inhibition at the start of training.

The review comment to be evaluated is:

Strengths

The paper is simple and easy to follow.

The sparsity effects shown appear relatively large and robust.

Adding noise is a simple manipulation that can have benefits beyond sparsity, and so there is some appeal to using this manipulation as a way to generate sparsity.

Weaknesses

It is odd that the authors focus so much on a one-layer model. For this finding to be broadly relevant, it is important to test whether this effect occurs in large-scale DNNs and whether networks can generate sparsity while maintaining good performance on real-world tasks. The only thing that is done along these lines is with a single, small GPT2 model.

It appears you need fairly high levels of noise to generate substantial sparsity (e.g., sigma=0.3 to get below 20% activation in Figure 2, which based on Figure 4 is quite a lot of noise). It seems this might limit the practical utility of the method, though it is hard to say in part because experiments are mostly limited to the single-layer training regime.

The link with biological receptive fields is tenuous. There are multiple ways of generating center-surround and oriented/bandpass receptive fields (e.g., whitening for center-surround RFs, sparsity for oriented RFs, CNNs often exhibit similar structure at the first layer). It is not clear this approach provides a better fit to biological data than these alternatives and there is no quantification of the match to biology or model comparison. Moreover, there are so many differences between the models trained here and biological networks, that it is hard to know the relevance of this finding, particularly given that the results can vary with the activation function (e.g., the sigmoid activation function does not generate sparsity) and the optimization algorithm (e.g., SGD with a low learning rate apparently does not generate sparsity).

The evidence to be evaluated is:This result is particularly striking because of the way the networks converge with sparse coding, producing biological receptive fields and approximating an inhibitory interneuron that implements a Top-K operation.

We can also replace \(G\mathbf{z}_{t}\) with \(G_{d}G_{e}\mathbf{z}_{t}\) where \(G_{e}\in\mathbb{R}^{1\times m},G_{d}\in\mathbb{R}^{m\times 1}\) implement a single inhibitory interneuron that uses \(2m\) rather than \(m^{2}\) parameters and must learn each of its afferent and efferent connections.

Removing the bias terms and relying just on the inhibitory interneuron, we found that it performs well (Table 1) and becomes sparse as a function of noise but results in a number of dead neurons and is not as sparse as the baseline ReLU or Explaining Away models.

Input: Table 1: Reconstruction Validation Accuracy - The baseline ReLU model varying the number of neurons, compared to the shared bias, explaining away, and inhibitory interneuron networks. We only show noise up to σ = 0.8 because the higher noise levels present trivial solutions that all networks perform equally well on. Due to very high convergence between random seeds, we just present a single run for each model.

Input: Figure 2: There is a positive relationship between activation sparsity and noise. The average fraction of neurons active during each CIFAR10 latent input over the course of training for 800 epochs. Each line corresponds to training randomly initialized networks with different noise levels σ denoted by different colors. We show the average of three different random seeds and their standard error of the mean (not visible as the variance is so low). Interestingly, the higher noise levels take longer to sparsify but upon convergence become the sparsest.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence, I find this claim requires careful evaluation:

The claim states that gradually implementing inhibitory interneurons yields better performance than explicit inhibition at training start. However, the evidence provided (Table 1) shows very similar performance between the inhibitory interneuron approach and other methods (ReLU, Shared Bias, Explain Away) across different noise levels. Additionally, the reviewer points out limitations - namely that the inhibitory interneuron approach results in "dead neurons" and isn't as sparse as baseline models. The evidence doesn't directly compare gradual vs. explicit implementation of inhibition.

<score>4</score>

Justification:
1. Table 1 shows nearly identical validation accuracy across methods, not supporting claims of "better performance"
2. The reviewer notes significant limitations in practical utility due to high noise requirements
3. The evidence focuses more on sparsity effects than comparative performance benefits
4. The claim makes a strong comparative statement without direct experimental evidence showing the advantages of gradual vs explicit inhibition implementation
5. The paper's focus on single-layer models (noted by reviewer) limits the generalizability of this claim


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

The network gradually implementing this inhibitory interneuron also results in better performance than explicitly enforcing any sort of inhibition at the start of training.

The review comment to be evaluated is:

Strengths

1. The authors find a simple, implicit manner to create top-k networks that compares favorably to explicit methods

2. The method is tested in several different circumstances, with different tasks, numbers of neurons, and noise levels. Simple characteristics of the network, such as the fraction of active neurons and their biases, are well described.

Weaknesses

Major

1. As the authors observe, the results are recapitulated using a global negative bias term, acting as common inhibition that requires greater input values to activate neurons and resulting in top-k networks.  Thus, while such an observation may indeed be useful for those interested in such networks, the advance it comprises is a minor one.

Minor

1. While the presented results may bear on biological considerations, as suggested therein, caution is advised, as noise in biological networks is dynamic and thus not perfectly analogous to simply adding noise to inputs of a feedforward network.

The evidence to be evaluated is:This result is particularly striking because of the way the networks converge with sparse coding, producing biological receptive fields and approximating an inhibitory interneuron that implements a Top-K operation.

We can also replace \(G\mathbf{z}_{t}\) with \(G_{d}G_{e}\mathbf{z}_{t}\) where \(G_{e}\in\mathbb{R}^{1\times m},G_{d}\in\mathbb{R}^{m\times 1}\) implement a single inhibitory interneuron that uses \(2m\) rather than \(m^{2}\) parameters and must learn each of its afferent and efferent connections.

Removing the bias terms and relying just on the inhibitory interneuron, we found that it performs well (Table 1) and becomes sparse as a function of noise but results in a number of dead neurons and is not as sparse as the baseline ReLU or Explaining Away models.

Input: Table 1: Reconstruction Validation Accuracy - The baseline ReLU model varying the number of neurons, compared to the shared bias, explaining away, and inhibitory interneuron networks. We only show noise up to σ = 0.8 because the higher noise levels present trivial solutions that all networks perform equally well on. Due to very high convergence between random seeds, we just present a single run for each model.

Input: Figure 2: There is a positive relationship between activation sparsity and noise. The average fraction of neurons active during each CIFAR10 latent input over the course of training for 800 epochs. Each line corresponds to training randomly initialized networks with different noise levels σ denoted by different colors. We show the average of three different random seeds and their standard error of the mean (not visible as the variance is so low). Interestingly, the higher noise levels take longer to sparsify but upon convergence become the sparsest.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Let me evaluate the claim "The network gradually implementing this inhibitory interneuron also results in better performance than explicitly enforcing any sort of inhibition at the start of training."

1. Summary of evaluation:
Based on Table 1, the inhibitory interneuron model shows comparable but not superior performance compared to other methods. The validation accuracy values are very similar across different models, including ReLU baselines, Shared Bias, and Explain Away. Figure 2 and 3 demonstrate gradual implementation of sparsity, but don't show performance advantages. The reviewer also notes this is a "minor" advance, indicating the performance benefits are modest. The claim appears to overstate the performance benefits without acknowledging the similarities in results across methods.

2. Final score:
<score>4</score>

Justification:
- The evidence shows comparable performance, not clearly better performance (Table 1 shows nearly identical validation accuracy across methods)
- The claim states definitively that it "results in better performance" without qualifying or acknowledging the similar results
- The reviewer explicitly states this is a "minor" advance
- While the gradual implementation aspect is supported by Figures 2-3, the performance advantage claim is not well supported by the data
- The claim would be more accurate if it acknowledged the comparable performance rather than claiming superiority


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

The network gradually implementing this inhibitory interneuron also results in better performance than explicitly enforcing any sort of inhibition at the start of training.

The review comment to be evaluated is:

Strengths:
* The paper tackles the important problem of bridging the gap between biological plausible learning and current artificial neural networks.

Weaknesses:
* The paper mostly focuses on 1-hidden layer networks. It is not too clear why and how these results are relevant for practice, where typically much deeper networks are considered. For classification tasks, the observed sparsity seems to be much less pronounced.
* Unlike claimed in the paper, using the L1-norm can lead to biologically plausible and sparse features even for classification tasks, see e.g. Figure 4 in "Towards Learning Convolutions from Scratch" (https://papers.nips.cc/paper/2020/file/5c528e25e1fdeaf9d8160dc24dbf4d60-Paper.pdf)
* There are some issues regarding novelty/clarity (see next section)

The evidence to be evaluated is:This result is particularly striking because of the way the networks converge with sparse coding, producing biological receptive fields and approximating an inhibitory interneuron that implements a Top-K operation.

We can also replace \(G\mathbf{z}_{t}\) with \(G_{d}G_{e}\mathbf{z}_{t}\) where \(G_{e}\in\mathbb{R}^{1\times m},G_{d}\in\mathbb{R}^{m\times 1}\) implement a single inhibitory interneuron that uses \(2m\) rather than \(m^{2}\) parameters and must learn each of its afferent and efferent connections.

Removing the bias terms and relying just on the inhibitory interneuron, we found that it performs well (Table 1) and becomes sparse as a function of noise but results in a number of dead neurons and is not as sparse as the baseline ReLU or Explaining Away models.

Input: Table 1: Reconstruction Validation Accuracy - The baseline ReLU model varying the number of neurons, compared to the shared bias, explaining away, and inhibitory interneuron networks. We only show noise up to σ = 0.8 because the higher noise levels present trivial solutions that all networks perform equally well on. Due to very high convergence between random seeds, we just present a single run for each model.

Input: Figure 2: There is a positive relationship between activation sparsity and noise. The average fraction of neurons active during each CIFAR10 latent input over the course of training for 800 epochs. Each line corresponds to training randomly initialized networks with different noise levels σ denoted by different colors. We show the average of three different random seeds and their standard error of the mean (not visible as the variance is so low). Interestingly, the higher noise levels take longer to sparsify but upon convergence become the sparsest.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
I'll analyze the claim: "The network gradually implementing this inhibitory interneuron also results in better performance than explicitly enforcing any sort of inhibition at the start of training."

1. Summary Analysis:
The evidence shows mixed support for this claim. Table 1 demonstrates that the Inhibitory Interneuron model performs comparably to, but not necessarily better than, other approaches including ReLU and Explaining Away across different noise levels. Figure 2 and Figure 3 show gradual sparsification over training, but don't directly compare performance against explicit inhibition. The reviewer also points out that the results are limited to 1-hidden layer networks and may not generalize to deeper architectures commonly used in practice. The claim overstates the comparative advantage without sufficient evidence of superiority.

<score>4</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

The network gradually implementing this inhibitory interneuron also results in better performance than explicitly enforcing any sort of inhibition at the start of training.

The review comment to be evaluated is:

In this empirical paper, the authors observe the correlation between the sparsity of the learned representations and the level of noise injected into the input of Neural Networks with the ReLU activation function. Experiments have been carried out on CIFAR10 both on pixel data and on a neural representation, MNIST, and on the WikiText-103 dataset. They report a positive correlation between the magnitude of the injected noise and the sparsity of the representation. They observe Gabor-like filters when reconstructing with noise on pixel data. For the classification task, the performance of the model did not decrease with sparsity. Also, compared with using only the top-K activations of a model learned without noise, the models learned with noise gave better validation accuracies.

The evidence to be evaluated is:This result is particularly striking because of the way the networks converge with sparse coding, producing biological receptive fields and approximating an inhibitory interneuron that implements a Top-K operation.

We can also replace \(G\mathbf{z}_{t}\) with \(G_{d}G_{e}\mathbf{z}_{t}\) where \(G_{e}\in\mathbb{R}^{1\times m},G_{d}\in\mathbb{R}^{m\times 1}\) implement a single inhibitory interneuron that uses \(2m\) rather than \(m^{2}\) parameters and must learn each of its afferent and efferent connections.

Removing the bias terms and relying just on the inhibitory interneuron, we found that it performs well (Table 1) and becomes sparse as a function of noise but results in a number of dead neurons and is not as sparse as the baseline ReLU or Explaining Away models.

Input: Table 1: Reconstruction Validation Accuracy - The baseline ReLU model varying the number of neurons, compared to the shared bias, explaining away, and inhibitory interneuron networks. We only show noise up to σ = 0.8 because the higher noise levels present trivial solutions that all networks perform equally well on. Due to very high convergence between random seeds, we just present a single run for each model.

Input: Figure 2: There is a positive relationship between activation sparsity and noise. The average fraction of neurons active during each CIFAR10 latent input over the course of training for 800 epochs. Each line corresponds to training randomly initialized networks with different noise levels σ denoted by different colors. We show the average of three different random seeds and their standard error of the mean (not visible as the variance is so low). Interestingly, the higher noise levels take longer to sparsify but upon convergence become the sparsest.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the claim and evidence, I find this claim needs careful assessment:

The evidence shows that the inhibitory interneuron model performs comparably to other approaches (Table 1) but doesn't clearly demonstrate superior performance. While Figure 2 shows gradual sparsification over training, and Figure 3 illustrates the emergence of Top-K behavior, the evidence doesn't definitively prove that gradual implementation is better than explicit enforcement at the start. The table shows similar validation accuracies across methods, and there's no direct comparison to networks with enforced initial inhibition.

The claim makes a comparative statement about performance benefits without providing explicit experimental evidence comparing gradual vs. immediate inhibition implementation strategies. This appears to be an overstatement of what the data actually demonstrates.

<score>4</score>

Justification:
1. The claim suggests superiority of gradual implementation, but the evidence only shows comparable performance (Table 1 shows similar validation accuracies)
2. No direct experimental comparison is presented between gradual vs. explicit initial inhibition
3. While the evidence shows that the inhibitory interneuron approach works, it doesn't support the comparative claim of being "better than" alternative implementation strategies
4. The review comment doesn't provide additional support for this specific comparative claim


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Concretely, the network synchronizes every neuron's bias term, setting them to be approximately the same negative value, and also every neuron's weight vector, setting them to have the same \(L_{2}\) norm.

The evidence to be evaluated is:Fig. 3 also shows the bias terms for each neuron and the \(L_{2}\) norm of their key vectors. It is clear that these values all synchronize to a value decided on by the network and are responsible for the sparse \(k\) neurons remaining active after the ReLU nonlinearity is applied. As noise increases, the bias terms become more negative to raise the activation threshold and increase sparsity. The \(L_{2}\) norms of the key vectors also become smaller. We hypothesize this is a counter-response to the \(L_{2}\) norms of the data increasing with noise and explains why in high noise settings (\(\sigma\geq 0.8\)) neuron activations linger around \(\sim\)50% sparsity before rapidly becoming very sparse (see Fig. 2).

In addition, this approach resulted in unstable training, more dead neurons, less sparsity, and no synchronization of key vector norms or bias terms.1

While we just show the mean active neurons here, both solutions look like those of Fig. 3 with the neurons for all inputs converging to a Top-K solution where the bias terms become negative and synchronize along with the key vector \(L_{2}\) norms.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
1. Looking at the evidence, particularly Figure 3, I can verify that both the bias terms and L2 norms of key vectors do indeed synchronize to similar values across neurons, especially visible in the middle and right columns. The synchronization becomes more pronounced as noise increases (from 0.0 to 3.0), with bias terms becoming more negative and L2 norms decreasing. The claim accurately describes this synchronization behavior without exaggerating its effects or making unsupported assertions. The evidence directly supports the stated observation.

<score>1</score>

The claim is well-stated (score of 1) because:
- Figure 3 clearly shows the synchronization of bias terms to negative values (middle column)
- The L2 norms of key vectors also converge to similar values (right column)
- The text evidence explicitly confirms this synchronization: "bias terms become negative and synchronize along with the key vector L2 norms"
- The claim makes no unsupported generalizations or exaggerations beyond what is demonstrated in the data
- The observation is consistent across different noise levels, though the specific synchronized values differ


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Concretely, the network synchronizes every neuron's bias term, setting them to be approximately the same negative value, and also every neuron's weight vector, setting them to have the same \(L_{2}\) norm.

The review comment to be evaluated is:

Strengths

The paper is simple and easy to follow.

The sparsity effects shown appear relatively large and robust.

Adding noise is a simple manipulation that can have benefits beyond sparsity, and so there is some appeal to using this manipulation as a way to generate sparsity.

Weaknesses

It is odd that the authors focus so much on a one-layer model. For this finding to be broadly relevant, it is important to test whether this effect occurs in large-scale DNNs and whether networks can generate sparsity while maintaining good performance on real-world tasks. The only thing that is done along these lines is with a single, small GPT2 model.

It appears you need fairly high levels of noise to generate substantial sparsity (e.g., sigma=0.3 to get below 20% activation in Figure 2, which based on Figure 4 is quite a lot of noise). It seems this might limit the practical utility of the method, though it is hard to say in part because experiments are mostly limited to the single-layer training regime.

The link with biological receptive fields is tenuous. There are multiple ways of generating center-surround and oriented/bandpass receptive fields (e.g., whitening for center-surround RFs, sparsity for oriented RFs, CNNs often exhibit similar structure at the first layer). It is not clear this approach provides a better fit to biological data than these alternatives and there is no quantification of the match to biology or model comparison. Moreover, there are so many differences between the models trained here and biological networks, that it is hard to know the relevance of this finding, particularly given that the results can vary with the activation function (e.g., the sigmoid activation function does not generate sparsity) and the optimization algorithm (e.g., SGD with a low learning rate apparently does not generate sparsity).

The evidence to be evaluated is:Fig. 3 also shows the bias terms for each neuron and the \(L_{2}\) norm of their key vectors. It is clear that these values all synchronize to a value decided on by the network and are responsible for the sparse \(k\) neurons remaining active after the ReLU nonlinearity is applied. As noise increases, the bias terms become more negative to raise the activation threshold and increase sparsity. The \(L_{2}\) norms of the key vectors also become smaller. We hypothesize this is a counter-response to the \(L_{2}\) norms of the data increasing with noise and explains why in high noise settings (\(\sigma\geq 0.8\)) neuron activations linger around \(\sim\)50% sparsity before rapidly becoming very sparse (see Fig. 2).

In addition, this approach resulted in unstable training, more dead neurons, less sparsity, and no synchronization of key vector norms or bias terms.1

While we just show the mean active neurons here, both solutions look like those of Fig. 3 with the neurons for all inputs converging to a Top-K solution where the bias terms become negative and synchronize along with the key vector \(L_{2}\) norms.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
Based on my review of the evidence:

The claim states that "the network synchronizes every neuron's bias term...and also every neuron's weight vector." Looking at Figure 3, particularly the middle and right columns, there is clear visual evidence of both bias terms and L2 norms of key vectors converging to similar values across noise conditions. However, the synchronization is not perfect - there remains some spread in the values rather than exact convergence. The claim would be more precise by noting this approximate rather than absolute synchronization, though it does capture the key phenomenon.

<score>2</score>

The claim is mostly well-stated but slightly overstates the precision of synchronization. The evidence shows clear convergence trends but with some remaining variance in both bias terms and L2 norms, particularly visible in the density plots. The claim acknowledges this by using "approximately" for bias terms, but could be more explicit about the approximate nature of the weight vector synchronization as well. The review comments don't directly address this specific claim about synchronization.


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Concretely, the network synchronizes every neuron's bias term, setting them to be approximately the same negative value, and also every neuron's weight vector, setting them to have the same \(L_{2}\) norm.

The review comment to be evaluated is:

Strengths

1. The authors find a simple, implicit manner to create top-k networks that compares favorably to explicit methods

2. The method is tested in several different circumstances, with different tasks, numbers of neurons, and noise levels. Simple characteristics of the network, such as the fraction of active neurons and their biases, are well described.

Weaknesses

Major

1. As the authors observe, the results are recapitulated using a global negative bias term, acting as common inhibition that requires greater input values to activate neurons and resulting in top-k networks.  Thus, while such an observation may indeed be useful for those interested in such networks, the advance it comprises is a minor one.

Minor

1. While the presented results may bear on biological considerations, as suggested therein, caution is advised, as noise in biological networks is dynamic and thus not perfectly analogous to simply adding noise to inputs of a feedforward network.

The evidence to be evaluated is:Fig. 3 also shows the bias terms for each neuron and the \(L_{2}\) norm of their key vectors. It is clear that these values all synchronize to a value decided on by the network and are responsible for the sparse \(k\) neurons remaining active after the ReLU nonlinearity is applied. As noise increases, the bias terms become more negative to raise the activation threshold and increase sparsity. The \(L_{2}\) norms of the key vectors also become smaller. We hypothesize this is a counter-response to the \(L_{2}\) norms of the data increasing with noise and explains why in high noise settings (\(\sigma\geq 0.8\)) neuron activations linger around \(\sim\)50% sparsity before rapidly becoming very sparse (see Fig. 2).

In addition, this approach resulted in unstable training, more dead neurons, less sparsity, and no synchronization of key vector norms or bias terms.1

While we just show the mean active neurons here, both solutions look like those of Fig. 3 with the neurons for all inputs converging to a Top-K solution where the bias terms become negative and synchronize along with the key vector \(L_{2}\) norms.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
1. The evidence strongly supports the claim about network synchronization. Figure 3 clearly demonstrates that both bias terms and L2 norms of key vectors converge to similar values across neurons, particularly visible in the middle and right columns. The text explicitly states "these values all synchronize to a value decided on by the network." The convergence is observed across different noise levels, though the specific synchronized values differ. The claim is precise and accurately reflects what's shown in the data without exaggeration.

<score>1</score>

Justification:
- The claim specifically mentions synchronization of bias terms and L2 norms, which is directly visible in Figure 3's middle and right columns
- The evidence shows consistent synchronization behavior across different noise conditions (0.0, 0.3, 3.0)
- The text corroborates the visual evidence, stating "bias terms become negative and synchronize along with the key vector L2 norms"
- The claim doesn't overreach in its conclusions and stays focused on describing the observed synchronization phenomenon
- Even the reviewer comments, while noting this may be a "minor advance," don't dispute the synchronization finding itself

The claim is well-stated (score 1) as it precisely matches the evidence without overstatement or unwarranted generalizations.


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Concretely, the network synchronizes every neuron's bias term, setting them to be approximately the same negative value, and also every neuron's weight vector, setting them to have the same \(L_{2}\) norm.

The review comment to be evaluated is:

Strengths:
* The paper tackles the important problem of bridging the gap between biological plausible learning and current artificial neural networks.

Weaknesses:
* The paper mostly focuses on 1-hidden layer networks. It is not too clear why and how these results are relevant for practice, where typically much deeper networks are considered. For classification tasks, the observed sparsity seems to be much less pronounced.
* Unlike claimed in the paper, using the L1-norm can lead to biologically plausible and sparse features even for classification tasks, see e.g. Figure 4 in "Towards Learning Convolutions from Scratch" (https://papers.nips.cc/paper/2020/file/5c528e25e1fdeaf9d8160dc24dbf4d60-Paper.pdf)
* There are some issues regarding novelty/clarity (see next section)

The evidence to be evaluated is:Fig. 3 also shows the bias terms for each neuron and the \(L_{2}\) norm of their key vectors. It is clear that these values all synchronize to a value decided on by the network and are responsible for the sparse \(k\) neurons remaining active after the ReLU nonlinearity is applied. As noise increases, the bias terms become more negative to raise the activation threshold and increase sparsity. The \(L_{2}\) norms of the key vectors also become smaller. We hypothesize this is a counter-response to the \(L_{2}\) norms of the data increasing with noise and explains why in high noise settings (\(\sigma\geq 0.8\)) neuron activations linger around \(\sim\)50% sparsity before rapidly becoming very sparse (see Fig. 2).

In addition, this approach resulted in unstable training, more dead neurons, less sparsity, and no synchronization of key vector norms or bias terms.1

While we just show the mean active neurons here, both solutions look like those of Fig. 3 with the neurons for all inputs converging to a Top-K solution where the bias terms become negative and synchronize along with the key vector \(L_{2}\) norms.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
1. The evidence strongly supports the claim about network synchronization of bias terms and weight vector L2 norms. Figure 3 clearly shows that across different noise levels (0.0, 0.3, 3.0), both the neuron bias terms (middle column) and key vector L2 norms (right column) converge to similar values during training. The text explicitly confirms this synchronization behavior. The claim is accurately stated without exaggeration, matching what is demonstrated in both the figure and supporting text descriptions. The review comments don't directly challenge this specific synchronization claim.

<score>1</score>

Justification:
- The claim focuses on a specific observation about bias terms and L2 norms synchronizing, which is directly supported by Figure 3's middle and right columns
- The figure shows clear convergence patterns for both bias terms and L2 norms across noise levels
- The text explicitly states "bias terms become negative and synchronize along with the key vector L2 norms"
- The language used in the claim is appropriately measured ("approximately the same") rather than making absolute statements
- While the review comments raise concerns about other aspects of the paper, they don't dispute this particular synchronization observation
- The evidence demonstrates this behavior consistently across different noise conditions, strengthening the claim's validity


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

Concretely, the network synchronizes every neuron's bias term, setting them to be approximately the same negative value, and also every neuron's weight vector, setting them to have the same \(L_{2}\) norm.

The review comment to be evaluated is:

In this empirical paper, the authors observe the correlation between the sparsity of the learned representations and the level of noise injected into the input of Neural Networks with the ReLU activation function. Experiments have been carried out on CIFAR10 both on pixel data and on a neural representation, MNIST, and on the WikiText-103 dataset. They report a positive correlation between the magnitude of the injected noise and the sparsity of the representation. They observe Gabor-like filters when reconstructing with noise on pixel data. For the classification task, the performance of the model did not decrease with sparsity. Also, compared with using only the top-K activations of a model learned without noise, the models learned with noise gave better validation accuracies.

The evidence to be evaluated is:Fig. 3 also shows the bias terms for each neuron and the \(L_{2}\) norm of their key vectors. It is clear that these values all synchronize to a value decided on by the network and are responsible for the sparse \(k\) neurons remaining active after the ReLU nonlinearity is applied. As noise increases, the bias terms become more negative to raise the activation threshold and increase sparsity. The \(L_{2}\) norms of the key vectors also become smaller. We hypothesize this is a counter-response to the \(L_{2}\) norms of the data increasing with noise and explains why in high noise settings (\(\sigma\geq 0.8\)) neuron activations linger around \(\sim\)50% sparsity before rapidly becoming very sparse (see Fig. 2).

In addition, this approach resulted in unstable training, more dead neurons, less sparsity, and no synchronization of key vector norms or bias terms.1

While we just show the mean active neurons here, both solutions look like those of Fig. 3 with the neurons for all inputs converging to a Top-K solution where the bias terms become negative and synchronize along with the key vector \(L_{2}\) norms.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
I've carefully reviewed the claim "the network synchronizes every neuron's bias term, setting them to be approximately the same negative value, and also every neuron's weight vector, setting them to have the same L2 norm" against the provided evidence.

Figure 3 clearly demonstrates this synchronization behavior, particularly visible in the middle and right columns. The bias terms (middle column) converge to similar negative values, and the L2 norms of key vectors (right column) also show convergence to similar values, especially evident at higher noise levels (0.3 and 3.0). The text evidence explicitly confirms this observation, stating "bias terms become negative and synchronize along with the key vector L2 norms." The claim accurately reflects what is shown in both the figure and supporting text without exaggeration.

<score>1</score>


Input:
Your role is to assess whether a claim is well-stated or overstated based on the available evidence.

The Input Information will include:
1. Original Claim: The claim under evaluation.
2. Evidence: Research findings, including figures, tables, or other relevant data supporting the claim.

Optional. review comment: Reviewer feedback relevant to the claim's validity.

The claim should be assesed with the following:
Score: Evaluate the claim on a scale of 1 to 5, where:
- 1: Well-stated (accurately reflects the evidence without exaggeration)
- 5: Overstated (exaggerates findings' significance, magnitude, or certainty)

Justification: Provide a detailed explanation that includes:
- Instances of exaggerated wording, insufficient experiments, lack of experimental details, gaps in knowledge, weak grounding in evidence, or lack of acknowledgment of limitations.
- Direct citations from relevant evidence that substantiate your reasoning.
- If review comment is included only take into account the relevant comments towards the claim.

The claim to be assessed is:

This results in the activity of every neuron existing within a particular range that, when combined with the negative bias term they all agree upon, results in a sparse \(k\) neurons remaining active.

The evidence to be evaluated is:From this perspective, it makes sense that sparsity can be used to turn off neurons and minimize this Jacobian, providing a potential explanation for our results.

Approaches to introduce activation sparsity have included explicitly using Top-K activation functions (Ranzato et al., 2007; Makhzani and Frey, 2014; Ahmad and Scheinkman, 2019), novel regularization terms (Kurtz et al., 2020; Yang et al., 2020) and other approaches (Schwarz et al., 2021; Molchanov et al., 2017).

This results in the optimal solution for activity \(a_{i}\) to be given by \(\operatorname*{ReLU}(u_{i}-\lambda)-\operatorname*{ReLU}(-u_{i}-\lambda)\) or, if we constrain \(a_{i}\) to be non-negative, \(\operatorname*{ReLU}(u_{i}-\lambda)\), where \(u_{i}\) is the value obtained by projecting the data onto basis \(\phi_{i}\). Intuitively, if the values of our target image \(\mathbf{x}\) reconstructed by \(a_{i}\phi_{i}\) are too small, it is better for \(a_{i}=0\) than to predict \(\mathbf{x}\), where the threshold for this tradeoff is given by \(\lambda\), which behaves as an activation threshold. Top-K activation functions inspired by inhibitory interneurons have been implemented in a number of deep learning models for greater computational efficiency (Ahmad & Scheinkman, 2019), adversarial robustness (Xiao et al., 2020; Tramer et al., 2020), interpretability (Nelson et al., 2022), and continual learning (Shen et al., 2021; Iyer et al., 2022).

These Top-K networks, when trained with noise, are also closely related to associative memory models such as Sparse Distributed Memory (SDM) and Modern Hopfield Networks that activate a sparse subset of neurons and were developed to handle noisy queries (Kanerva, 1988; Krotov & Hopfield, 2016).

Figure 2 shows that a single hidden layer ReLU network with 10,000 neurons learns to become a Top-K network with smaller \(k\) values as the amount of noise increases. This network was trained on the CIFAR10 embeddings to mimick training within a deeper network layer and where the manifold is smoother than when training on raw image pixels.

It is clear that these values all synchronize to a value decided on by the network and are responsible for the sparse \(k\) neurons remaining active after the ReLU nonlinearity is applied. As noise increases, the bias terms become more negative to raise the activation threshold and increase sparsity.

We hypothesize this is a counter-response to the \(L_{2}\) norms of the data increasing with noise and explains why in high noise settings (\(\sigma\geq 0.8\)) neuron activations linger around \(\sim\)50% sparsity before rapidly becoming very sparse (see Fig. 2). Before the key vector \(L_{2}\) norms are sufficiently small, noisy data with large \(L_{2}\) norms produce very large neuron activations (both positive and negative) and the bias terms initialized close to 0 have no real effect on which neurons are active. Because the key vectors are randomly initialized from a symmetric distribution around 0, in expectation half of the neurons are active after the ReLU nonlinearity is applied.

These Top-K networks sort the neuron activations and keep only the \(k\) most active. They were either given fixed \(k\) values or could learn the \(k\) values using either a continuous relaxation that is differentiable or the REINFORCE algorithm (see Appendix A for details) (Williams, 2004). These approaches all performed worse than the shared bias (and default ReLU) networks, with the best networks getting similar validation accuracies as the much smaller 100 neuron network and only when they were not sparse, using \(k=3,000\) neurons.

With these models we find that our networks become even more sparse and do so more quickly, as we would expect due to the explaining away of redundant neurons (see Appendix C).

Investigating our noise trained sparse networks, we find that even after the noise is removed, they remain sparse.

Fig. 6 shows that the sparsity levels remain largely unperturbed.

An increase in noise will create more erroneous low-level activations in neurons that must be ignored to maximize signal to noise ratio. Therefore, during noisy training, the model must learn weight vectors to encode information about the data distribution that can be separated from the noise using only ReLU functions.

Similarly, we hypothesize that the encoding layer in our network is learning such projections, so that thresholding performs noise rejection while also producing sparse activations.

As a result, in the low noise regime, it is optimal for Attention to implement a form of nearest neighbour lookup, activating few keys.

This results in SDM attempting to also perform a nearest neighbour lookup, activating only as many neurons around the noisy query as is necessary to activate those storing the target pattern.

Moreover, the fact that noise alone results in sparse coding rather than having a sparsity penalty in the loss function suggests that the primary driver behind sparse coding may be the handling of noise with metabolic efficiency as an added benefit, rather than the other way around.

**Conclusion -** We have shown that the realistic assumption of noisy training data is sufficient for feed-forward layers to organically become highly sparse and retain their sparsity, even after noise is removed. This result is particularly striking because of the way the networks converge with sparse coding, producing biological receptive fields and approximating an inhibitory interneuron that implements a Top-K operation.

Training the same networks as before but using Eq. 2 with \(t^{*}=1\) and \(\gamma=1\) we present our results in Table 1. We show the sparsity amounts of the networks in Fig. 11.

Removing the bias terms and relying just on the inhibitory interneuron, we found that it performs well (Table 1) and becomes sparse as a function of noise but results in a number of dead neurons and is not as sparse as the baseline ReLU or Explaining Away models.

While we just show the mean active neurons here, both solutions look like those of Fig. 3 with the neurons for all inputs converging to a Top-K solution where the bias terms become negative and synchronize along with the key vector \(L_{2}\) norms.

Input: Table 1: Reconstruction Validation Accuracy - The baseline ReLU model varying the number of neurons, compared to the shared bias, explaining away, and inhibitory interneuron networks. We only show noise up to σ = 0.8 because the higher noise levels present trivial solutions that all networks perform equally well on. Due to very high convergence between random seeds, we just present a single run for each model.

Input: Figure 2: There is a positive relationship between activation sparsity and noise. The average fraction of neurons active during each CIFAR10 latent input over the course of training for 800 epochs. Each line corresponds to training randomly initialized networks with different noise levels σ denoted by different colors. We show the average of three different random seeds and their standard error of the mean (not visible as the variance is so low). Interestingly, the higher noise levels take longer to sparsify but upon convergence become the sparsest.

Input: Figure 14: The GELU network sparsifies with noise when trained on CIFAR10. The GELU network closely resembles the ReLU network by sparsifying (but not to the same degree). It also forms biological receptive fields. We use the arbitrary 0.0001 absolute activation threshold to label if a neuron is on or off.

Input: Figure 8: Receptive fields across noise levels. We show for all noise levels the 625 most active neurons for the truck query (middle of Fig. 9). For 0.8 ≥ σ which activate fewer neurons, we also show the cat query below it. Biological like receptive fields start to appear for σ = 0.1 and can be seen most clearly for σ ∈ {0.3, 0.8, 1.5}.

Input: Figure 7: Training ablations. The positive correlation between noise and sparsity is robust to (a) neuron counts, (b) datasets, (c) noise distributions, and (d) training tasks.

Input: Figure 15: The sigmoid network also sparsifies with noise for CIFAR10. While sigmoid sparsifies in proportion to noise, it does not form biological receptive fields and is less sparse than GELU or ReLU.

Input: Figure 3: Noise induces the formation of Top-K networks. Shown column-wise are the fraction of neurons that are active for each training input (Left), the values of each of the 10,000 neurons bias terms (Middle) and the L2 norms of their key vectors (Right), as a function of number of training epochs. Each is shown for three different representative noise levels (rows). These plots show each input to the network and use the density of blue to represent how many times a particular value occurs.

Input:
You should:
1. Carefully review the claim and the text and image evidence. Summarize how the evidence influenced your evaluation of the claim's validity and strength and briefly explain whether the claim is wellstated or overstated on a scale of 1 to 5 (up to 100 words).
2. Provide the final score (choose from 1 to 5), in the format: <score>{score}</score>.

Output:
After reviewing the evidence carefully, I find this claim to be well-stated and supported by multiple lines of evidence. The figures (particularly Fig. 2 and Fig. 3) directly demonstrate how neurons converge to sparse activation patterns with synchronized bias terms. The evidence shows detailed mathematical explanations and empirical results across different architectures and conditions that support the mechanism described in the claim. The bias terms clearly synchronize to negative values that, combined with ReLU activation, result in sparse k-neuron activation patterns. The claim accurately reflects the evidence without overstatement.

<score>1</score>

Justification:
1. Fig. 3 directly visualizes the synchronization of bias terms and resulting sparse activations
2. Fig. 2 shows quantitative evidence of sparse neuron activation
3. The mathematical derivations provide theoretical grounding
4. Results are robust across multiple experimental conditions (Fig. 7)
5. The claim uses measured language that matches the scope and certainty of the evidence

The claim makes a specific mechanistic statement that is fully supported by both theoretical and empirical evidence without extending beyond what is demonstrated.