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 degree to which our network becomes a sparse coding, Top-K network is proportional to the amount of noise applied, up to a noise limit.

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:Gaussian noise injection has been interpreted as a form of model regularization, to help avoid overfitting (Zur et al., 2009) and improve generalization (Sietsma and Dow, 1991; Matsuoka, 1992).

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.

However, we are unaware of any existing work which finds that noisy training with a ReLU activation function not only results in sparsity but also converges to a sparse coding, Top-K network.

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).

By default, we train a single hidden layer ReLU network with different amounts of random Gaussian noise applied to the input. The objective is to remove the noise and reconstruct the original input. Formally, noise is applied from an isotropic Gaussian with variance \(\sigma\) to the input \(\mathbf{x}\).

To ensure our results are robust, we vary a number of settings, finding that in every case the relationship between noise and network sparsity holds.

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.

This reveals that as noise increases, the variance for how many neurons are active shrinks, so that the mean is an accurate summary statistic.

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).

This is a similar result to that of sparse coding (Olshausen & Field, 1997), however, here we use noise with the ReLU activation function instead of a sparsity penalty and train on full images instead of 8x8 patches.

When we tried training the network without any noise but instead with an \(L_{1}\) activation penalty motivated by the original sparse coding setup (Olshausen & Field, 1997), no biological receptive fields were observed. In addition, this approach resulted in unstable training, more dead neurons, less sparsity, and no synchronization of key vector norms or bias terms.1

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.

For classification, it is clear that while the correlation between noise and sparsity holds, it is not quite as strong.

In fact, for classification \(\sigma\in\{0.1,0.3\}\) both get 94.3% validation accuracy instead of the 93.4% that the baseline gets, showing slightly better generalization while also being more sparse (66% for baseline versus 55% for \(\sigma=0.1\) and 45% for \(\sigma=0.3\)). Note that for the networks with \(\sigma\geq 0.8\) for reconstruction and \(\sigma\geq 3.0\) for classification, annealing the noise results in dead neurons, presumably because the data manifold no longer spans as large a space.

The correlation between noise and activation sparsity remains and is again retained even after noise is removed.

Figure 7(d) shows the final sparsity amounts of the first model layer with each of the other layers giving similar results with \(\sim\)3x to \(\sim\)9x more sparsity when \(\sigma=3.0\), compared to \(\sigma=0.0\).

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. In natural images, for example, certain projections (e.g., with Gabor filters) have high kurtosis which allows them to be easily distinguished from noise via thresholding or "coring" (Simoncelli and Adelson, 1996). 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.

The positive correlation between noise and sparsity is opposite to Transformer Attention and associative memory models such as SDM and Hopfield Networks (Bricken and Pehlevan, 2021).

As a result, in the low noise regime, it is optimal for Attention to implement a form of nearest neighbour lookup, activating few keys. When there is more noise, especially noise that moves the query so far from its target key that it is no longer the nearest, it is optimal to activate more keys and average over them, losing accuracy but giving a solution in the correct neighbourhood.

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. Combining noisy training with other approaches to induce sparsity, including taking additional ideas from sparse coding, may result in even higher degrees of sparsity.

* Zur et al. (2009) Richard M. Zur, Yulei Jiang, Lorenzo L. Pesce, and Karen Drukker. Noise injection for training artificial neural networks: a comparison with weight decay and early stopping. _Medical physics_, 36 10:4810-8, 2009.

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 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 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 6: Noisy pretraining retains network sparsity. The vertical purple lines denote the start of noise annealing where each noise level is linearly decayed down to σ = 0. For both reconstruction (left) and classification (right) tasks the networks remain highly sparse even after all noise is removed. Moreover, there is no noticeable performance difference between any of the networks while some of those trained with moderate noise perform slightly better than the noise free baseline. We truncate the x-axis to start at epoch 600 for the sake of clarity. The classification networks continue to sparsify even when noise annealing has started because unlike in the reconstruction task, the sparsity level did not converge within the first 800 epochs.

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 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 12: Dead Neurons during the reconstruction task. During noise annealing, the higher noise levels σ ≥ 0.8 see a number of dead neurons. However, this does not full explain their sparsity levels and on this trivial task it does not hurt their reconstruction performance.

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 evaluate the claim: "The degree to which our network becomes a sparse coding, Top-K network is proportional to the amount of noise applied, up to a noise limit."

Summary:
The evidence strongly supports this claim through multiple experiments and visualizations. Figures 2, 3, 7, and 14-15 consistently show that increasing noise levels lead to greater sparsity across different architectures, datasets, and training tasks. The relationship holds up to certain noise thresholds (σ≥0.8 for reconstruction, σ≥3.0 for classification), beyond which networks exhibit dead neurons. The claim is carefully qualified with "up to a noise limit" and accurately reflects the demonstrated relationship without overstating the findings.

<score>1</score>

Justification:
1. Figure 2 directly shows the positive correlation between noise and sparsity
2. Figure 7 demonstrates robustness across multiple variables (neurons, datasets, distributions, tasks)
3. The evidence acknowledges limitations (dead neurons at high noise levels)
4. Results are validated across multiple architectures (ReLU, GELU, Sigmoid)
5. The relationship is weaker for classification tasks but still holds
6. The claim's wording is precise and includes appropriate caveats

The reviewer's comment about classification tasks having less pronounced sparsity is acknowledged in the paper's evidence, but doesn't invalidate the fundamental relationship claimed.


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 degree to which our network becomes a sparse coding, Top-K network is proportional to the amount of noise applied, up to a noise limit.

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:Gaussian noise injection has been interpreted as a form of model regularization, to help avoid overfitting (Zur et al., 2009) and improve generalization (Sietsma and Dow, 1991; Matsuoka, 1992).

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.

However, we are unaware of any existing work which finds that noisy training with a ReLU activation function not only results in sparsity but also converges to a sparse coding, Top-K network.

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).

By default, we train a single hidden layer ReLU network with different amounts of random Gaussian noise applied to the input. The objective is to remove the noise and reconstruct the original input. Formally, noise is applied from an isotropic Gaussian with variance \(\sigma\) to the input \(\mathbf{x}\).

To ensure our results are robust, we vary a number of settings, finding that in every case the relationship between noise and network sparsity holds.

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.

This reveals that as noise increases, the variance for how many neurons are active shrinks, so that the mean is an accurate summary statistic.

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).

This is a similar result to that of sparse coding (Olshausen & Field, 1997), however, here we use noise with the ReLU activation function instead of a sparsity penalty and train on full images instead of 8x8 patches.

When we tried training the network without any noise but instead with an \(L_{1}\) activation penalty motivated by the original sparse coding setup (Olshausen & Field, 1997), no biological receptive fields were observed. In addition, this approach resulted in unstable training, more dead neurons, less sparsity, and no synchronization of key vector norms or bias terms.1

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.

For classification, it is clear that while the correlation between noise and sparsity holds, it is not quite as strong.

In fact, for classification \(\sigma\in\{0.1,0.3\}\) both get 94.3% validation accuracy instead of the 93.4% that the baseline gets, showing slightly better generalization while also being more sparse (66% for baseline versus 55% for \(\sigma=0.1\) and 45% for \(\sigma=0.3\)). Note that for the networks with \(\sigma\geq 0.8\) for reconstruction and \(\sigma\geq 3.0\) for classification, annealing the noise results in dead neurons, presumably because the data manifold no longer spans as large a space.

The correlation between noise and activation sparsity remains and is again retained even after noise is removed.

Figure 7(d) shows the final sparsity amounts of the first model layer with each of the other layers giving similar results with \(\sim\)3x to \(\sim\)9x more sparsity when \(\sigma=3.0\), compared to \(\sigma=0.0\).

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. In natural images, for example, certain projections (e.g., with Gabor filters) have high kurtosis which allows them to be easily distinguished from noise via thresholding or "coring" (Simoncelli and Adelson, 1996). 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.

The positive correlation between noise and sparsity is opposite to Transformer Attention and associative memory models such as SDM and Hopfield Networks (Bricken and Pehlevan, 2021).

As a result, in the low noise regime, it is optimal for Attention to implement a form of nearest neighbour lookup, activating few keys. When there is more noise, especially noise that moves the query so far from its target key that it is no longer the nearest, it is optimal to activate more keys and average over them, losing accuracy but giving a solution in the correct neighbourhood.

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. Combining noisy training with other approaches to induce sparsity, including taking additional ideas from sparse coding, may result in even higher degrees of sparsity.

* Zur et al. (2009) Richard M. Zur, Yulei Jiang, Lorenzo L. Pesce, and Karen Drukker. Noise injection for training artificial neural networks: a comparison with weight decay and early stopping. _Medical physics_, 36 10:4810-8, 2009.

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 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 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 6: Noisy pretraining retains network sparsity. The vertical purple lines denote the start of noise annealing where each noise level is linearly decayed down to σ = 0. For both reconstruction (left) and classification (right) tasks the networks remain highly sparse even after all noise is removed. Moreover, there is no noticeable performance difference between any of the networks while some of those trained with moderate noise perform slightly better than the noise free baseline. We truncate the x-axis to start at epoch 600 for the sake of clarity. The classification networks continue to sparsify even when noise annealing has started because unlike in the reconstruction task, the sparsity level did not converge within the first 800 epochs.

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 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 12: Dead Neurons during the reconstruction task. During noise annealing, the higher noise levels σ ≥ 0.8 see a number of dead neurons. However, this does not full explain their sparsity levels and on this trivial task it does not hurt their reconstruction performance.

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 careful review, the claim that "the degree to which our network becomes a sparse coding, Top-K network is proportional to the amount of noise applied, up to a noise limit" is well-supported by extensive empirical evidence. Multiple figures (2, 3, 7, 14, 15) consistently demonstrate this relationship across different architectures, datasets, and noise levels. The evidence shows clear correlation between noise levels and sparsity, with higher noise leading to greater sparsity until reaching certain thresholds. The claim is appropriately qualified with "up to a noise limit" acknowledging the upper bounds observed in the data. The relationship is robust across multiple experimental conditions and carefully documented with quantitative results.

<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:

To validate that the network approximates an inhibitory interneuron, we replace each neuron's bias term with a single, shared bias term.

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).

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.

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. This means the network must wait to first shrink its key vector \(L_{2}\) norms before the bias terms can affect activation sparsity.

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. 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:
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, the statement that "replacing each neuron's bias term with a single, shared bias term validates that the network approximates an inhibitory interneuron" appears overstated. While Table 1 shows comparable performance between the shared bias and inhibitory interneuron models, the evidence actually suggests that the inhibitory interneuron solution is merely "plausible." The text specifically states "this shows that the full inhibitory interneuron solution is at least plausible" - a much more measured conclusion than claiming it validates the approximation. Additionally, the evidence indicates that removing bias terms and relying solely on the inhibitory interneuron results in dead neurons and less sparsity than baseline models.

<score>4</score>

Justification:
1. The evidence shows similar performance metrics but doesn't definitively validate the approximation
2. The authors themselves use more cautious language ("plausible") rather than claiming validation
3. The evidence reveals limitations when using only the inhibitory interneuron approach (dead neurons, less sparsity)
4. The claim overstates the strength of the evidence by suggesting "validation" when the data only supports plausibility
5. While there is a relationship between shared bias and inhibitory interneuron behavior, the evidence doesn't fully validate the approximation 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:

To validate that the network approximates an inhibitory interneuron, we replace each neuron's bias term with a single, shared bias term.

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: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).

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.

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. This means the network must wait to first shrink its key vector \(L_{2}\) norms before the bias terms can affect activation sparsity.

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. 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:
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, the evidence shows that replacing individual bias terms with a shared bias does produce functioning networks, as demonstrated by comparable validation accuracy in Table 1. However, the claim that this "validates that the network approximates an inhibitory interneuron" appears overstated. While the shared bias model performs similarly to other architectures, the evidence doesn't definitively prove it functionally mimics biological inhibitory interneurons. The reviewer also points out that the biological link is tenuous and lacks quantitative comparison to actual biological data. The claim makes stronger conclusions about biological relevance than the empirical results support.

<score>4</score>

Justification:
1. The evidence shows the shared bias model achieves similar performance metrics to other architectures (Table 1), but this alone doesn't validate biological approximation
2. The reviewer notes "the link with biological receptive fields is tenuous" and that "there are multiple ways of generating center-surround and oriented/bandpass receptive fields"
3. There's no direct quantitative comparison to biological interneuron behavior
4. The claim suggests a stronger biological validation than what's demonstrated by the computational experiments
5. The reviewer points out that "there are so many differences between the models trained here and biological networks, that it is hard to know the relevance of this finding"

The claim would be better stated by focusing on the computational performance rather than making strong assertions about biological approximation without sufficient comparative evidence.


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:

To validate that the network approximates an inhibitory interneuron, we replace each neuron's bias term with a single, shared bias term.

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).

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.

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. This means the network must wait to first shrink its key vector \(L_{2}\) norms before the bias terms can affect activation sparsity.

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. 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:
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, the statement appears somewhat overstated. While Table 1 shows comparable performance between the inhibitory interneuron model and other approaches, and the evidence demonstrates that replacing individual bias terms with a shared bias term can work, the claim of "validating" that the network approximates an inhibitory interneuron is too strong. The evidence shows it's plausible and performs similarly, but doesn't definitively validate the biological analogy. The review comment also specifically cautions against over-interpreting biological implications. A more measured claim would acknowledge this as a demonstration of functional similarity rather than validation.

<score>4</score>

Justification:
1. The evidence shows similar performance metrics but doesn't conclusively validate biological approximation
2. The review explicitly warns about biological analogies, noting "caution is advised, as noise in biological networks is dynamic"
3. While the model performs well with a shared bias term (Table 1), this demonstrates functional equivalence rather than biological validation
4. The paper itself uses more measured language elsewhere, calling the inhibitory interneuron solution "plausible" rather than validated
5. The claim would be better stated as demonstrating functional similarity or providing evidence supporting the possibility of interneuron-like behavior


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:

To validate that the network approximates an inhibitory interneuron, we replace each neuron's bias term with a single, shared bias term.

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).

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.

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. This means the network must wait to first shrink its key vector \(L_{2}\) norms before the bias terms can affect activation sparsity.

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. 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:
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 assess the claim: "To validate that the network approximates an inhibitory interneuron, we replace each neuron's bias term with a single, shared bias term."

Based on the evidence provided:
- The evidence shows that replacing individual bias terms with shared bias terms works comparably well to the baseline ReLU model (Table 1).
- However, the evidence doesn't definitively validate that this substitution proves the network approximates an inhibitory interneuron. The paper shows it's "plausible" but not conclusively validated.
- The reviewer points out limitations regarding network depth and generalizability.
- The authors themselves use more cautious language elsewhere, stating it "shows that the full inhibitory interneuron solution is at least plausible."

The claim appears somewhat overstated by using "validate" when the evidence only supports plausibility. A more accurate statement would acknowledge this as supportive evidence rather than validation.

<score>3</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:

To validate that the network approximates an inhibitory interneuron, we replace each neuron's bias term with a single, shared bias term.

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).

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.

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. This means the network must wait to first shrink its key vector \(L_{2}\) norms before the bias terms can affect activation sparsity.

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. 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:
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, the claim that "replacing each neuron's bias term with a single, shared bias term validates that the network approximates an inhibitory interneuron" appears to be overstated. While the evidence shows that a shared bias approach can work (as demonstrated in Table 1) and produces sparse representations, it doesn't conclusively validate that this approximates an inhibitory interneuron. The paper actually shows that when using a dedicated inhibitory interneuron architecture (Gd,Ge), the results are different - it "performs well... but results in a number of dead neurons and is not as sparse as the baseline."

<score>4</score>

Justification:
1. The evidence shows shared bias works, but doesn't prove it validates interneuron approximation
2. The actual inhibitory interneuron implementation produced different results from the shared bias approach
3. The paper notes "this shows that the full inhibitory interneuron solution is at least plausible" - suggesting possibility rather than validation
4. The review comment doesn't specifically address this claim's validity
5. Table 1 shows similar performance between approaches but doesn't validate biological approximation

A better claim would focus on the shared bias term's ability to produce sparse representations rather than making strong claims about biological validation.


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:

Further investigating the degree to which this network uses sparse coding, we find that it learns receptive fields similar to those of mammalian V1 with Gabor filters and retinal ganglion cells with on/off center surround (Sterling and Laughlin, 2015; Olshausen and Field, 1997).

The evidence to be evaluated is:However, we are unaware of any existing work which finds that noisy training with a ReLU activation function not only results in sparsity but also converges to a sparse coding, Top-K network. Learning reconstructions of training data with sparse activations is the mainstay of sparse coding (Olshausen & Field, 1997). Sparse coding uses an overcomplete basis to learn a reconstruction of data with an \(L_{1}\) regularization penalty on neuron activity. The image reconstruction can be written as \(\hat{\mathbf{x}}=\sum_{i}^{N}a_{i}\phi_{i}\) where \(\phi_{i}\) is a basis vector from the matrix or "dictionary" \(\Phi\); \(a_{i}\) is the activity of this basis vector, and the activation weighted sum of basis vectors produces the output \(\hat{\mathbf{x}}\). The objective function aims to minimize the mean squared-error between the reconstructed image and the original image while having sparse neuron activity: \(\operatorname*{arg\,min}_{\Phi,\mathbf{n}}(\mathbf{x}-\hat{\mathbf{x}})^{2}+ \lambda\sum_{i}^{N}|a_{i}|\). This sparse coding task is an example of a statistical model converging with neuroscience because, in addition to producing sparse representations, the basis functions learn to become Gabor filters like those found in area V1 of the visual system (Olshausen & Field, 1997).

To ensure our results are robust, we vary a number of settings, finding that in every case the relationship between noise and network sparsity holds.

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. While Fig. 2 only shows the mean number of neurons that are active across all 50,000 CIFAR10 inputs per epoch, Figure 3 shows the fraction of active neurons for every input.

Looking more closely at the sparse solutions found by our ReLU networks, we discovered that for \(\sigma\geq 0.3\), neurons begin to form receptive fields reminiscent of V1 Gabor filters and on/off center surround retinal ganglion cells (Sterling & Laughlin, 2015; Olshausen & Field, 1997).

This is a similar result to that of sparse coding (Olshausen & Field, 1997), however, here we use noise with the ReLU activation function instead of a sparsity penalty and train on full images instead of 8x8 patches.

The longer training progressed, the more similar the receptive fields appeared to those found in biology.

When we tried training the network without any noise but instead with an \(L_{1}\) activation penalty motivated by the original sparse coding setup (Olshausen & Field, 1997), no biological receptive fields were observed.

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.

In natural images, for example, certain projections (e.g., with Gabor filters) have high kurtosis which allows them to be easily distinguished from noise via thresholding or "coring" (Simoncelli and Adelson, 1996). 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.

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.

Here we show additional images of the receptive fields for networks trained with different amounts of noise (Fig. 8), the queries used to activate these neurons (Fig. 9) and how the receptive fields look more biological as the network is trained for longer (Fig. 10).

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: 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: 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:
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 careful review, the claim about learning receptive fields similar to mammalian V1 with Gabor filters and retinal ganglion cells appears well-supported by the evidence. The figures, particularly Figure 5 and Figure 8, clearly demonstrate the emergence of Gabor-like filters and center-surround receptive fields at specific noise levels (σ ≥ 0.1, especially at σ = 0.8). The evidence provides comprehensive visual demonstrations and quantitative analysis showing these biological-like patterns emerge consistently under certain noise conditions. The claim is measured in its scope and accurately reflects what the data shows without overextending the findings.

<score>1</score>

Justification:
1. The evidence directly demonstrates the claimed receptive field patterns through multiple visualizations (Figs 5, 8)
2. The paper provides robust experimental validation across different noise levels
3. The claim is carefully worded ("similar to") rather than claiming exact equivalence
4. The results are consistent across different experimental conditions
5. The paper acknowledges this is a "similar result" to previous work while noting key methodological differences
6. References to biological studies (Sterling & Laughlin, 2015; Olshausen & Field, 1997) appropriately ground the comparison


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:

Further investigating the degree to which this network uses sparse coding, we find that it learns receptive fields similar to those of mammalian V1 with Gabor filters and retinal ganglion cells with on/off center surround (Sterling and Laughlin, 2015; Olshausen and Field, 1997).

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:However, we are unaware of any existing work which finds that noisy training with a ReLU activation function not only results in sparsity but also converges to a sparse coding, Top-K network. Learning reconstructions of training data with sparse activations is the mainstay of sparse coding (Olshausen & Field, 1997). Sparse coding uses an overcomplete basis to learn a reconstruction of data with an \(L_{1}\) regularization penalty on neuron activity. The image reconstruction can be written as \(\hat{\mathbf{x}}=\sum_{i}^{N}a_{i}\phi_{i}\) where \(\phi_{i}\) is a basis vector from the matrix or "dictionary" \(\Phi\); \(a_{i}\) is the activity of this basis vector, and the activation weighted sum of basis vectors produces the output \(\hat{\mathbf{x}}\). The objective function aims to minimize the mean squared-error between the reconstructed image and the original image while having sparse neuron activity: \(\operatorname*{arg\,min}_{\Phi,\mathbf{n}}(\mathbf{x}-\hat{\mathbf{x}})^{2}+ \lambda\sum_{i}^{N}|a_{i}|\). This sparse coding task is an example of a statistical model converging with neuroscience because, in addition to producing sparse representations, the basis functions learn to become Gabor filters like those found in area V1 of the visual system (Olshausen & Field, 1997).

To ensure our results are robust, we vary a number of settings, finding that in every case the relationship between noise and network sparsity holds.

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. While Fig. 2 only shows the mean number of neurons that are active across all 50,000 CIFAR10 inputs per epoch, Figure 3 shows the fraction of active neurons for every input.

Looking more closely at the sparse solutions found by our ReLU networks, we discovered that for \(\sigma\geq 0.3\), neurons begin to form receptive fields reminiscent of V1 Gabor filters and on/off center surround retinal ganglion cells (Sterling & Laughlin, 2015; Olshausen & Field, 1997).

This is a similar result to that of sparse coding (Olshausen & Field, 1997), however, here we use noise with the ReLU activation function instead of a sparsity penalty and train on full images instead of 8x8 patches.

The longer training progressed, the more similar the receptive fields appeared to those found in biology.

When we tried training the network without any noise but instead with an \(L_{1}\) activation penalty motivated by the original sparse coding setup (Olshausen & Field, 1997), no biological receptive fields were observed.

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.

In natural images, for example, certain projections (e.g., with Gabor filters) have high kurtosis which allows them to be easily distinguished from noise via thresholding or "coring" (Simoncelli and Adelson, 1996). 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.

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.

Here we show additional images of the receptive fields for networks trained with different amounts of noise (Fig. 8), the queries used to activate these neurons (Fig. 9) and how the receptive fields look more biological as the network is trained for longer (Fig. 10).

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: 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: 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:
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, the claim about learning receptive fields similar to mammalian V1 appears somewhat overstated. While Figures 5 and 8 do show some Gabor-like and center-surround patterns emerging at certain noise levels (particularly σ ≥ 0.3), the reviewer correctly points out that multiple mechanisms can generate such patterns, and there is no quantitative comparison to biological data. The paper also acknowledges limitations, noting these patterns only emerge under specific conditions (noise levels, activation functions). The similarity to biological receptive fields exists but the strength of this connection is overstated without more rigorous validation.

<score>4</score>

Justification:
1. The evidence shows qualitative visual similarities between learned receptive fields and biological patterns, but lacks:
- Quantitative comparisons to biological data
- Model comparisons against alternative mechanisms
- Robust testing across different architectures/conditions

2. Key limitations cited in review:
- Results vary significantly with activation function and optimization algorithm
- Many differences exist between these models and biological networks
- Multiple other approaches can generate similar patterns

3. The claim language ("similar to") implies stronger biological relevance than supported by the evidence presented, though some visual similarity is demonstrated in Figures 5 and 8.


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:

Further investigating the degree to which this network uses sparse coding, we find that it learns receptive fields similar to those of mammalian V1 with Gabor filters and retinal ganglion cells with on/off center surround (Sterling and Laughlin, 2015; Olshausen and Field, 1997).

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:However, we are unaware of any existing work which finds that noisy training with a ReLU activation function not only results in sparsity but also converges to a sparse coding, Top-K network. Learning reconstructions of training data with sparse activations is the mainstay of sparse coding (Olshausen & Field, 1997). Sparse coding uses an overcomplete basis to learn a reconstruction of data with an \(L_{1}\) regularization penalty on neuron activity. The image reconstruction can be written as \(\hat{\mathbf{x}}=\sum_{i}^{N}a_{i}\phi_{i}\) where \(\phi_{i}\) is a basis vector from the matrix or "dictionary" \(\Phi\); \(a_{i}\) is the activity of this basis vector, and the activation weighted sum of basis vectors produces the output \(\hat{\mathbf{x}}\). The objective function aims to minimize the mean squared-error between the reconstructed image and the original image while having sparse neuron activity: \(\operatorname*{arg\,min}_{\Phi,\mathbf{n}}(\mathbf{x}-\hat{\mathbf{x}})^{2}+ \lambda\sum_{i}^{N}|a_{i}|\). This sparse coding task is an example of a statistical model converging with neuroscience because, in addition to producing sparse representations, the basis functions learn to become Gabor filters like those found in area V1 of the visual system (Olshausen & Field, 1997).

To ensure our results are robust, we vary a number of settings, finding that in every case the relationship between noise and network sparsity holds.

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. While Fig. 2 only shows the mean number of neurons that are active across all 50,000 CIFAR10 inputs per epoch, Figure 3 shows the fraction of active neurons for every input.

Looking more closely at the sparse solutions found by our ReLU networks, we discovered that for \(\sigma\geq 0.3\), neurons begin to form receptive fields reminiscent of V1 Gabor filters and on/off center surround retinal ganglion cells (Sterling & Laughlin, 2015; Olshausen & Field, 1997).

This is a similar result to that of sparse coding (Olshausen & Field, 1997), however, here we use noise with the ReLU activation function instead of a sparsity penalty and train on full images instead of 8x8 patches.

The longer training progressed, the more similar the receptive fields appeared to those found in biology.

When we tried training the network without any noise but instead with an \(L_{1}\) activation penalty motivated by the original sparse coding setup (Olshausen & Field, 1997), no biological receptive fields were observed.

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.

In natural images, for example, certain projections (e.g., with Gabor filters) have high kurtosis which allows them to be easily distinguished from noise via thresholding or "coring" (Simoncelli and Adelson, 1996). 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.

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.

Here we show additional images of the receptive fields for networks trained with different amounts of noise (Fig. 8), the queries used to activate these neurons (Fig. 9) and how the receptive fields look more biological as the network is trained for longer (Fig. 10).

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: 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: 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:
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, the claim that the network learns receptive fields similar to mammalian V1 with Gabor filters and retinal ganglion cells appears well-supported. The evidence shows:
- Clear visualization of Gabor-like filters and center-surround patterns in Figures 5 and 8, particularly at noise levels σ ≥ 0.3
- Quantitative results showing sparsification effects (Figures 2-3)
- Direct comparisons to biological systems with appropriate citations
- Appropriate acknowledgment of when the patterns emerge (σ ≥ 0.3)
- Conservative language ("similar to" rather than claiming exact equivalence)

The claim is well-stated and accurately reflects the visual and quantitative evidence without exaggeration.

<score>1</score>