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

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

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

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

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

The claim to be assessed is:

This observation holds even when we control for the number of trainable parameters.

The review comment to be evaluated is:

This paper as the name suggests, tries to figure out whether and through which ways bpe can affect Transformer’s memorization capacity. It evaluates Transformer’s memorization under these 4 settings: memorizing random synthetic data, memorizing random labeled natural language data, recognizing training data with lower output entropy, and training data recovery QA. Experiments show that if we have more merge times for bpe (larger vocabulary size), the model’s performance on all the four settings would improve on 3 architectures, which shows that bpe indeed can affect the model’s memorization capacity. Larger the vocabulary size is, the better the model would perform on memorizing. Then, the paper tries to figure out why more merges in bpe would lead to better memorization. By excluding two other hypotheses, the paper concludes that more merges in bpe results in shorter input sequence and that makes memorizing easier for transformers.

The evidence to be evaluated is:To avoid this confounding factor, we complement our study with experiments where we control for the change in the number of embedding parameters. To do so, we replace the embedding layer by a combination of an embedding and a fully-connected layer. This way, we can change the dimensionality of the input & output token embeddings and control the number of the learned parameters while maintaining the rest of the model isolated from any changes.

In preliminary experiments, we found that a 4-layer Encoder model quickly achieves 100% label prediction accuracy (on train), irrespective of the number of subwords. Hence, in this experiment we used a 1-layer version for that model type with embedding and FFN sizes of 256 & 512.

We also run complementary experiments where we fix the number of learned parameters to stay roughly the same for each vocabulary size (see SS3.2).

In Figure 0(a) we report results for "vanilla" architectures (without an additional FFN layer that allows to control for the number of learned parameters) and in Figure 0(b) we provide results for the models with the number of parameters fixed.

This tendency persists when controlling for the number of learned parameters (Figure 0(b)).

Focusing on the models with the number of parameters fixed, we see that even when correcting for the total number of embedding parameters, the size of the learned vocabulary greatly affects the ability of recovering training data. In SS4 we established that larger vocabularies, learned by BPE, lead to stronger memorization in Transformer models, even when we control for the number of the learned parameters.

In this experiment, for small vocabulary sizes, the total number of learned parameters is nearly constant.

We report results of this experiment using the LM model in Figure 3(b), contrasting it to the BPE-induced memorization results. We see that the resulting curves exhibit considerably different patterns. The line that corresponds to the doubling procedure has a sharp fall in the beginning.

We have observed a strong and monotonic influence of the BPE vocabulary size on how successful Transformer models are at memorizing training data. With higher granularity vocabulary (i.e., more BPE merge operations), Transformers (a) _can_ memorize random mappings better, hence they have higher memory capacity, and (b) _do memorize_ more of training data in realistic tasks.

Is the increase perhaps _due to the increase in the number of trainable parameters?_

We show that while this growth does play a role, the effect persists when we ensure that the number of trained parameters remains constant when the granularity of the vocabulary grows.

After ruling out the two alternative possibilities, we are left with our initial hypothesis that using higher-cardinality BPE subword vocabularies implies having to manage shorter sentences on average, which in turn enable easier memorization.

Our experiments provide a clear demonstration that both in artificial and natural data, the simple choice of the number of subwords used has a large impact on the extent to which models memorize training data, a fact that is not at all obvious when merely looking at performance on i.i.d. train/test splits. This therefore calls for a more careful consideration of how many subwords to use for a particular task, a decision that, in practical scenarios, is rarely thoroughly motivated or investigated. In cases where a lot of memorization is desirable (e.g., QA-tasks) or undesirable (e.g., public models trained on medical data), the number of subwords could provide an important factor in tuning the amount of memorization that happens inside a model.

This time, we have fixed the BPE vocabulary size (8 merges) and varied the number of heads used in each layer as \(\{1,2,4,8,16\}\) and measured the training accuracy. Our results in Figure 5 confirm our expectations: more heads allow more successful memorization. Indeed it seems that the attention serves as a representation bottleneck that does not allow to easily model complex interactions between tokens and, in turn, limits the memorization.

We used the standard Transformer LM models of fairseq that are specified by the --arch=transformer_1m_big (large) and --arch=transformer_1m (base). We use fixed (sinusoidal) positional embeddings. The base architecture has 6 layers with 8 attention heads, embedding dimensionality of 512 and FFN dimensionality of 2048. The large architecture has 12 layers, 16 attention heads, embedding dimension of 1024 and FFN dimension of 2048.

In experiments where we control the number of learned parameters, input token embedding size is no longer attached to the embedding size within the Transformer model (which remains identical to the vanilla, non-controlled model).

In the main text, we considered three factors that accompany growing BPE vocabulary sizes: reduction in sequence length, increased number of tokens, and decrease in the redundancy. Another potential confounding behavior is that BPE affects the (relative) frequency of the tokens used for modelling the data.

To rule this possibility out, we run an experiment where the token distribution is fixed to be uniform, but the sequence length is reduced. To achieve this, we start from the same dataset of random strings as in Section 5.1. In this dataset, the initial distribution of 0s and 1s is uniform as we enumerate _all_ binary strings of a fixed length. Next, we replace BPE with an "idealized" subword learning procedure which maintains the uniform distribution of tokens but reduces the lengths of the strings.

We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed and fixed to be uniform, thus disproving the hypothesis that the observed effect is due to frequency and not token length.

Input: Figure 3: Training data recovery: top-1 and top-5 accuracy on extracting the correct answer when prompted with a query.

Input: Figure 5: Random label memorization accuracy vs. number of heads.

Input: Figure 2: Membership inference attack, SNLI dataset. Shaded area represents ±1 SEM.

Input: Figure 1: Training accuracy for fitting random labels on SNLI. Shaded area represents ±1 SEM (Standard Error of the Mean).

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 "This observation holds even when we control for the number of trainable parameters" appears to be well-stated. Multiple experiments explicitly controlled for parameter count:

1. They modified architectures with additional FFN layers to maintain constant parameters across vocabulary sizes
2. Figures 1(b), 2(b), and 3(b) show results with fixed parameters, demonstrating persistent effects
3. They conducted additional controlled experiments with uniform token distribution
4. The evidence consistently shows the memorization effects remain even after controlling for parameters

The claim is measured and accurately reflects what the evidence demonstrates, without overextending beyond what was proven.

<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:

Next, we artificially double the vocabulary size by introducing "synonym" tokens and observe that the vocabulary growth, in isolation, leads to a different memorization pattern.

The evidence to be evaluated is:as the vocabulary size grows, the models become universally more successful in fitting random labels. Encoder fits around 87% of the random labels with the subword vocabulary size of 611 and has a training accuracy of more than 98% when the vocabulary size is increased to 18,336. LM and MLM - that have more layers than Encoder - start off with a slightly higher accuracy (94% and 97%, respectively), their accuracy quickly climbs up to 100% when increasing the number of subwords.

Mirroring the results of our previous experiment, we observe a monotonic dependency of the membership attack success rate in function of the size of the vocabulary used: for all architectures, larger vocabulary granularity implies more memorisation.

Next, we see that both models confirm the pattern we observed in the previous experiments: vocabulary growth consistently leads to a growth in the memorization accuracy. Focusing on the models with the number of parameters fixed, we see that even when correcting for the total number of embedding parameters, the size of the learned vocabulary greatly affects the ability of recovering training data.

We hypothesise that the primary cause of the observed behavior is that with the growth of the BPE vocabulary the input sequences become shorter (_length hypothesis_). In turn, shorter sequences are easier to memorize as the work of attention is simplified.

Second, BPE increases the vocabulary size and it is possible that each individual token becomes more predictive of the label (_vocabulary size hypothesis_). As an illustration, in the limit case of the vocabulary growth, every sequence might have a unique token. 4 In this case, there is a one-to-one mapping between those tokens and labels (answers) that will, again, simplify the work of self-attention.

To study how the chosen level of representation affects the models' memorization capacity, we apply BPE with {0, 4, 8, 16, 32, 64, 128, 256} steps on the generated data. This allows us to start from a binary dataset with sufficiently large sequences and produce a sequence of datasets _of the same storage complexity_ (in bits), but with varied vocabulary sizes. In Figure 4 we report the accuracy on fitting the training data with random labels as a function of the logarithm of the vocabulary size. Again, we observe that for all three architectures the dependency is very consistent: as the vocabulary size grows, the models become universally more successful in fitting random labels.6 We conclude that the increased memorization success is thus not caused by BPE compressing-out redundancies in more natural data.

To investigate the _vocabulary size_ hypothesis we set up an experiment in which we increase the vocabulary size, while keeping sequence lengths constant.

To increase the number of tokens in this vocabulary, we randomly replace each unique token's occurrence with either of two new tokens, with equal probability, roughly doubling the vocabulary size. 7 For instance, say that the current vocabulary has a token "cat". We then iterate over the corpus and replace half of its occurrences with "cat1" and the other half with "cat2" (making sure that those do not happen in the prior vocabulary). Thus, if the vocabulary growth alone can explain the observed effect, we will see that the datasets with "duplicated" tokens would also be easier to memorize.

We report results of this experiment using the LM model in Figure 3(b), contrasting it to the BPE-induced memorization results. We see that the resulting curves exhibit considerably different patterns. The line that corresponds to the doubling procedure has a sharp fall in the beginning. Later, as the vocabulary size grows, in accordance with in our thought experiment, tokens become increasingly more unique to sequences which boosts the train accuracy.

We have observed a strong and monotonic influence of the BPE vocabulary size on how successful Transformer models are at memorizing training data. With higher granularity vocabulary (i.e., more BPE merge operations), Transformers (a) _can_ memorize random mappings better, hence they have higher memory capacity, and (b) _do memorize_ more of training data in realistic tasks.

We show that while this growth does play a role, the effect persists when we ensure that the number of trained parameters remains constant when the granularity of the vocabulary grows.

Further, can the _growth of the vocabulary size_ explain the behavior?

our experiment with artificially duplicating tokens shows that this only starts to improve memorization with relatively large vocabularies and is detrimental for memory at the beginning.

Our experiments provide a clear demonstration that both in artificial and natural data, the simple choice of the number of subwords used has a large impact on the extent to which models memorize training data, a fact that is not at all obvious when merely looking at performance on i.i.d. train/test splits. This therefore calls for a more careful consideration of how many subwords to use for a particular task, a decision that, in practical scenarios, is rarely thoroughly motivated or investigated.

We recursively repeat this procedure, obtaining a sequence of views of the same dataset, at each step growing the vocabulary size quadratically (2, 4, 16, and 256) and reducing the string length by two.

Using the obtained series of datasets, we repeat the random label memorization experiment (Section 5.1) and report the results obtained in Figure 6(b). We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed and fixed to be uniform, thus disproving the hypothesis that the observed effect is due to frequency and not token length.

Input: Figure 4: Analysing potential causes of the increased memorization: fitting random labels on random strings (left) and SNLI (right) datasets. Everywhere shaded area represents ±1 SEM.

Input: Figure 3: Training data recovery: top-1 and top-5 accuracy on extracting the correct answer when prompted with a query.

Input: Figure 6: Training data recovery: top-20 accuracy on extracting the correct answer when prompted with a query (sampling).

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 "artificially doubling vocabulary size leads to a different memorization pattern" is well-supported by the evidence. Figure 3(b) directly contrasts BPE-induced memorization with artificially doubled vocabulary, showing distinctly different patterns. The artificial doubling leads to an initial sharp decrease in memorization before eventually increasing at larger vocabulary sizes, while BPE shows consistent increases. The evidence explicitly states "resulting curves exhibit considerably different patterns" and provides detailed experimental methodology explaining how the vocabulary doubling was performed. The claim accurately reflects these findings without overstatement.

<score>1</score>

Justification:
1. The claim is precise and measured in stating there is "a different memorization pattern"
2. Evidence directly demonstrates this through:
   - Clear experimental methodology of token duplication
   - Figure 3(b) showing contrasting patterns
   - Direct quotes confirming different behaviors
3. The claim makes no exaggerated claims about superiority or broader implications
4. The statement stays strictly within the scope of what the evidence demonstrates


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:

Next, we artificially double the vocabulary size by introducing "synonym" tokens and observe that the vocabulary growth, in isolation, leads to a different memorization pattern.

The review comment to be evaluated is:

Pros:
1. The experiments are comprehensive. The authors design three different types of experiments to thoroughly compare the memorization ability differences between three different models (Encoder, LM, MLM).
2. The paper explores the relationship between the memorization and generalization capabilities of the model, and shows that generalization is not directly at odds with memorization, which can inspire future model design.

Cons:
1. The authors focus on three candidate causes, which the authors claimed are principal (side-)effects of applying BPE: (i) removing redundancy in the data (due to compression), (ii) increase in the number of the unique units used to represent the data, or (iii) reducing the length of the training sequences. Other factors that are closely related to the BPE vocabulary may be also important, such as the subword frequency. Can the authors explain why the three factors examined in this paper are more likely the causes than other factors (e.g., subword frequency).
2. Although the paper presents several interesting conclusions, they can not be directly used to determine a suitable vocabulary size in practical tasks, where the demand of the model's memorization is unknowable.

Concerns:
1. The conclusions in this study are only validated on the SNLI dataset (PAQ is only used for the training data recovery experiment), which may threat the universality of the findings. Experiments on other datasets and tasks (e.g. the machine translation task where Transformer was invented) are necessary.

The evidence to be evaluated is:as the vocabulary size grows, the models become universally more successful in fitting random labels. Encoder fits around 87% of the random labels with the subword vocabulary size of 611 and has a training accuracy of more than 98% when the vocabulary size is increased to 18,336. LM and MLM - that have more layers than Encoder - start off with a slightly higher accuracy (94% and 97%, respectively), their accuracy quickly climbs up to 100% when increasing the number of subwords.

Mirroring the results of our previous experiment, we observe a monotonic dependency of the membership attack success rate in function of the size of the vocabulary used: for all architectures, larger vocabulary granularity implies more memorisation.

Next, we see that both models confirm the pattern we observed in the previous experiments: vocabulary growth consistently leads to a growth in the memorization accuracy. Focusing on the models with the number of parameters fixed, we see that even when correcting for the total number of embedding parameters, the size of the learned vocabulary greatly affects the ability of recovering training data.

We hypothesise that the primary cause of the observed behavior is that with the growth of the BPE vocabulary the input sequences become shorter (_length hypothesis_). In turn, shorter sequences are easier to memorize as the work of attention is simplified.

Second, BPE increases the vocabulary size and it is possible that each individual token becomes more predictive of the label (_vocabulary size hypothesis_). As an illustration, in the limit case of the vocabulary growth, every sequence might have a unique token. 4 In this case, there is a one-to-one mapping between those tokens and labels (answers) that will, again, simplify the work of self-attention.

To study how the chosen level of representation affects the models' memorization capacity, we apply BPE with {0, 4, 8, 16, 32, 64, 128, 256} steps on the generated data. This allows us to start from a binary dataset with sufficiently large sequences and produce a sequence of datasets _of the same storage complexity_ (in bits), but with varied vocabulary sizes. In Figure 4 we report the accuracy on fitting the training data with random labels as a function of the logarithm of the vocabulary size. Again, we observe that for all three architectures the dependency is very consistent: as the vocabulary size grows, the models become universally more successful in fitting random labels.6 We conclude that the increased memorization success is thus not caused by BPE compressing-out redundancies in more natural data.

To investigate the _vocabulary size_ hypothesis we set up an experiment in which we increase the vocabulary size, while keeping sequence lengths constant.

To increase the number of tokens in this vocabulary, we randomly replace each unique token's occurrence with either of two new tokens, with equal probability, roughly doubling the vocabulary size. 7 For instance, say that the current vocabulary has a token "cat". We then iterate over the corpus and replace half of its occurrences with "cat1" and the other half with "cat2" (making sure that those do not happen in the prior vocabulary). Thus, if the vocabulary growth alone can explain the observed effect, we will see that the datasets with "duplicated" tokens would also be easier to memorize.

We report results of this experiment using the LM model in Figure 3(b), contrasting it to the BPE-induced memorization results. We see that the resulting curves exhibit considerably different patterns. The line that corresponds to the doubling procedure has a sharp fall in the beginning. Later, as the vocabulary size grows, in accordance with in our thought experiment, tokens become increasingly more unique to sequences which boosts the train accuracy.

We have observed a strong and monotonic influence of the BPE vocabulary size on how successful Transformer models are at memorizing training data. With higher granularity vocabulary (i.e., more BPE merge operations), Transformers (a) _can_ memorize random mappings better, hence they have higher memory capacity, and (b) _do memorize_ more of training data in realistic tasks.

We show that while this growth does play a role, the effect persists when we ensure that the number of trained parameters remains constant when the granularity of the vocabulary grows.

Further, can the _growth of the vocabulary size_ explain the behavior?

our experiment with artificially duplicating tokens shows that this only starts to improve memorization with relatively large vocabularies and is detrimental for memory at the beginning.

Our experiments provide a clear demonstration that both in artificial and natural data, the simple choice of the number of subwords used has a large impact on the extent to which models memorize training data, a fact that is not at all obvious when merely looking at performance on i.i.d. train/test splits. This therefore calls for a more careful consideration of how many subwords to use for a particular task, a decision that, in practical scenarios, is rarely thoroughly motivated or investigated.

We recursively repeat this procedure, obtaining a sequence of views of the same dataset, at each step growing the vocabulary size quadratically (2, 4, 16, and 256) and reducing the string length by two.

Using the obtained series of datasets, we repeat the random label memorization experiment (Section 5.1) and report the results obtained in Figure 6(b). We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed and fixed to be uniform, thus disproving the hypothesis that the observed effect is due to frequency and not token length.

Input: Figure 4: Analysing potential causes of the increased memorization: fitting random labels on random strings (left) and SNLI (right) datasets. Everywhere shaded area represents ±1 SEM.

Input: Figure 3: Training data recovery: top-1 and top-5 accuracy on extracting the correct answer when prompted with a query.

Input: Figure 6: Training data recovery: top-20 accuracy on extracting the correct answer when prompted with a query (sampling).

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

Output:
Let me evaluate the claim "artificially double the vocabulary size by introducing 'synonym' tokens and observe that the vocabulary growth, in isolation, leads to a different memorization pattern."

The evidence strongly supports this claim through Figure 3(b) which directly compares BPE-based vocabulary growth with artificially duplicated vocabulary. The graph shows markedly different patterns - the duplicated vocabulary line shows an initial sharp decline before increasing, while BPE shows steady growth. The evidence explicitly states "we see that the resulting curves exhibit considerably different patterns" and explains the mechanics of the token duplication experiment in detail.

The claim is well-stated (score of 1) because it:
1. Accurately describes the methodology of doubling vocabulary through synonyms
2. Correctly notes that this leads to "different" patterns without overstating the nature/magnitude of differences
3. Is directly supported by experimental evidence and figures
4. Makes no exaggerated claims about implications or causation

<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:

Next, we artificially double the vocabulary size by introducing "synonym" tokens and observe that the vocabulary growth, in isolation, leads to a different memorization pattern.

The review comment to be evaluated is:

This work is placed on the border for me as it is investigating well crafted question and does some empirical validation of multiple hypotheses. On the other hand, there is not much of discussion on what can we do with long sequences when we require memorization? Authors provide very high-level paths such as 'Our findings can provide guidance for tuning the learned data structures', but I would be very curious to read more details. I think it would nicely fit as findings paper rather than work with the novel contribution.

When it comes to strengths, I like the construction of memorization properties which allows to quantify the memorization by using the proposed probing tasks. In addition, authors tried to provide many details on specific hyper-parameters they used, although I left some comments below where more details would be welcome.

Regarding weaknesses: while the memorization properties are clearly outlined, the construction of model parameterization in probing tasks is written on very high-level without any discussion of why this specific method of casting the model as classifier is chosen and how it may or may not provide necessary information towards research questions about memorization, this is mainly addressing section 3.3).
In addition, authors mention 'SOTA \ state of the art' several times during the work while they do not much relate to the actual SOTA models. Please correct me here if I am wrong, but considered models are not in the same ballpark as SOTA models. I want to stress that the latter fact is not a bad thing, but then there is no need to relate with SOTA then.

Below I have noted multiple comments where it was hard to me to get all the details or where I felt the minor change / addon would improve the presentation:

Page 3, *"At test-time, we prompt the trained LM by a query followed with the separator token and check whether the trained LM reproduces the correct answer within top-1 or top-5 results returned by beam search (beam size 5)."* : This is very specific design choice, why did you choose it? Model conditioned on the q gives the entire distribution on sequence-level and beam search is very sensitive to the beam size? I see an alternative as doing unbiased sampling and computing expected similarity with the answer. Some discussion on that would help to clarify this.

Bottom of page 3: you used word *setups* to refer to both tasks and models (right?) which is a bit confusing.

Section 3.3: as I wrote above, in my opinion this section needs to be larger as it defines very important design of the model parameterization, right now it is not even clear enough what are 'target class' in the context of vocabulary tokens? I believe explaining this would improve the presentation of that part a lot.

Page 5: *achieves 100% train accuracy* : in cases of MLM, was acc measured only on task class prediction or on other masked tokens as well?

Page 5: *Hence, in this experiment we used a 1-layer*:  Could you explain why you chose to reduce the model size? In my understanding the task itself might be too easy so the other way is to alter the underlying task (since you specifically construct it).

Page 5: *which was enough for the training loss to converge*: Converge to what? Was there an early stopping criteria on loss or acc?

Page 8: *Thus, if the vocabulary growth alone can explain the observed effect, we will see that the datasets with “duplicated” tokens would also be easier to memorize.* : In your proposed construction the frequency distribution of tokens doesn't change relatively to each other, right?. Is it the same for BPE learning when number of merges is growing? Would be great to show this, otherwise it is hard to buy this statement.

The evidence to be evaluated is:as the vocabulary size grows, the models become universally more successful in fitting random labels. Encoder fits around 87% of the random labels with the subword vocabulary size of 611 and has a training accuracy of more than 98% when the vocabulary size is increased to 18,336. LM and MLM - that have more layers than Encoder - start off with a slightly higher accuracy (94% and 97%, respectively), their accuracy quickly climbs up to 100% when increasing the number of subwords.

Mirroring the results of our previous experiment, we observe a monotonic dependency of the membership attack success rate in function of the size of the vocabulary used: for all architectures, larger vocabulary granularity implies more memorisation.

Next, we see that both models confirm the pattern we observed in the previous experiments: vocabulary growth consistently leads to a growth in the memorization accuracy. Focusing on the models with the number of parameters fixed, we see that even when correcting for the total number of embedding parameters, the size of the learned vocabulary greatly affects the ability of recovering training data.

We hypothesise that the primary cause of the observed behavior is that with the growth of the BPE vocabulary the input sequences become shorter (_length hypothesis_). In turn, shorter sequences are easier to memorize as the work of attention is simplified.

Second, BPE increases the vocabulary size and it is possible that each individual token becomes more predictive of the label (_vocabulary size hypothesis_). As an illustration, in the limit case of the vocabulary growth, every sequence might have a unique token. 4 In this case, there is a one-to-one mapping between those tokens and labels (answers) that will, again, simplify the work of self-attention.

To study how the chosen level of representation affects the models' memorization capacity, we apply BPE with {0, 4, 8, 16, 32, 64, 128, 256} steps on the generated data. This allows us to start from a binary dataset with sufficiently large sequences and produce a sequence of datasets _of the same storage complexity_ (in bits), but with varied vocabulary sizes. In Figure 4 we report the accuracy on fitting the training data with random labels as a function of the logarithm of the vocabulary size. Again, we observe that for all three architectures the dependency is very consistent: as the vocabulary size grows, the models become universally more successful in fitting random labels.6 We conclude that the increased memorization success is thus not caused by BPE compressing-out redundancies in more natural data.

To investigate the _vocabulary size_ hypothesis we set up an experiment in which we increase the vocabulary size, while keeping sequence lengths constant.

To increase the number of tokens in this vocabulary, we randomly replace each unique token's occurrence with either of two new tokens, with equal probability, roughly doubling the vocabulary size. 7 For instance, say that the current vocabulary has a token "cat". We then iterate over the corpus and replace half of its occurrences with "cat1" and the other half with "cat2" (making sure that those do not happen in the prior vocabulary). Thus, if the vocabulary growth alone can explain the observed effect, we will see that the datasets with "duplicated" tokens would also be easier to memorize.

We report results of this experiment using the LM model in Figure 3(b), contrasting it to the BPE-induced memorization results. We see that the resulting curves exhibit considerably different patterns. The line that corresponds to the doubling procedure has a sharp fall in the beginning. Later, as the vocabulary size grows, in accordance with in our thought experiment, tokens become increasingly more unique to sequences which boosts the train accuracy.

We have observed a strong and monotonic influence of the BPE vocabulary size on how successful Transformer models are at memorizing training data. With higher granularity vocabulary (i.e., more BPE merge operations), Transformers (a) _can_ memorize random mappings better, hence they have higher memory capacity, and (b) _do memorize_ more of training data in realistic tasks.

We show that while this growth does play a role, the effect persists when we ensure that the number of trained parameters remains constant when the granularity of the vocabulary grows.

Further, can the _growth of the vocabulary size_ explain the behavior?

our experiment with artificially duplicating tokens shows that this only starts to improve memorization with relatively large vocabularies and is detrimental for memory at the beginning.

Our experiments provide a clear demonstration that both in artificial and natural data, the simple choice of the number of subwords used has a large impact on the extent to which models memorize training data, a fact that is not at all obvious when merely looking at performance on i.i.d. train/test splits. This therefore calls for a more careful consideration of how many subwords to use for a particular task, a decision that, in practical scenarios, is rarely thoroughly motivated or investigated.

We recursively repeat this procedure, obtaining a sequence of views of the same dataset, at each step growing the vocabulary size quadratically (2, 4, 16, and 256) and reducing the string length by two.

Using the obtained series of datasets, we repeat the random label memorization experiment (Section 5.1) and report the results obtained in Figure 6(b). We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed and fixed to be uniform, thus disproving the hypothesis that the observed effect is due to frequency and not token length.

Input: Figure 4: Analysing potential causes of the increased memorization: fitting random labels on random strings (left) and SNLI (right) datasets. Everywhere shaded area represents ±1 SEM.

Input: Figure 3: Training data recovery: top-1 and top-5 accuracy on extracting the correct answer when prompted with a query.

Input: Figure 6: Training data recovery: top-20 accuracy on extracting the correct answer when prompted with a query (sampling).

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

Output:
After reviewing the claim and evidence, I find the claim to be somewhat overstated. While the evidence does show that artificially doubling vocabulary size leads to a different memorization pattern, Figure 3(b) demonstrates this pattern is more complex than simply "different" - it shows an initial sharp decrease in accuracy followed by eventual improvement. The claim oversimplifies these nuanced findings and doesn't acknowledge the initial negative impact on memorization that occurs before the eventual improvement at larger vocabulary sizes. A more precise statement would have described this specific pattern rather than just noting it was "different."

<score>3</score>

Justification:
1. The evidence clearly shows in Figure 3(b) a more specific pattern with:
- Initial sharp decline in memorization accuracy
- Later improvement as vocabulary size grows
- Distinct contrast with BPE-induced memorization

2. The paper states "We see that the resulting curves exhibit considerably different patterns. The line that corresponds to the doubling procedure has a sharp fall in the beginning. Later, as the vocabulary size grows...tokens become increasingly more unique to sequences which boosts the train accuracy."

3. The claim uses vague language ("different memorization pattern") when the evidence supports more specific characterization of how the pattern differs.

4. The reviewer comments don't specifically address this claim, so they weren't factored into the scoring.


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:

Next, we artificially double the vocabulary size by introducing "synonym" tokens and observe that the vocabulary growth, in isolation, leads to a different memorization pattern.

The review comment to be evaluated is:

This paper as the name suggests, tries to figure out whether and through which ways bpe can affect Transformer’s memorization capacity. It evaluates Transformer’s memorization under these 4 settings: memorizing random synthetic data, memorizing random labeled natural language data, recognizing training data with lower output entropy, and training data recovery QA. Experiments show that if we have more merge times for bpe (larger vocabulary size), the model’s performance on all the four settings would improve on 3 architectures, which shows that bpe indeed can affect the model’s memorization capacity. Larger the vocabulary size is, the better the model would perform on memorizing. Then, the paper tries to figure out why more merges in bpe would lead to better memorization. By excluding two other hypotheses, the paper concludes that more merges in bpe results in shorter input sequence and that makes memorizing easier for transformers.

The evidence to be evaluated is:as the vocabulary size grows, the models become universally more successful in fitting random labels. Encoder fits around 87% of the random labels with the subword vocabulary size of 611 and has a training accuracy of more than 98% when the vocabulary size is increased to 18,336. LM and MLM - that have more layers than Encoder - start off with a slightly higher accuracy (94% and 97%, respectively), their accuracy quickly climbs up to 100% when increasing the number of subwords.

Mirroring the results of our previous experiment, we observe a monotonic dependency of the membership attack success rate in function of the size of the vocabulary used: for all architectures, larger vocabulary granularity implies more memorisation.

Next, we see that both models confirm the pattern we observed in the previous experiments: vocabulary growth consistently leads to a growth in the memorization accuracy. Focusing on the models with the number of parameters fixed, we see that even when correcting for the total number of embedding parameters, the size of the learned vocabulary greatly affects the ability of recovering training data.

We hypothesise that the primary cause of the observed behavior is that with the growth of the BPE vocabulary the input sequences become shorter (_length hypothesis_). In turn, shorter sequences are easier to memorize as the work of attention is simplified.

Second, BPE increases the vocabulary size and it is possible that each individual token becomes more predictive of the label (_vocabulary size hypothesis_). As an illustration, in the limit case of the vocabulary growth, every sequence might have a unique token. 4 In this case, there is a one-to-one mapping between those tokens and labels (answers) that will, again, simplify the work of self-attention.

To study how the chosen level of representation affects the models' memorization capacity, we apply BPE with {0, 4, 8, 16, 32, 64, 128, 256} steps on the generated data. This allows us to start from a binary dataset with sufficiently large sequences and produce a sequence of datasets _of the same storage complexity_ (in bits), but with varied vocabulary sizes. In Figure 4 we report the accuracy on fitting the training data with random labels as a function of the logarithm of the vocabulary size. Again, we observe that for all three architectures the dependency is very consistent: as the vocabulary size grows, the models become universally more successful in fitting random labels.6 We conclude that the increased memorization success is thus not caused by BPE compressing-out redundancies in more natural data.

To investigate the _vocabulary size_ hypothesis we set up an experiment in which we increase the vocabulary size, while keeping sequence lengths constant.

To increase the number of tokens in this vocabulary, we randomly replace each unique token's occurrence with either of two new tokens, with equal probability, roughly doubling the vocabulary size. 7 For instance, say that the current vocabulary has a token "cat". We then iterate over the corpus and replace half of its occurrences with "cat1" and the other half with "cat2" (making sure that those do not happen in the prior vocabulary). Thus, if the vocabulary growth alone can explain the observed effect, we will see that the datasets with "duplicated" tokens would also be easier to memorize.

We report results of this experiment using the LM model in Figure 3(b), contrasting it to the BPE-induced memorization results. We see that the resulting curves exhibit considerably different patterns. The line that corresponds to the doubling procedure has a sharp fall in the beginning. Later, as the vocabulary size grows, in accordance with in our thought experiment, tokens become increasingly more unique to sequences which boosts the train accuracy.

We have observed a strong and monotonic influence of the BPE vocabulary size on how successful Transformer models are at memorizing training data. With higher granularity vocabulary (i.e., more BPE merge operations), Transformers (a) _can_ memorize random mappings better, hence they have higher memory capacity, and (b) _do memorize_ more of training data in realistic tasks.

We show that while this growth does play a role, the effect persists when we ensure that the number of trained parameters remains constant when the granularity of the vocabulary grows.

Further, can the _growth of the vocabulary size_ explain the behavior?

our experiment with artificially duplicating tokens shows that this only starts to improve memorization with relatively large vocabularies and is detrimental for memory at the beginning.

Our experiments provide a clear demonstration that both in artificial and natural data, the simple choice of the number of subwords used has a large impact on the extent to which models memorize training data, a fact that is not at all obvious when merely looking at performance on i.i.d. train/test splits. This therefore calls for a more careful consideration of how many subwords to use for a particular task, a decision that, in practical scenarios, is rarely thoroughly motivated or investigated.

We recursively repeat this procedure, obtaining a sequence of views of the same dataset, at each step growing the vocabulary size quadratically (2, 4, 16, and 256) and reducing the string length by two.

Using the obtained series of datasets, we repeat the random label memorization experiment (Section 5.1) and report the results obtained in Figure 6(b). We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed and fixed to be uniform, thus disproving the hypothesis that the observed effect is due to frequency and not token length.

Input: Figure 4: Analysing potential causes of the increased memorization: fitting random labels on random strings (left) and SNLI (right) datasets. Everywhere shaded area represents ±1 SEM.

Input: Figure 3: Training data recovery: top-1 and top-5 accuracy on extracting the correct answer when prompted with a query.

Input: Figure 6: Training data recovery: top-20 accuracy on extracting the correct answer when prompted with a query (sampling).

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

Output:
After reviewing the claim and evidence, I find that the claim is partially well-stated but needs more nuance. The evidence shows that artificially doubling vocabulary size through synonym tokens does lead to a different memorization pattern, as demonstrated in Figure 3(b). However, this pattern is more complex than simply being "different" - it shows an initial sharp decline in memorization before improving at larger vocabulary sizes. The claim oversimplifies this relationship by not specifying the nature of the "different" pattern or acknowledging the non-linear relationship observed.

The evidence directly contrasts BPE-induced memorization with artificially doubled vocabulary, showing distinctly different curves. While the claim is technically correct that the patterns differ, it understates the complexity of the relationship and omits important details about how and why they differ.

<score>2</score>

Justification:
1. The claim is supported by empirical evidence showing different patterns between BPE and artificial vocabulary doubling (Figure 3b)
2. However, it oversimplifies by:
- Not specifying the initial negative impact of vocabulary doubling
- Omitting the non-linear nature of the relationship
- Not mentioning that the effect only becomes positive at larger vocabulary sizes
3. The evidence provides more nuanced details that could have been incorporated into the claim for better accuracy.


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:

Thus, by exclusion, we conjecture that reducing utterance length is, at least, a very important factor of memorization.

The evidence to be evaluated is:In this section, we discuss our first main finding: that the number of BPE merges influences the extent to which a model memorizes training data. This finding is persistent across the three different experimental setups we described earlier: random label memorization, membership inference and question-answer recovery. In all these experiments, we systematically control the number of merges, which is roughly the same as the vocabulary size. We also run complementary experiments where we fix the number of learned parameters to stay roughly the same for each vocabulary size (see SS3.2).

Mirroring the results of our previous experiment, we observe a monotonic dependency of the membership attack success rate in function of the size of the vocabulary used: for all architectures, larger vocabulary granularity implies more memorisation.

We hypothesise that the primary cause of the observed behavior is that with the growth of the BPE vocabulary the input sequences become shorter (_length hypothesis_). In turn, shorter sequences are easier to memorize as the work of attention is simplified.

At the same time, shorter sequences would shift the responsibility for memorization onto FFN layers, which are known to memorize well (Zhang et al., 2016).

To summarize, the above experiments allowed us to rule out the alternative explanations (redundancy and vocabulary growth hypotheses) and _we conclude that reduction of the sequence length is the primary factor of the observed memorization effect_.

We have observed a strong and monotonic influence of the BPE vocabulary size on how successful Transformer models are at memorizing training data. With higher granularity vocabulary (i.e., more BPE merge operations), Transformers (a) _can_ memorize random mappings better, hence they have higher memory capacity, and (b) _do memorize_ more of training data in realistic tasks.

Next, we conjecture that the phenomenon is caused by the reduction in the sequence length that correlates with using larger-cardinality BPE vocabularies. It can simplify memorization, as the latter will no longer require learning complex attention patterns "explaining" the data and offset complexity onto fully-connected layers, which are known to be good in memorization (Zhang et al., 2016).

After ruling out the two alternative possibilities, we are left with our initial hypothesis that using higher-cardinality BPE subword vocabularies implies having to manage shorter sentences on average, which in turn enable easier memorization.

Our experiments provide a clear demonstration that both in artificial and natural data, the simple choice of the number of subwords used has a large impact on the extent to which models memorize training data, a fact that is not at all obvious when merely looking at performance on i.i.d. train/test splits. This therefore calls for a more careful consideration of how many subwords to use for a particular task, a decision that, in practical scenarios, is rarely thoroughly motivated or investigated. In cases where a lot of memorization is desirable (e.g., QA-tasks) or undesirable (e.g., public models trained on medical data), the number of subwords could provide an important factor in tuning the amount of memorization that happens inside a model.

In the main text, we considered three factors that accompany growing BPE vocabulary sizes: reduction in sequence length, increased number of tokens, and decrease in the redundancy.

To rule this possibility out, we run an experiment where the token distribution is fixed to be uniform, but the sequence length is reduced. To achieve this, we start from the same dataset of random strings as in Section 5.1. In this dataset, the initial distribution of 0s and 1s is uniform as we enumerate _all_ binary strings of a fixed length. Next, we replace BPE with an "idealized" subword learning procedure which maintains the uniform distribution of tokens but reduces the lengths of the strings.

We recursively repeat this procedure, obtaining a sequence of views of the same dataset, at each step growing the vocabulary size quadratically (2, 4, 16, and 256) and reducing the string length by two.

We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed and fixed to be uniform, thus disproving the hypothesis that the observed effect is due to frequency and not token length.

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

Output:
Let me evaluate the claim and evidence:

The claim "by exclusion, we conjecture that reducing utterance length is, at least, a very important factor of memorization" appears to be well-supported by the evidence, but with appropriate caution in its wording. The authors:

1. Systematically tested multiple hypotheses
2. Provided experimental evidence ruling out alternative explanations
3. Used appropriately measured language ("conjecture", "at least", "important factor") rather than making absolute claims
4. Demonstrated the effect across multiple experimental setups
5. Included control experiments with uniform token distribution

The claim's careful wording matches the strength of the evidence while acknowledging uncertainty.

<score>1</score>

Justification:
- The claim uses appropriately cautious language ("conjecture", "at least") reflecting the experimental nature of the findings
- Multiple lines of evidence support the conclusion, including controlled experiments ruling out alternative hypotheses
- The authors demonstrated the effect persists "even in the case when the relative frequencies of tokens are not changed"
- The conclusion is drawn after systematically eliminating alternative explanations
- The claim doesn't overstate beyond what the evidence shows - it presents sequence length reduction as "a very important factor" rather than claiming it's the only factor


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:

Thus, by exclusion, we conjecture that reducing utterance length is, at least, a very important factor of memorization.

The review comment to be evaluated is:

Pros:
1. The experiments are comprehensive. The authors design three different types of experiments to thoroughly compare the memorization ability differences between three different models (Encoder, LM, MLM).
2. The paper explores the relationship between the memorization and generalization capabilities of the model, and shows that generalization is not directly at odds with memorization, which can inspire future model design.

Cons:
1. The authors focus on three candidate causes, which the authors claimed are principal (side-)effects of applying BPE: (i) removing redundancy in the data (due to compression), (ii) increase in the number of the unique units used to represent the data, or (iii) reducing the length of the training sequences. Other factors that are closely related to the BPE vocabulary may be also important, such as the subword frequency. Can the authors explain why the three factors examined in this paper are more likely the causes than other factors (e.g., subword frequency).
2. Although the paper presents several interesting conclusions, they can not be directly used to determine a suitable vocabulary size in practical tasks, where the demand of the model's memorization is unknowable.

Concerns:
1. The conclusions in this study are only validated on the SNLI dataset (PAQ is only used for the training data recovery experiment), which may threat the universality of the findings. Experiments on other datasets and tasks (e.g. the machine translation task where Transformer was invented) are necessary.

The evidence to be evaluated is:In this section, we discuss our first main finding: that the number of BPE merges influences the extent to which a model memorizes training data. This finding is persistent across the three different experimental setups we described earlier: random label memorization, membership inference and question-answer recovery. In all these experiments, we systematically control the number of merges, which is roughly the same as the vocabulary size. We also run complementary experiments where we fix the number of learned parameters to stay roughly the same for each vocabulary size (see SS3.2).

Mirroring the results of our previous experiment, we observe a monotonic dependency of the membership attack success rate in function of the size of the vocabulary used: for all architectures, larger vocabulary granularity implies more memorisation.

We hypothesise that the primary cause of the observed behavior is that with the growth of the BPE vocabulary the input sequences become shorter (_length hypothesis_). In turn, shorter sequences are easier to memorize as the work of attention is simplified.

At the same time, shorter sequences would shift the responsibility for memorization onto FFN layers, which are known to memorize well (Zhang et al., 2016).

To summarize, the above experiments allowed us to rule out the alternative explanations (redundancy and vocabulary growth hypotheses) and _we conclude that reduction of the sequence length is the primary factor of the observed memorization effect_.

We have observed a strong and monotonic influence of the BPE vocabulary size on how successful Transformer models are at memorizing training data. With higher granularity vocabulary (i.e., more BPE merge operations), Transformers (a) _can_ memorize random mappings better, hence they have higher memory capacity, and (b) _do memorize_ more of training data in realistic tasks.

Next, we conjecture that the phenomenon is caused by the reduction in the sequence length that correlates with using larger-cardinality BPE vocabularies. It can simplify memorization, as the latter will no longer require learning complex attention patterns "explaining" the data and offset complexity onto fully-connected layers, which are known to be good in memorization (Zhang et al., 2016).

After ruling out the two alternative possibilities, we are left with our initial hypothesis that using higher-cardinality BPE subword vocabularies implies having to manage shorter sentences on average, which in turn enable easier memorization.

Our experiments provide a clear demonstration that both in artificial and natural data, the simple choice of the number of subwords used has a large impact on the extent to which models memorize training data, a fact that is not at all obvious when merely looking at performance on i.i.d. train/test splits. This therefore calls for a more careful consideration of how many subwords to use for a particular task, a decision that, in practical scenarios, is rarely thoroughly motivated or investigated. In cases where a lot of memorization is desirable (e.g., QA-tasks) or undesirable (e.g., public models trained on medical data), the number of subwords could provide an important factor in tuning the amount of memorization that happens inside a model.

In the main text, we considered three factors that accompany growing BPE vocabulary sizes: reduction in sequence length, increased number of tokens, and decrease in the redundancy.

To rule this possibility out, we run an experiment where the token distribution is fixed to be uniform, but the sequence length is reduced. To achieve this, we start from the same dataset of random strings as in Section 5.1. In this dataset, the initial distribution of 0s and 1s is uniform as we enumerate _all_ binary strings of a fixed length. Next, we replace BPE with an "idealized" subword learning procedure which maintains the uniform distribution of tokens but reduces the lengths of the strings.

We recursively repeat this procedure, obtaining a sequence of views of the same dataset, at each step growing the vocabulary size quadratically (2, 4, 16, and 256) and reducing the string length by two.

We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed and fixed to be uniform, thus disproving the hypothesis that the observed effect is due to frequency and not token length.

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 "Thus, by exclusion, we conjecture that reducing utterance length is, at least, a very important factor of memorization."

The evidence shows the authors:
1. Systematically tested three potential factors affecting memorization
2. Used multiple experimental setups (random label, membership inference, Q&A recovery)
3. Conducted controlled experiments ruling out alternative explanations (redundancy and vocabulary growth)
4. Demonstrated persistence of the length effect even with uniform token distribution

However, key limitations exist:
1. Testing was primarily on SNLI dataset, limiting generalizability (noted in review)
2. Other potential factors weren't fully explored (e.g., subword frequency noted in review)
3. The claim appropriately uses cautious language ("conjecture", "at least", "important factor") rather than claiming definitiveness

The claim is well-stated as it:
- Accurately reflects the evidence without overextending
- Acknowledges uncertainty through careful wording
- Aligns with the experimental findings while not claiming exclusivity

<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:

Thus, by exclusion, we conjecture that reducing utterance length is, at least, a very important factor of memorization.

The review comment to be evaluated is:

This work is placed on the border for me as it is investigating well crafted question and does some empirical validation of multiple hypotheses. On the other hand, there is not much of discussion on what can we do with long sequences when we require memorization? Authors provide very high-level paths such as 'Our findings can provide guidance for tuning the learned data structures', but I would be very curious to read more details. I think it would nicely fit as findings paper rather than work with the novel contribution.

When it comes to strengths, I like the construction of memorization properties which allows to quantify the memorization by using the proposed probing tasks. In addition, authors tried to provide many details on specific hyper-parameters they used, although I left some comments below where more details would be welcome.

Regarding weaknesses: while the memorization properties are clearly outlined, the construction of model parameterization in probing tasks is written on very high-level without any discussion of why this specific method of casting the model as classifier is chosen and how it may or may not provide necessary information towards research questions about memorization, this is mainly addressing section 3.3).
In addition, authors mention 'SOTA \ state of the art' several times during the work while they do not much relate to the actual SOTA models. Please correct me here if I am wrong, but considered models are not in the same ballpark as SOTA models. I want to stress that the latter fact is not a bad thing, but then there is no need to relate with SOTA then.

Below I have noted multiple comments where it was hard to me to get all the details or where I felt the minor change / addon would improve the presentation:

Page 3, *"At test-time, we prompt the trained LM by a query followed with the separator token and check whether the trained LM reproduces the correct answer within top-1 or top-5 results returned by beam search (beam size 5)."* : This is very specific design choice, why did you choose it? Model conditioned on the q gives the entire distribution on sequence-level and beam search is very sensitive to the beam size? I see an alternative as doing unbiased sampling and computing expected similarity with the answer. Some discussion on that would help to clarify this.

Bottom of page 3: you used word *setups* to refer to both tasks and models (right?) which is a bit confusing.

Section 3.3: as I wrote above, in my opinion this section needs to be larger as it defines very important design of the model parameterization, right now it is not even clear enough what are 'target class' in the context of vocabulary tokens? I believe explaining this would improve the presentation of that part a lot.

Page 5: *achieves 100% train accuracy* : in cases of MLM, was acc measured only on task class prediction or on other masked tokens as well?

Page 5: *Hence, in this experiment we used a 1-layer*:  Could you explain why you chose to reduce the model size? In my understanding the task itself might be too easy so the other way is to alter the underlying task (since you specifically construct it).

Page 5: *which was enough for the training loss to converge*: Converge to what? Was there an early stopping criteria on loss or acc?

Page 8: *Thus, if the vocabulary growth alone can explain the observed effect, we will see that the datasets with “duplicated” tokens would also be easier to memorize.* : In your proposed construction the frequency distribution of tokens doesn't change relatively to each other, right?. Is it the same for BPE learning when number of merges is growing? Would be great to show this, otherwise it is hard to buy this statement.

The evidence to be evaluated is:In this section, we discuss our first main finding: that the number of BPE merges influences the extent to which a model memorizes training data. This finding is persistent across the three different experimental setups we described earlier: random label memorization, membership inference and question-answer recovery. In all these experiments, we systematically control the number of merges, which is roughly the same as the vocabulary size. We also run complementary experiments where we fix the number of learned parameters to stay roughly the same for each vocabulary size (see SS3.2).

Mirroring the results of our previous experiment, we observe a monotonic dependency of the membership attack success rate in function of the size of the vocabulary used: for all architectures, larger vocabulary granularity implies more memorisation.

We hypothesise that the primary cause of the observed behavior is that with the growth of the BPE vocabulary the input sequences become shorter (_length hypothesis_). In turn, shorter sequences are easier to memorize as the work of attention is simplified.

At the same time, shorter sequences would shift the responsibility for memorization onto FFN layers, which are known to memorize well (Zhang et al., 2016).

To summarize, the above experiments allowed us to rule out the alternative explanations (redundancy and vocabulary growth hypotheses) and _we conclude that reduction of the sequence length is the primary factor of the observed memorization effect_.

We have observed a strong and monotonic influence of the BPE vocabulary size on how successful Transformer models are at memorizing training data. With higher granularity vocabulary (i.e., more BPE merge operations), Transformers (a) _can_ memorize random mappings better, hence they have higher memory capacity, and (b) _do memorize_ more of training data in realistic tasks.

Next, we conjecture that the phenomenon is caused by the reduction in the sequence length that correlates with using larger-cardinality BPE vocabularies. It can simplify memorization, as the latter will no longer require learning complex attention patterns "explaining" the data and offset complexity onto fully-connected layers, which are known to be good in memorization (Zhang et al., 2016).

After ruling out the two alternative possibilities, we are left with our initial hypothesis that using higher-cardinality BPE subword vocabularies implies having to manage shorter sentences on average, which in turn enable easier memorization.

Our experiments provide a clear demonstration that both in artificial and natural data, the simple choice of the number of subwords used has a large impact on the extent to which models memorize training data, a fact that is not at all obvious when merely looking at performance on i.i.d. train/test splits. This therefore calls for a more careful consideration of how many subwords to use for a particular task, a decision that, in practical scenarios, is rarely thoroughly motivated or investigated. In cases where a lot of memorization is desirable (e.g., QA-tasks) or undesirable (e.g., public models trained on medical data), the number of subwords could provide an important factor in tuning the amount of memorization that happens inside a model.

In the main text, we considered three factors that accompany growing BPE vocabulary sizes: reduction in sequence length, increased number of tokens, and decrease in the redundancy.

To rule this possibility out, we run an experiment where the token distribution is fixed to be uniform, but the sequence length is reduced. To achieve this, we start from the same dataset of random strings as in Section 5.1. In this dataset, the initial distribution of 0s and 1s is uniform as we enumerate _all_ binary strings of a fixed length. Next, we replace BPE with an "idealized" subword learning procedure which maintains the uniform distribution of tokens but reduces the lengths of the strings.

We recursively repeat this procedure, obtaining a sequence of views of the same dataset, at each step growing the vocabulary size quadratically (2, 4, 16, and 256) and reducing the string length by two.

We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed and fixed to be uniform, thus disproving the hypothesis that the observed effect is due to frequency and not token length.

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

Output:
1. The claim stating "by exclusion, we conjecture that reducing utterance length is, at least, a very important factor of memorization" appears relatively well-stated based on the evidence. The authors:
- Systematically tested alternative hypotheses
- Demonstrated persistence of the effect across multiple experimental setups
- Conducted controlled experiments isolating sequence length from other factors
- Used appropriately cautious language ("conjecture", "a very important factor")
- Acknowledged limitations through their careful wording

However, the reviewer points out some methodological concerns about model parameterization and probing task design that weren't fully addressed, suggesting slight uncertainty in the strength of conclusions.

<score>2</score>

Justification:
1. The claim uses appropriately measured language ("conjecture", "at least") that acknowledges uncertainty
2. Evidence shows systematic investigation:
- "We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed"
- Multiple experimental setups tested ("random label memorization, membership inference and question-answer recovery")
- Controlled experiments isolating sequence length effects

3. Limitations/uncertainties acknowledged:
- The reviewer raises valid concerns about model parameterization details
- The experiments used simplified models rather than SOTA architectures
- The mechanism isn't fully explained ("not much of discussion on what can we do with long sequences")

While scored slightly above perfectly well-stated (1) due to some methodological uncertainties raised by the reviewer, the claim's careful wording and systematic evidence make it predominantly well-supported.


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:

Thus, by exclusion, we conjecture that reducing utterance length is, at least, a very important factor of memorization.

The review comment to be evaluated is:

This paper as the name suggests, tries to figure out whether and through which ways bpe can affect Transformer’s memorization capacity. It evaluates Transformer’s memorization under these 4 settings: memorizing random synthetic data, memorizing random labeled natural language data, recognizing training data with lower output entropy, and training data recovery QA. Experiments show that if we have more merge times for bpe (larger vocabulary size), the model’s performance on all the four settings would improve on 3 architectures, which shows that bpe indeed can affect the model’s memorization capacity. Larger the vocabulary size is, the better the model would perform on memorizing. Then, the paper tries to figure out why more merges in bpe would lead to better memorization. By excluding two other hypotheses, the paper concludes that more merges in bpe results in shorter input sequence and that makes memorizing easier for transformers.

The evidence to be evaluated is:In this section, we discuss our first main finding: that the number of BPE merges influences the extent to which a model memorizes training data. This finding is persistent across the three different experimental setups we described earlier: random label memorization, membership inference and question-answer recovery. In all these experiments, we systematically control the number of merges, which is roughly the same as the vocabulary size. We also run complementary experiments where we fix the number of learned parameters to stay roughly the same for each vocabulary size (see SS3.2).

Mirroring the results of our previous experiment, we observe a monotonic dependency of the membership attack success rate in function of the size of the vocabulary used: for all architectures, larger vocabulary granularity implies more memorisation.

We hypothesise that the primary cause of the observed behavior is that with the growth of the BPE vocabulary the input sequences become shorter (_length hypothesis_). In turn, shorter sequences are easier to memorize as the work of attention is simplified.

At the same time, shorter sequences would shift the responsibility for memorization onto FFN layers, which are known to memorize well (Zhang et al., 2016).

To summarize, the above experiments allowed us to rule out the alternative explanations (redundancy and vocabulary growth hypotheses) and _we conclude that reduction of the sequence length is the primary factor of the observed memorization effect_.

We have observed a strong and monotonic influence of the BPE vocabulary size on how successful Transformer models are at memorizing training data. With higher granularity vocabulary (i.e., more BPE merge operations), Transformers (a) _can_ memorize random mappings better, hence they have higher memory capacity, and (b) _do memorize_ more of training data in realistic tasks.

Next, we conjecture that the phenomenon is caused by the reduction in the sequence length that correlates with using larger-cardinality BPE vocabularies. It can simplify memorization, as the latter will no longer require learning complex attention patterns "explaining" the data and offset complexity onto fully-connected layers, which are known to be good in memorization (Zhang et al., 2016).

After ruling out the two alternative possibilities, we are left with our initial hypothesis that using higher-cardinality BPE subword vocabularies implies having to manage shorter sentences on average, which in turn enable easier memorization.

Our experiments provide a clear demonstration that both in artificial and natural data, the simple choice of the number of subwords used has a large impact on the extent to which models memorize training data, a fact that is not at all obvious when merely looking at performance on i.i.d. train/test splits. This therefore calls for a more careful consideration of how many subwords to use for a particular task, a decision that, in practical scenarios, is rarely thoroughly motivated or investigated. In cases where a lot of memorization is desirable (e.g., QA-tasks) or undesirable (e.g., public models trained on medical data), the number of subwords could provide an important factor in tuning the amount of memorization that happens inside a model.

In the main text, we considered three factors that accompany growing BPE vocabulary sizes: reduction in sequence length, increased number of tokens, and decrease in the redundancy.

To rule this possibility out, we run an experiment where the token distribution is fixed to be uniform, but the sequence length is reduced. To achieve this, we start from the same dataset of random strings as in Section 5.1. In this dataset, the initial distribution of 0s and 1s is uniform as we enumerate _all_ binary strings of a fixed length. Next, we replace BPE with an "idealized" subword learning procedure which maintains the uniform distribution of tokens but reduces the lengths of the strings.

We recursively repeat this procedure, obtaining a sequence of views of the same dataset, at each step growing the vocabulary size quadratically (2, 4, 16, and 256) and reducing the string length by two.

We observe that the reported effect persists even in the case when the relative frequencies of tokens are not changed and fixed to be uniform, thus disproving the hypothesis that the observed effect is due to frequency and not token length.

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 assess the claim "Thus, by exclusion, we conjecture that reducing utterance length is, at least, a very important factor of memorization."

1. Summary of evaluation:
The claim is moderately overstated based on the evidence. While the researchers did conduct experiments to rule out alternative hypotheses (token distribution and vocabulary growth) and showed correlation between shorter sequences and increased memorization, the causal relationship isn't definitively proven. The use of "by exclusion" implies stronger certainty than the evidence supports. The paper itself uses more cautious language elsewhere, referring to this as a "hypothesis" and "conjecture." However, they did provide substantial experimental evidence supporting sequence length as an important factor.

<score>3</score>

Justification:
1. The evidence shows correlation but not definitive causation
2. The paper itself uses more cautious language in other sections (e.g., "we hypothesise," "we conjecture")
3. While alternative explanations were tested, the experimental design can't rule out all other possible factors
4. The evidence does strongly support sequence length as an important factor, but calling it "the primary factor" through exclusion overstates the certainty
5. The review comment confirms the paper's methodical approach but also frames it as an investigation of possibilities rather than definitive conclusions


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:

We propose a simple architecture for incorporating structural data into the Transformer, Graph Diffuser (GD).

The evidence to be evaluated is:In contrast, Graph Diffuser learns to combine multiple distances.

However, all of the works above use the original adjacency matrix or Laplacian to learn positional or relative encoding, unlike this work that learns the adjacency matrix using node and edge features.

Diffusion and other distance measures were used before to increase the expressivity of MP-GNNs Li et al. (2020), replace the local message passing scheme( Atwood and Towsley (2016); Wu et al. (2019); Klicpera et al. (2019, 2018)) or modulate the Transformers attention Mialon et al. (2021).

To the best of our knowledge, this work is the first Graph Transformer to: (1) learn to construct a new adjacency matrix using node and edge features to generate positional or relative encoding, and (2) learn to combine information propagation over multiple different propagation steps in an end-to-end manner.

We now describe our approach for taking a graph \(G=(X,A)\) with a node embeddings matrix \(X\) and edges \(A\) and processing it using the Transformer, which usually takes only a single matrix \(X\) as input. Our approach consists of 2 stages, illustrated in the left and right halves of Figure 3. First, GD embeds the structural relations between distant nodes in what we refer to as Virtual Edges. Then, the Transformer processes the nodes while using the virtual edges to direct the computation at different layers. _Virtual Edges_ are high-dimensional representations constructed between distant nodes in the graph. They contain rich information on the structural and positional relationships. To consider relations between distant nodes, the first step is broadening the receptive field on which the architecture operates.

We stack different powers of \(A\) into a 3 dimensional tensor \(E\in R^{n\times n\times k}\) \[E=[I|A|A^{2}|..|A^{k}] \tag{1}\] where \(k\) is the number of stacks and \(|\) denotes stacking matrices along the 3ed dimension and \(I\) is the identity matrix.

Virtual Edges contain structural information such as if nodes are on an odd length cycle, can distinguish many non-isomorphic graphs, and cover many distance measures such as shortest distance and generalized PageRank Li et al. (2020). In order to mix information between different propagation steps and extract meaningful structural relations, each stack is processed by a fully connected edge-wise feed-forward network. Each layer consists of 1 hidden layer with batch norm, ReLU activation, and a residual connection. \[Edge\text{-}FFN(E_{ij})=ReLU(BN(E_{ij}W1))W2^{1} \tag{2}\] \[E_{ij}=Edge\text{-}FFN(E_{ij})+E_{ij} \tag{3}\]

Rather than using the original adjacency matrix in equation 1, we found it beneficial to learn a new adjacency matrix using the node and edge features. \[\hat{A_{ij}}=ReLU(BN([x_{i};x_{j},e_{ij}]W_{1}))W_{2} \tag{4}\] \[A_{ij}=normalize(\sigma(\hat{A_{ij}})) \tag{5}\] Where \(;\) means contacting vectors, \(\sigma\) is the sigmoid function and normalize means \(l1\) row normalization. \(x_{i}\),\(x_{j}\in R^{d}\), \(e_{ij}\in R^{d_{edge}}\), \(W_{1}\in R^{(2d+d_{edge})\times 2d}\) and \(W_{2}\in R^{2d\times 1}\). If there are no edge features, we use only the nodes. This aligns with existing approaches such as GAT (Velickovic et al. (2018); Brody et al. (2022)), which find it beneficial to dynamically learn a new adjacency matrix. Most Graph Transformers use the graph structure to either alter the node's representations or to affect the attention mechanism itself. Graph Diffuser combines the 2 approaches. In the input layer, Self-Virtual Edges are added to the node representation as positional encoding, and at each attention layer, the Virtual Edges are reduced to an attention matrix that is combined with the standard dot-product attention. At each of the Transformer attention layers, we linearly project each virtual edge \(E_{ij}\) separately to get the positional attention score between \(i\) and \(j\). \[\hat{Att}_{ij}^{Position}=E_{ij}W_{p} \tag{6}\]We then combine the positional attention and the content(dot-product) attention scores and apply row-wise normalization. \[\hat{Att}^{Content}_{ij}=\frac{QK^{T}}{\sqrt{d}}_{ij} \tag{7}\] \[Att=normalize(exp(\hat{Att}^{Content})\odot\sigma(\hat{Att}^{Position})) \tag{8}\] Where \(\sigma\) is the sigmoid function and \(\odot\) means element-wise multiplication. In multi-head attention with \(h\) heads, the projection in equation 6 is done \(h\) times. equation 8 can be viewed as scaling the content attention coefficients based on the positional attention. As we will see in the next section, separating the attention based on content and positions and then combining them seems to assist with learning meaningful connections in the data and provides a natural visualization mechanism. Self-Virtual-Edges, \(E_{ii}\), are Virtual Edges between a node to itself. They contain important structural information, such as whether the node is part of an odd length cycle and the degrees of adjacent nodes. We project Self-Virtual-Edges to the node's representation dimensionality and add them as positional encoding. \[X_{i}=X_{i}+Relu(E_{ii}W_{pe}) \tag{9}\]

Self-walks were shown (Dwivedi et al. (2022)) to be an effective positional encoding. Adding such features to the node representations allows the Transformer to use structural information in all of its layers, including the feed-forward network.

Finally, Graph Diffuser nearly solves the task entirely by combining both positional and content attention. Looking at Figure 1(b), we can see the model learns to use the different attention mechanisms in an intuitive way, with content attention detecting nodes in the same color and position attention detecting nodes in the same row or column. Throughout our experiments, we take an existing Graph Transformer architecture and use it "as is" as our Transformer module without doing any hyper-parameter search. That is, we take a graph Transformer with the same hyperparameters used by the original work and only add our positional attention and encoding.2

In this work, we introduced a simple and effective architecture for machine learning on graphs, Graph Diffuser. Using a controlled example, we demonstrated its effectiveness in modeling long-range interactions while providing better interpretability. We then showed that this translates to real-world problems by evaluating GD on eight benchmarks from multiple domains. With minimal hyperparameter tuning, Graph Diffuser achieves a new state-of-the-art on most datasets and reaches very competitive results on the rest.

Our architecture integrates with the Transformer and consequently suffers from the quadratic memory complexity of the attention mechanism, which can restrict its applicability to larger graphs.

We describe Graph Diffuser in detail in the text and figures and mention all relevant hyperparameters to reproduce our experiments in the appendix.

We use GatedGCN as GNN modules, and four attention heads in Transformer modules. Transformer models use six layers, \(GNN\to Transformer\) uses 3 GNN layers and 3 Transformer layers.

We Conducted a simplified experiment to see the effects of GD when used as an out-of-the-box addition to different Transformer compositions, with no hyperparameter tuning.

Input: Figure 1: Illustration of our positional attention, focusing on node B. Information propagation from multiple propagation steps is combined to create Virtual Edges(colored) between distant nodes, which then direct the Transformer’s attention in each layer.

Input: Figure 3: An illustration of Graph Diffuser with 2 Transformer layers. Virtual Edges are created by combining multiple powers of the weighted adjacency matrix(left). Virtual Edges modulate each of the Transformers attention layers(right). Self-Virtual Edges are added to the Transformer input as positional encoding(bottom right)

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

Output:
After reviewing the claim and evidence, I find the claim "We propose a simple architecture for incorporating structural data into the Transformer, Graph Diffuser (GD)" to be relatively well-stated, warranting a score of 2. While GD does introduce novel elements like learning to construct adjacency matrices and combining multiple propagation steps, the architecture builds upon existing concepts and frameworks. The evidence thoroughly details the technical implementation through equations, figures, and clear explanations. Though innovative, calling it "simple" is fair as it primarily combines and extends established approaches like virtual edges, positional encoding, and attention mechanisms in a straightforward way.

<score>2</score>