Output Alignment: A Top-down Approach to Length Generalization

Authors: Tianqi Du, Haotian Huang, Yifei Wang, Yisen Wang
Primary area: foundation or frontier models, including LLMs
Keywords: Length Generalization, Output Alignment

Abstract:
Recently, large language models have exhibited impressive performance and surprising emergent properties. However, their abilities remain constrained by the preset context window of the Transformer architecture, and they continue to struggle with length generalization. In this work, we propose a new perspective on length generalization by focusing on the output distribution rather than the input, as most prior studies have done (e.g., through positional encodings or data structure). First, through case studies on simple synthetic tasks, we highlight the importance of **output alignment**---the consistency of output distributions across sequences of varying lengths. We then extend this observation to natural language tasks and introduce a metric named Long-Short Misalignment to quantify output alignment, finding a strong correlation between this metric and length generalization performance. Based on these insights, we propose a regularization loss during training that improves output alignment. Extensive experiments confirm the effectiveness of this approach. Overall, our work provides a novel perspective for understanding and enhancing length generalization in large language models.

Decision: reject
Reviewer scores: 6, 5, 6, 5

Reviews and discussion:
<thread>
creation date:
1730619922770

thread_type:
official_review

<thread_object>
creator: reviewer_nsdt

<content>
summary:
This paper presents output alignment as a method for enhancing the length generalization performance. The author initiates with the observation that the output space is significant in length generalization as demonstrated by a synthetic task. Through both theoretical and experimental analyses, the author validates that the output space has an impact on performance. The paper then proceeds to propose an approach for constructing a robust output space for natural language tasks. The performance of the proposed loss is advantaged by the experiments.

strengths:
The strength is evident:
1. A novel perspective from the output space of the Language Learning Model (LLM) when addressing the length generalization problem rather than the common input space analysis.
2. A well-defined synthetic task is proposed to drive the motivation and is strongly supported by theoretical analysis and experiments.
3. The proposed training loss is straightforward to implement and brings a relatively significant improvement to the length generalization performance.

weaknesses:
The weaknesses are as follows:

1. There is a lack of understanding regarding the design of mean value prediction tasks. Given that 0 and 1 have an equal probability (as indicated on line 143), does this imply that both 0 and 1 have a probability of 0.5? If so, does it mean that predicting 0.5 under a length of 50 would yield an approximate test loss of 0.005? Despite the actual test loss being around 0.001, this design appears suboptimal.

2. The distinct scaling behavior in mean and length is highly evident, particularly when a feed-forward layer is added to predict a scalar of the length. Predicting out-of-distribution values is a well-known challenge. Since the input and weight have fixed scales, but the output is expected to be scalable with respect to the length, the synthetic tasks seem rather explicit. This is not necessarily a weakness but rather emphasizes the need to clarify the purpose of such a preliminary experiment, which will be my next question.

3. The question arises as to how the synthetic task is actually related to natural language cases where the misalign loss is proposed. The only connection observed is “output space matter”. However, there appears to be a fundamental difference in “the output space/output distribution/output alignment” between the two scenarios. In the former case, it is more of a “scale/magnitude” issue. As the scale of x is changed to logx or 1/sqrt(x), the scale/magnitude becomes less out-of-distribution when scaling the length. In contrast, in the natural language case, it is primarily an “actual distribution” issue since the “scale/magnitude” does not change significantly. While both cases can be understood, the connection between them remains unclear. From this perspective, the term “misalignment” seems to be misused. The author could provide further clarification.

4. The experiment appears to be relatively weak. For natural language tasks, the author only evaluates it on LongBench, and the performance improvement is marginal. There are two potential ways to enhance the robustness of the results. Firstly, conducting experiments on more tasks such as Need-in-a-haystack, InfiniteBench, BABILong, etc. Secondly, analyzing the generations of the baselines and the proposed methods and providing randomly sampled output samples to show that the use of the additional loss is demonstrably better.

questions:
Small issues in writing:

1. L150,  ... embedding used, the test loss dramatically...  => ... embedding used, the test loss of length prediction task dramatically... 
2. L298-L299, A bit confusing about sufficies.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730668934455

thread_type:
official_review

<thread_object>
creator: reviewer_af82

<content>
summary:
The paper addresses the challenge of length generalization in LLMs. Instead of focusing on input structure or positional encoding, the authors present a novel approach centered on the output distribution to enhance length generalization. They highlight the concept of output alignment and introduce the Long-Short Misalignment metric to measure and quantify the consistency of output distributions for varying sequence lengths. Empirical results from synthetic tasks and natural language tasks validate their approach, demonstrating that output misalignment significantly impacts model performance on longer sequences. The paper further proposes a regularization loss based on their metric, which improves length generalization as shown through extensive experiments.

strengths:
1. The paper is well-written and easy to follow. The explanations and the illustrations are clear.
2. The proposed output alignment method for improving LLMs' length generalization is novel. The long-short misalignment regularization loss can be beneficial for future long-context LLM training.
3. The long-short misalignment loss is an interesting and useful probe for long-context LLM performance.

weaknesses:
1. Although the authors include extensive theoretical analysis of the proposed metric and method, the proofs of the theorems are based on some very strong assumptions, which need to be justified. More details in the Questions part.
2. The analysis of the synthetic tasks and the natural language tasks seems disjointed. The cause of the errors is different for these two types of tasks. This makes the OutRep method proposed in Section 3.2 seem unrelated to the rest of the paper and has a very limited use case on only non-pretrained small models. It would be beneficial to make a stronger connection between Section 3.2 and the following sections.
3. The experiments show that a higher regularization coefficient can negatively affect performance. More analysis is needed to mitigate the risk of over-regularization.

questions:
1. The proof of Theorem 1 is based on an autoregressive expression (Eqn 9). However, it is unclear why self-attention can be reformulated in this way. Also, it seems like Assumption 1 assumes that the function $K$ can disregard part of the input context. In an extreme situation where $l_{train}$ is very small, this assumption means that $K$ neglects a large portion of the prompt. Could you please elaborate more on the validity of Eqn 9 and Assumption 1?
2. Assumption 2 assumes that a Transformer model is Lipschitz continuous. However, this is not true for Transformers. Please refer to [1].
3. Regarding the long-short misalignment regularization, in a situation where $l_{train}$ is small, will the model learn to neglect some proportion of the input at the front?
4. Some key references are missing. For example, the mean prediction task is similar to the parity counter task in [2], and there has been similar length extrapolation analysis on synthetic tasks in [3].
5. In Line 400, the sequences should overlap by $l_{extra}$ tokens.

[1] Hyunjik Kim, George Papamakarios, and Andriy Mnih. 2021. The Lipschitz Constant of Self-Attention. ICML.

[2] Bingbin Liu, Jordan T Ash, Surbhi Goel, Akshay Krishnamurthy, and Cyril Zhang. 2022. Transformers Learn Shortcuts to Automata. ICLR.

[3] Suyuchen Wang, Ivan Kobyzev, Peng Lu, Mehdi Rezagholizadeh, and Bang Liu. 2024. Resonance RoPE: Improving Context Length Generalization of Large Language Models. ACL Findings.
</content>
</thread_object>

</thread>
<thread>
creation date:
1730677583885

thread_type:
official_review

<thread_object>
creator: reviewer_1pa5

<content>
summary:
This paper presents a novel approach to enhancing length generalization in large language models by focusing on output alignment (i.e., the consistency of output distributions across sequences of varying lengths), a departure from the more commonly explored input-focused strategies. The authors introduce a metric termed Long-Short Misalignment, which is shown to have a  correlation with length generalization performance. Additionally, the paper proposes a regularization loss aimed at improving this alignment and a reparameterization technique (OutRep) to explicitly align output distributions across different sequence lengths. Experimental results are provided to show that these techniques improve length generalization capabilities in both synthetic and natural language tasks.

strengths:
1. Novel Perspective: The focus on output alignment as a means to improve length generalization is a fresh perspective that diverges from traditional input or positional encoding-based methods. This unique angle provides a valuable contribution to the ongoing discourse on enhancing transformer model capabilities.

2. Clear Presentation: The paper is well-written, with a clear presentation of ideas and experimental results.

weaknesses:
1. Theoretical Issues: The theoretical proof of Theorem 3 could be problematic given the problematic definition of length generalization loss in the appendix (see detailed questions below), which weakens the theoretical soundness of the proposed approach. The empirical analysis cannot fully support the claim that minimizing the Long-Short Misalignment metric could lead to better length generalization  (see detailed questions below).

2. Computational Complexity: The implementation of the Long-Short Misalignment metric as a regularization loss introduces additional computational overhead. Moreover, the implementation details and complexity analysis, including their impact on model performance, are not adequately provided, which limits understanding of its scalability.

3. Lack of Comparison with Other Length Generalization Approaches: The paper does not provide a direct comparison between the proposed output alignment approach and other length generalization approaches (e.g., positional encoding-based approaches). Such a comparison would be beneficial to understand the relative strengths and weaknesses of the proposed method compared to existing approaches.

questions:
1. Encouraging LLMs to be less sensitive to small input sequence length variations, given that the semantic meanings of these input sequences are very similar, is essentially a form of robustness. However, when input sequence length differences are significant, encouraging output alignment may not be appropriate, as the outputs are expected to differ substantially. In your regularization term computation, when you sample l1 and l2 from the interval [ltrain / 2, ltrain], could you conduct an ablation study examining how different sampling ranges |l1 - l2| affect performance?

2. The mathematical equation for length generalization loss (Eq. 43) defined in Theorem 3 in the appendix is problematic. It doesn't explicitly compare model performance across different input lengths. A more reasonable definition you might consider is Egen_{long inputs} / Egen_{short inputs} - 1, where Egen is your original definition (Eq. 43). Could you incorporate this definition into your analysis and discuss how it might affect the theoretical results and empirical findings?

3. In Tables 2 and 3, it might not make sense to compare the proposed approach with the baseline approach by setting the same training steps since the proposed approach requires more computation. Could you provide a comparison based on total computation time or FLOPs rather than training steps, which would give a more accurate picture of the efficiency-performance tradeoff?

4. Table 1 shows that more powerful LLMs, which achieve better evaluation scores on some long-context benchmarks, also tend to have smaller Long-Short Misalignment scores. However, it is insufficient to conclude that a smaller Long-Short Misalignment metric directly leads to better length generalization ability based solely on these results. Could you conduct additional experiments or analyses to establish a more direct link?

5. Can you compute the length generalization loss and add it to Tables 2 and 3 to better demonstrate that the proposed approach leads to improved length generalization?

6. There is a lack of details on the sampling strategies and complexity analysis of the Long-Short Misalignment regularization term computation, including their impact on model performance. Could you provide more information on these aspects?

7. How does the proposed output alignment technique compare with other length generalization approaches (e.g., positional encoding-based approaches)?
</content>
</thread_object>

</thread>
<thread>
creation date:
1730707350577

thread_type:
official_review

<thread_object>
creator: reviewer_v4pp

<content>
summary:
This paper proposes a new view of achieving length generalization of LLMs by the output distribution adjustment/alignment. It identifies output alignment, the consistency of output distributions across varying sequence lengths, as a key factor in length generalization. The authors introduce the Long-Short Misalignment metric to quantify this alignment and demonstrate its strong correlation with models' performance on long-context tasks. Hence, they propose a regularization loss based on this metric, which, when incorporated into training, significantly improves models' ability to handle longer sequences. The evaluation is conducted on language modeling (Redpajama and PG19) and LongBench, where the proposed method demonstrates certain effectiveness.

strengths:
1. Considering that inputs of variable lengths significantly vary the output of LLMs, the view of achieving length generalization by addressing the output distribution gap between short and long inputs is novel and makes sense.

2. The evaluation of language modeling and LongBench demonstrated the effectiveness of the proposed misalign loss and verified the authors' postulation.

weaknesses:
1. In your settings, the short input is usually the truncated local context window of a long input, and the output distribution from the short input would serve as the "ground truth" distribution in SCE loss in Eq. (5). However, if the output relies on previous context information that's been removed, the output distribution given short input is also divergent and even wrong. For such a situation, the alignment may mislead the long-context output distribution and limit the capabilities (the model may tend to attend to local context only).

2. The models in experiments are trained based on CLEX. CLEX and some similar methods (e.g., YaRN) would dynamically adjust the frequency of RoPE according to the input length. In your implementation (line #376 to #404), the long and short inputs would be incorporated into one sentence, which would make the "short output distribution" be accessed based on "long RoPE frequency". Such short output distribution may deviate from the naive one and potentially affect the model's capabilities.

3. The evaluation length is up to 8K, which may be insufficient for a method designed for length generalization. I believe the evaluations over longer sequences may help to validate the effectiveness of the proposed method.

4. Section 3 seems to be redundant. The motivation and the proposed method are straightforward but the case study in section 3 is somewhat difficult to follow.

questions:
Please refer to the weaknesses.
</content>
</thread_object>

</thread>
<thread>
creation date:
1732395667580

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Updates in the manuscript

comment:
We sincerely thank all reviewers for their efforts, detailed comments, and thoughtful suggestions. We are encouraged by all the reviewers’ recognition of the novelty of our work. In response to their feedback, we have updated the manuscript, with the main changes highlighted in blue. These updates include:

1. **Revision of Section 3:**
We refined Section 3 to more clearly emphasize the motivations behind our work. This section has been condensed to slightly more than one page, with detailed theoretical content (Original Theorem 1 and Original Theorem 2) and explanations moved to the appendix. This refinement aims to make the purpose of the synthetic tasks clearer.

2. **Theoretical Adjustments:**
We revised the theoretical framework in Appendix B by adjusting certain assumptions to strengthen the validity of our conclusions.

3. **Discussion of Synthetic vs. Natural Language Tasks:**
Section 6 now includes an in-depth discussion of the relationship and comparisons between synthetic tasks and natural language tasks.

4. **Additional Experiments:**
We conducted several new experiments to address the reviewers’ suggestions:
- **Ablation Studies:** We performed ablation studies on the regularization coefficient $\alpha$ and the sampling range (Section 5.3), providing guidance for hyperparameter selection.
- **Evaluation on BABILong Benchmark:** Results in Section 5.4 demonstrate the effectiveness of our method in improving length generalization.
- **Comparison under Equivalent Computation Time:** Appendix E includes results showing our method consistently outperforms the baseline when compared under the same computational cost.
- **Additional Dataset Experiments:** Appendix F supplements the original mean prediction task experiments with a different dataset setting.
- **Comparison Without Model Adjustment:** Appendix G presents experiments to compare our approach without applying model adjustment methods.
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</thread>


Metareview:
metareview:
Reviewers find the papers approach novel and interesting at addressing length generalization for LMs. However they raised significant concerns about the initial manuscript - concerns about assumptions and proof of the theorems, limited evaluations for long context generalization. In response authors significantly revised manuscript introducing new assumptions and updating the theoretical results. they also present more long context evaluations. While reviewers appreciate the new experimental results, they do not find sufficient contributions and hence do not recommend acceptance at this stage. Overall I think the paper is on borderline, the paper can use another round of rewrite with the substantial changes to the theoretical analysis and the new experimental results, and can benefit from another round of reviews. Hence I recommend rejection.