Exploring Representations and Interventions in Time Series Foundation Models

Dear Reviewer MRNR,

Thank you very much for your thoughtful and detailed review of our paper. We are glad that you found our contributions to be well-timed and well-motivated, and that they “provide guidance for future TSFM architecture design.” We are delighted that you found the figures and tables in our paper to be “aesthetically pleasing,” as we devoted considerable effort to their design to convey our methods clearly and effectively.

You highlighted two key areas for improvement: (1) expanding the Introduction section to provide readers with a more comprehensive overview, and (2) adjusting the layout of figures to better correspond with the text content. Based on your feedback, we have made several revisions to address these points. For your convenience, we have highlighted these changes in blue ink in the revised manuscript.

1. Expanded introduction: We have revised the Introduction section to provide a more comprehensive overview of our motivation, methods, and experimental results, offering readers better context and a stronger logical structure.
2. Enhanced Subsection Organization in Section 3.2: Based on your feedback and additional input from Reviewer kpxg, we have restructured Section 3.2 by incorporating \subsubsections to enhance its readability and coherence.
3. Adjusted Figure Layout: We have realigned Figures 5–9 to place them closer to the corresponding text, ensuring a more seamless connection between the figures and their discussion.

Questions

I am a bit unclear about the concept of "block" in the article. Does it refer to some adjacent layers? What does it mean to prune Block3 of MOMENT-large at line 426?

1. Thank you for this clarifying question. In our paper, the term "block" refers to groups of consecutive layers within a transformer that exhibit high representational similarity. Consistent with prior work [1], we use "layer" to refer to individual transformer encoder or decoder blocks consistent with prior work, while "block" refers to a higher-level structure made up of multiple such layers that share similar representations [2].
2. As an example, consider Figure 1 which illustrates the pairwise similarity between the 24 layers of $`MOMENT-Large`$. In this figure, lighter colors (yellow) represent higher representational similarity, as measured by Centered Kernel Alignment (CKA) (Kornblith et al., 2019). The identified blocks are outlined with red bounding boxes. For example, Block 1 comprises layers 1–5, Block 2 comprises layers 9–18, and Block 3 comprises layers 19–23.
3. Our pruning algorithm is summarized in Algorithm 1, and lines 152–154. Regarding your specific question about pruning Block 3 of $`MOMENT-Large`$, our pruning method involves retaining the first and last layers of each block while zeroing out the weights of the intermediate layers. This approach preserves the structural integrity of the block while leveraging the skip connections within transformer blocks to ensure that signals and gradients continue to flow through the network. In the case of Block 3, composed of layers 19–23, this means that layers 19 and 23 are retained, while the weights of layers 20, 21, and 22 are zeroed out. We have added a dedicated section on pruning in Appendix C to further clarify this process.
4. We identify redundant blocks in a TSFM through visual inspection, which aligns with prior work [2]. Table 1 lists all the identified blocks in $`MOMENT-Large`$ and $`Chronos-Large`$. In addition to visual inspection, redundant blocks can also be identified using algorithmic approaches. As an example we outline a simple algorithmic approach in Appendix C.

References

1. Phang, Jason, Haokun Liu, and Samuel R. Bowman. "Fine-tuned transformers show clusters of similar representations across layers." arXiv preprint arXiv:2109.08406 (2021).
2. Nguyen, Thao, Maithra Raghu, and Simon Kornblith. "Do wide and deep networks learn the same things? uncovering how neural network representations vary with width and depth." arXiv preprint arXiv:2010.15327 (2020).

Dear Reviewer MRNR,

Thank you for your thoughtful feedback and for engaging with us. We are glad to hear that our response has addressed your concerns. If there are any remaining points or questions that require further clarification or elaboration, we would be more than happy to address them. If possible, we would be grateful for any additional insights into areas where you think our paper could be strengthened or improved in order to merit a higher score. Once again, we greatly appreciate your constructive input, which has helped improve the quality of our paper.

Dear Reviewer QT6A,

Thank you so much for your time and thoughtful feedback! Thank you for recognizing that our findings are “not limited to a single model but span multiple TSFMs, enhancing the generality of the findings.” We have put significant thought into your feedback, and carried out multiple experiments to address your concerns.

1. Effectiveness of pruning on large models: We conducted pruning experiments on two of the largest open-source models: MOMENT-Large (385M parameters) and Chronos-Large (710M parameters) at the time of writing this paper (see Table 8 in [1]). The results from these experiments are summarized in Tables 2–10, and Figure 18 of the revised manuscript. Unfortunately, we were unable to include TimeGPT in these experiments, as it is a closed-source model only accessible via paid API. Consequently, we could not obtain the necessary access for direct pruning experiments on TimeGPT.
2. On selecting the parameter $\alpha$: We rename $\alpha$ to $\lambda$ in the revised manuscript for clarity. Below we provide some guidance on selecting good values of $\lambda$ and insights into its properties:
   1. Selection and Impact of the Steering Strength Parameter $\lambda$:
      1. Optimal Range: Based on our empirical experiments, we found that the steering strength parameter $\lambda$ is most effective for interventions when its value lies within the interval $[0.1, 2.0]$.
      2. Lower Bound Considerations: Values of $\lambda < 0.1$ often result in insufficient perturbation of the activation patterns, leading to suboptimal intervention effects that may not manifest visibly in the model's output.
      3. Upper Bound Effects: Setting $\lambda > 2.0$ induces excessive perturbations that push activations beyond their typical distribution bounds, potentially resulting in degenerate or semantically meaningless outputs. In the PCA/latent space visualizations, these cases simply appear as more distant points along the steering direction.
   2. Directional Properties:
      1. Reversibility: Multiplying the steering vector by $-1$ effectively reverses the direction of intervention, enabling bidirectional control (e.g., transforming concept $A \rightarrow B$ into $B \rightarrow A$).
      2. Example Application: For a steering vector trained to increase signal magnitude, applying its negative counterpart (-$\lambda$ $\mathbf{S}$) produces controlled signal decrease, demonstrating the symmetric nature of the steering operation.
   3. Practical Guidelines:
      1. Initial Calibration: We recommend starting with $\lambda = 1.0$ and adjusting based on the observed intervention strength. In most cases value $\lambda = 1.0$ works well and does not need tuning.
      2. Task and Model-Specific Tuning: If $\lambda = 1.0$ does not yield satisfactory results, the optimal value requires tuning based on both the specific steering objective and target model, necessitating empirical calibration to achieve the desired intervention strength.
      3. Monitoring: When applying steering interventions, practitioners should monitor both the immediate output and latent space representations to ensure meaningful transformations while maintaining output coherence.

References

1. Shi, Xiaoming, et al. "Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts." arXiv preprint arXiv:2409.16040 (2024).

Dear Reviewer kpxg,

Thank you for taking the time to review our paper and provide thoughtful feedback. We greatly appreciate your recognition of our contributions, particularly your observation that our findings “help us understand the TSFMs, and the knowledge can potentially be used to improve their capabilities.”

You have highlighted two key areas for improvement: (1) the development of analysis techniques tailored to time series models, and (2) enhancing the readability of Section 3.2. We have carefully considered your suggestions and made revisions to address these concerns. Below, we detail our responses and summarize the changes implemented in the paper. All revisions are highlighted in blue ink for ease of review.

1. Based on your suggestions, we have re-organized Section 3.2 by using \subsubsections to improve readability.
2. Regarding the design of time series specific techniques: We appreciate your feedback and would like to clarify the following points:
   1. The primary goal of our study was to uncover the inner workings of time series foundation models (TSFMs) and leverage these insights to enhance their capabilities and trustworthiness. We are pleased that you acknowledged the importance of this effort, noting that the “findings in this paper help us understand [the] TSFMs, and the knowledge can potentially be used to improve their capabilities.”
   2. Most TSFMs are based on the Transformer architecture: Given that most TSFMs, except Tiny Time Mixers, are built on the transformer architecture, we focused on established analysis techniques for transformer architectures. Our work is the first to adapt these existing techniques to transformer-based TSFMs.
   3. Our findings with standard techniques are also valuable: The success of using general transformer probing techniques in studying TSFMs is itself a key finding, as it highlights that: (1) the fundamental mechanisms of representation learning in transformers are largely consistent across modalities, (2) TSFMs learn structured, interpretable concepts, akin to their language and vision counterparts, and (3) certain techniques for studying transformer architectures are effective across modalities.
   4. Our experiments are specific to time series: Nonetheless, our study remains firmly rooted in time-series-specific phenomena and concepts: we employed time series models ($`MOMENT, Chronos, MOIRAI`$), evaluated them on time series tasks (forecasting, classification, anomaly detection, and imputation), and explored concepts central to time series data, such as periodicity, trend, and amplitude.
   5. That said, we agree that developing modality-specific probing techniques is a promising research direction. We look forward to exploring how such techniques can further enrich the understanding and utility of TSFMs.