SynEVO: A neuro-inspired spatiotemporal evolutional framework for cross-domain adaptation

Dear reviewer ci9Q,

We deeply appreciate the time and efforts you have invested in reviewing our paper. We are honored to receive your recognition of the novelty and theoretical contribution. Your comprehensive feedback is helpful in guiding our revisions.

W1. Why skip spatial adaptation

Urban space is relatively static. Over a long period of time, data distribution and data sources will switch and change, but urban space will remain relatively invariant. The change of urban space can be divided into two aspects: 1) the land use of urban space, e.g., the urban land increases. 2) the model transfer among cities. Actually, our research paper focuses on the same urban system, and the scenarios of urban space expansion and cross-city model transfer may be out of the research scope of this work. Instead, we mostly focus on the collective intelligence in the same system, i.e., the data temporal domain distribution shift or the source domain shift, which is more usual in real-world practices. We study the problem of how spatiotemporal learning models adaptively evolve with data by capturing commonality and transfer the regularities to new scenario, so as to achieve the ability of learning whenever new data arrives. For abovementioned urban expansion or cross-city transfer scenarios, we can still take the core idea of this work, reordering new sample groups and make the elastic container grow based on SynEVO to quickly optimize and fine-tune existing models, realizing rapid transfer across different spaces.

W2&Q1Q2. A list of typos

Thanks for your careful check of our paper and we have thoroughly corrected the spelling mistakes and typos. The detailed correction are listed as below.

1. Line 133 and 557, 'spatiotemoporal' -> 'spatiotemporal';

2. Line 134-135, 'the there must shre' -> 'there must be shared';

3. Line 380-381, 'signifcant' -> 'significant'.

Thanks again for your expert review of our paper and we will incorporate the discussions and supplement more close literature to facilitate the validness of our paper.

Authors of Paper 5506

Dear reviewer n3PZ,

Thanks for your constructive feedback of our research. Your valuable advice contributes a lot to our work.

W1&Q1(1). Explanations of 'harmony with diversity'.

The concept of 'harmony with diversity' in our paper means that in order to build a generic spatiotemporal learning framework, there should be a certain degree of similarity (correlation) between sample groups or tasks, but they are not completely the same. To this end, a commonality learning container can be trained to capture the common patterns and enable distinguished representation learning from personal patterns. Then our learning framework can quickly transfer this commonality patterns to new tasks and obtain rapid generalization. We will supplement more clarification to improve the conciseness of such phrase.

W2&Q1(2). Explanations of ‘domains from the same source are not necessarily next to each other in the ordered sequence S’ in section 5.6.

This sentence means that the sample groups from the same source (intra-source sample groups) do not necessarily show greater similarity than sample groups of different sources (inter-source sample groups). This sentence is the interpretation and further discussion of Fig.3(a) in our paper. In the figure, we find sample groups [2,0], [2,1], [2,2] and [2,3] from the second source domain are between the first source domain samples [1,0] and [1,3], which indicates above phenomenon.

Q2. Elaborate how diverse aspects of human learning facilitate the deep neural network for cross-domain learning and transfers requires clarification in a holistic perspective.

Neuroscience reveals how brain structure impacts human cognitive and behaviors. The core of this paper is to design the learning process of cross-domain knowledge generalization by imitating neuroscience mechanisms from human brain. Specifically, our paper is divided into two aspects: (1) curriculum learning and (2) synapse structure with elastic neural networks.

Curriculum learning reveals the rule of human brain learning. People usually start to learn from simple tasks, and then learn to master more complex skills with increasing difficulty of learning tasks. Actually, the learning efficiency of such practice is higher than directly resolving new difficult problems [1,2]. To this end, task ordering from easy to difficult and the similarity between tasks are important to facilitate the transfer, which is emphasized in Sec.4.2 of our paper.

Synapse structure. From the perspective of human brain evolution, information in the human brain is transmitted through the synapse structure. This information passes through the synapse and forms an effective memory. At this time, if a new task needs to be learned, the stored information (i.e., memory in brain) becomes active, the presynaptic neurotransmitter will be released according to the correlation between tasks, so as to enable the original learned knowledge to be effectively transferred to learning process of new task. Thus, the long-term stable memory and new knowledge learning can supplement with each other, i.e., memory is transferred to empower learning while learning (mastering knowledge) expands and enriches the content of memory.

Thanks again for taking time to review our paper and we will incorporate above deeper analysis and explanations of concepts into our paper.

[1] Wang X, Chen Y, Zhu W. A survey on curriculum learning[J]. IEEE transactions on pattern analysis and machine intelligence, 2021, 44(9): 4555-4576.

[2] Blessing D, Celik O, Jia X, et al. Information maximizing curriculum: A curriculum-based approach for learning versatile skills[J]. Advances in Neural Information Processing Systems, 2023, 36: 51536-51561.

Authors of Paper 5506

Dear reviewer esVG,

Thanks for your constructive comments on our research.

W1. Why not use LLM?

LLM is popular to empower diverse applications but it is more specific to language processing and generation tasks. The reasons for not using LLM in this research are two-fold.

(1) The core of this research is data-adaptive model evolution, which is essentially a new training paradigm. Our model can be coupled with other deep learning models to achieve efficient data-adaptive model updates. This research is orthogonal to the study of large models.

(2) In fact, studies have demonstrated that smaller models are more suitable for numerical series-level predictions [1], while LLMs tend to excel in language generation tasks including question&answer [2] and planning [3].

In the future, it is interesting to take LLM as an agent to facilitate the learning process and then guide and schedule the adaptation and evolution process. Thanks again for your insightful question.

W2. Why skip cross-spatial domain adaptation?

Thanks for your valuable question. We list the reasons in the W1&Q1 response to Reviewer ci9Q

W3&Q3 How to derive Eq.(8) and from Eq.(8) to Eq.(10)

Our analysis is based Ref.[4] and [5]. Ref.[4] proposes an exponential model of the transmitter release probability: $P_r=1-e^{[Ca^{2+}]^n/K}$ where K combines parameters such as calcium binding rate and vesicle fusion efficiency, which affect information absorption in synapses. This formula explains the randomness of the combination of calcium ions with synaptotagmin.

After that, Ref.[5] directly measured the relationship between calcium concentration and transmitter release rate, and verified the applicability of the above exponential model. Finally, we reduce ${{[{Ca}^{2+}]}^n/K}$ to a variable $\tau$ to obtain Eq(8).

In our task reordering module, tasks are ordered from easy to difficult, by ranking the gradient from small to large. Since the smaller the dropout factor p, the more active the model is and the easier to achieve difficult tasks, our dropout factor p needs to decrease as the gradient gets larger. Hence, we can achieve Eq.(10). We let the exponent be $l(d_c)-d_{max}$ to make $0<p_c(d_c)\le1$.

Q1.Why gradients determine the order?

For each parameter w in the neural network, each step of parameter update is related to its own gradient, i.e. $W_k=W_{k-1}-\eta\nabla_k W=W_{k-1}-\eta∂E/∂W$ where $W_k$ is the parameter of k-th step, $\eta$ is the learning rate, $\eta∂E/∂W$ is the gradient of training loss to W.

From the equation above, we can see that the closeness of the model to learning samples (data) can be described by the gradient of each iteration. Larger gradients indicate the current model is farther from the real function which perfectly fits the data, then the learning process is harder. To this end, gradients can determine the training order of sample groups.

Q2. Relationship between neuroscience and transfer learning

The goal of transfer learning is to effectively transfer the knowledge of model A to a relevant task B. During the process, similarity counts. Based on theories of curriculum learning, humans master skills better when learning from easy to hard. During the learning process, similarity also exists between tasks. From the perspective of human brain evolution, information is transmitted through synapses in the human brain. This information passes through the synapse and forms a long-time stable memory. When facing similar new tasks, the brain releases presynaptic neurotransmitters based on the similarity between tasks, transferring the original knowledge to the new task. During the process, memory and learning can complement with each other, i.e., new well-learned knowledge can be expanded into memory, while existing memory can be retrieved when new knowledge is being learned.

We are truly grateful for your meticulous review and constructive comments on our manuscript. They have significantly contributed to enhancing the clarity and rigor of our work. We will add above deeper discussions into our next version.

[1] Tan M, et al. Are language models actually useful for time series forecasting?[J]. Advances in Neural Information Processing Systems, 2024, 37: 60162-60191.

[2] Feng P, et al. AGILE: A Novel Reinforcement Learning Framework of LLM Agents[C]//The Thirty-eighth Annual Conference on Neural Information Processing Systems.

[3] Ni H, et al. Planning, Living and Judging: A Multi-agent LLM-based Framework for Cyclical Urban Planning[J]. arXiv preprint arXiv:2412.20505, 2024.

[4] Bertram, Richard, Arthur Sherman, and ELIS F. Stanley. "Single-domain/bound calcium hypothesis of transmitter release and facilitation." Journal of Neurophysiology 75.5 (1996): 1919-1931.

[5] Schneggenburger, Ralf, and Erwin Neher. "Intracellular calcium dependence of transmitter release rates at a fast central synapse." Nature 406.6798 (2000): 889-893.

Authors of Paper 5506

Dear reviewer Nb7e,

Thanks for your encouraging comments!

Relations between SynEVO and transfer learning, optimizer design, evolutionary algorithms

Transfer learning is also a freeze-finetune mechanism where finetune is varied and specific to the problem itself. It does not involve active evolutions under different data distributions, while for SynEVO, it actively and continuously evolves by updating parameters when new data comes.

Evolutionary algorithm tends to evolve by adaptive fusion among peer models. It can be viewed as a passive evolution, while SynEVO updates spontaneously according to data.

Optimizer design includes various gradient-based adaptiveness and regularizations. In our work, we take gradients to measure correlations between model and data. We let it reorder sample groups to imitate curriculum learning of brain. Besides, we enable the regularization coefficient $\lambda$ to change dynamically with increasing learning capacity. These schemes are devised for easy optimization in our evolution contexts.

Detailed empirical analysis and training efficiency

(1) More empirical analysis on task reordering.

We supplement the experiments of reordering tasks from hard to easy to emphasize the importance of training order. The results of errors are listed in the order of MAE/RMSE/MAPE.

NYC: 7.217/18.807/0.415, CHI: 1.632/3.066/0.405;

SIP: 0.705/1.394/0.208, SD: 11.636/19.789/0.163.

The reversed order falls into inferior performances, which emphasizes the significance of reordering the tasks from easy to difficult in our design. Moreover, above hard-to-easy performances are better than random ordering of SynEVO-REO, which may be attributed to common relations between neighboring tasks as they are ordered even the reverse one.

(2) Design of commonality extraction.

a) If iterative learning for commonality removed, only train and test on one dataset. Results are listed in order of MAE/RMSE/MAPE:

NYC: 8.201/19.090/0.423, CHI: 1.554/2.887/0.385;

SIP: 0.711/1.412/0.216, SD: 13.128/20.890/0.220.

b) We set a different neural expansion rate $p_c$, e.g., $p_c=p_0/l(d_c)$

NYC: 7.213/16.310/0.422, CHI:1.550/2.765/0.367; SIP: 0.705/1.399/0.207, SD:11.944/19.599/0.168.

With above results, we can conclude our commonality learner and the setting of p are reasonable and empirically justified.

(3) Training efficiency.

Our training process can be 4 parts. I. Model warm-up with existing data. II. Complementary dual learners with elastic common container. III. Contrastive learning to obtain distinguished patterns. IV. Couple elastic common container and personality extractor to train on new data.

Comparison. On NYC, the above 4 parts cost about 800s, 795s, 545s and 111s respectively and the total time cost is about 2251s. The total time costs of baselines: AGCRN:1896s, ASTGCN:1884s, GWN:2233s, STGCN:823s, STGODE:3515s, STTN:1910s, CMuST: 2817s. Given increased generalization capacity (MAE reduced 42% at most) and inference efficiency (GPU cost reduced 78% at most), thus training costs are tolerable. Specifically, in our ablation studies, we can further confirm the importance of each module as shown in Tab.4.

Further theoretical analysis

(1) Information theory. Based on Appendix A, collective intelligence within a system increases with the input of data, i.e., $H(X_i|X_1,X_2,\ldots,X_{i-1})> H(X_{i+1}|X_1,X_2,\ldots,X_i)$ Thus, we can take full advantage of the collective intelligence in the system to empower task generalization.

(2) Synaptic structure is the medium of information transmission in human brain. The probability of synaptic neurotransmitter release can be defined as, $P_r=P_0(1-e^{-\tau})$, $\tau$ is the successive activeness difference between apre-synaptic-neuron and after-synaptic-neuron.

Since the probability is exponentially correlated with the parameter $\tau$, we envisage placing the gradient in an exponential position to map it. In task reordering, the tasks are ordered by gradients from small to large. Considering that decreasing dropout factor $p$ increases model activeness and enhancing its ability to cope with complex tasks, we further deduce Eq.(10). Meanwhile, we let the exponent be $l(d_c)-d_{max}$ to ensure $0<p_c(d_c)\le1$.

Broader application.

Our model can be generally nested within other neural networks. For example, in geological prospecting, the available shallow-layer data and precious deep-layer information share both commonality and personalization. It is applicable to utilize our evolvable "data-model" collaboration to decouple the invariant and variable patterns, and reconstruct the OOD distribution with new patterns. More broadly, our solution can also be extended to dynamic systems such as molecular interactions, agent collaborations, with necessary adaptation.

Thanks again for your advice and we will include additional results and discussions into our next version.

Authors of Paper 5506