Computational models can be considered as complete, quantified implementations of theories (Dijkstra & De Smedt, 1996). By specifying theoretical details, they allow explanations and predictions to go beyond the obvious and ordinal. The arrival of computational models in the cognitive domain of second language learning indicates that it is growing out of its infancy. This is because model implementation, clearly, can never be complete if the underlying theories are not.

What phenomena should cognitive models of second language learning account for, and how should they be progressively developed? Any good theory of language use and, hence, any computational model should cover at least four dimensions: representations in long-term memory, processes, cognitive control, and working memory. Representations can differ considerably across languages and participants (monolinguals or multilinguals, heritage speakers or native speakers, and so on). Representations can have different mutual relations within and between languages (e.g., cognates and false friends). The processing of representations depends on their intralingual and interlingual properties. Task requirements may induce various processing strategies that models need to take into account. Finally, working memory is paramount for second language learning. In our view, Li and Xu do not fully make these distinctions explicit.

Furthermore, models of second language learning should be built while adhering to certain developmental strategies, as recommended by Jacobs and Grainger (1994). Their strategies include, for instance, nested modeling, model-to-model comparison, and the application of precise criteria to model building and evaluation. Because second language learning is not a general or unified phenomenon, these strategies are indispensable. We stress these notions as important additions to Li and Xu's considerations.

As the authors explain, there are many different approaches to modeling. Some of them date back to the 1980s; others are currently under development. Much has changed over the decades. New information sources, including neuroscientific evidence, have become available for second language learning (van Heuven & Dijkstra, 2010). New questions have been formulated about cognitive processes in the brain (where? how?), but cognitive functionality is still a primary focus for many researchers.

We have noted a tendency in the literature (carefully avoided by Li and Xu) to consider new approaches as “better.” Of course, new approaches may offer new possibilities for simulation, but they also have new limitations. For instance, deep learning is much more powerful than simple learning as in the old parallel distributed processing models (although its learning rules may be questionable from a neuroscientific perspective). However, it has the exacerbated problem of having many degrees of freedom (making cognitive models difficult to specify). Other issues are that most attention is focused on accuracy rather than response times, and that what happens takes place in a “black box” that replaces the human black box that researchers wanted to open up. Without new empirical evidence (possibly collected with innovative techniques), the new models cannot be specified any further than the older existing models. In fact, because they are older, existing models have often been specified and tested already in much more detail, depth, and breadth.

At the same time, older models have their own problems that may or may not have been resolved. For instance, interactive activation (IA) models so far have not accounted well for learning aspects. A theoretical attempt was made with BIA-d (Grainger et al., 2010), but the implementation of learning rules (as in ACT-R; Anderson et al., 2004) should be systematically explored. The modest conclusion is that at the current stage of second language learning research, the best that can be hoped for is a model that helps in understanding the basic mechanisms underlying processing and learning. In addition, every new model represents a particular view on a limited cognitive domain and has a particular function (models are like sketches). This is in line with the multipronged approach of Li and Xu.

However, this approach will have to deal with at least two issues. First, it is problematic to replace old models with new ones or build hybrid models combining two paradigms. Li and Xu argue that their “pluralist approach” will lead to the emergence of new models that will make significant contributions to research on bilingual learning and representation. We agree that there are advantages in using new empirical data and higher level theoretical insights, but not necessarily in replacing existing models with new ones. The implementation of any model requires a considerable amount of effort, and simply dumping existing models is a waste of scientific energy. Furthermore, we note that certain approaches to hybrid modeling are simply incompatible due to inconsistent assumptions. Their comparison is fruitful, but not their integration. Our proposed modeling approach is therefore to work within one particular cognitive framework, allowing us to clarify or add pieces of the cognitive puzzle.

Second, encompassing models of second language learning cannot be built as long as the underlying mechanisms of explicit and implicit learning are unclear. There currently does not exist a detailed, valid theory of second language learning. Although models like DevLex-II are promising, there is still a lack of knowledge, for instance, about long-term learning curves or changes in the second language lexicon over time. Thus, it is not fully clear what models of second language learning should account for.

Therefore, the best top-down approach to modeling monolingual and bilingual language performance and second language learning is still to be determined. For several reasons, we argue that developing an IA-account for second language learning phenomena will be most fruitful. First of all, human researchers think and interact in terms of symbols—the basic units of IA-models. Symbolic representations are easy to use for communication and comprehension purposes. We do not deny that “reality” has a much finer-grained size, but we would argue that the IA-models do “carve nature at its joints” (Fodor, 1983, pp. 127–128). Every model is a simplification, but as long as the core mechanisms are captured (even when in reality their underlying nature is fuzzy), the model fulfills our purposes.

There are successful IA-inspired models of monolingual language processing, such as the spatial coding model (Davis, 2010) and WEAVER++ (Roelofs, 1992). Extending these models to second language learning is useful and allows for nested modeling. A model like Multilink (Dijkstra et al., 2019) accounts for monolingual and multilingual word retrieval of different word types in different languages, participants, and tasks. In principle, learning mechanisms can be added to the model. Alternatively, because they share fundamental assumptions, we may approach second language learning by considering IA-models as the end point of parallel distributed processing models (as in BIA-d).

In sum, we agree with Li and Xu that cross-disciplinary work “is not a luxury but a necessity for success.” Indeed, to reach the enduring goal of capturing the basic cognitive mechanisms underlying bilingual processing and learning, relating to different research fields is a sine qua non. Here, we have pointed out additional notions, areas, and insights to be considered. Importantly, we conclude that second language learning should be studied in interaction with monolingual and bilingual processing in general.

计算模型可以被认为是理论的完整、量化的实现（Dijkstra & De Smedt, 1996）。通过指定理论细节，它们允许解释和预测超越显而易见的和有序的。计算模型在第二语言学习认知领域的到来表明它正在走出婴儿期。这是因为如果基础理论不完整，模型实现显然永远不会完整。

第二语言学习的认知模型应该解释哪些现象，应该如何逐步发展？任何好的语言使用理论，因此，任何计算模型都应该至少涵盖四个维度：长期记忆、过程、认知控制和工作记忆中的表征。不同语言和参与者（单语或多语、传统演讲者或母语者等）的表述可能有很大差异。表示可以在语言内部和语言之间具有不同的相互关系（例如，同源词和假朋友）。表征的处理取决于它们的语内和语际属性。任务要求可能会引发模型需要考虑的各种处理策略。最后，工作记忆对于第二语言学习至关重要。

此外，正如 Jacobs 和 Grainger ( 1994 )所建议的那样，应该在坚持某些发展策略的同时建立第二语言学习模型。例如，他们的策略包括嵌套建模、模型间比较以及将精确标准应用于模型构建和评估。因为第二语言学习不是一个普遍或统一的现象，这些策略是不可或缺的。我们强调这些概念是对李和徐考虑的重要补充。

正如作者所解释的，有许多不同的建模方法。其中一些可以追溯到 1980 年代；其他的目前正在开发中。几十年来发生了很大变化。新的信息来源，包括神经科学证据，已可用于第二语言学习（van Heuven & Dijkstra, 2010）。关于大脑中的认知过程（在哪里？如何？）已经提出了新的问题，但认知功能仍然是许多研究人员的主要关注点。

我们注意到文献中有一种倾向（李和徐小心避免）认为新方法“更好”。当然，新方法可能会为模拟提供新的可能性，但它们也有新的局限性。例如，深度学习比在旧的并行分布式处理模型中的简单学习要强大得多（尽管从神经科学的角度来看，它的学习规则可能是有问题的）。然而，它具有许多自由度的问题（使认知模型难以指定）。其他问题是，大多数注意力都集中在准确性而不是响应时间上，并且发生的事情发生在一个“黑匣子”中，它取代了研究人员想要打开的人类黑匣子。如果没有新的经验证据（可能通过创新技术收集），不能比旧的现有模型进一步指定新模型。事实上，由于它们较旧，现有模型通常已经在更详细、更深入和更广度上进行了指定和测试。

同时，旧型号也有自己的问题，可能已经解决，也可能没有解决。例如，到目前为止，交互式激活 (IA) 模型还没有很好地考虑学习方面。对 BIA-d 进行了理论上的尝试（Grainger 等人，2010 年），但学习规则的实施（如 ACT-R；Anderson 等人，2004 年）) 应系统地探讨。适度的结论是，在第二语言学习研究的现阶段，可以期望的最好的模型是有助于理解加工和学习的基本机制的模型。此外，每个新模型都代表了有限认知领域的特定视图，并具有特定的功能（模型就像草图）。这与李和徐的多管齐下的方法是一致的。

但是，这种方法至少要处理两个问题。首先，用新模型替换旧模型或构建结合两种范式的混合模型是有问题的。Li 和 Xu 认为，他们的“多元主义方法”将导致新模型的出现，这些模型将为双语学习和表征的研究做出重大贡献。我们同意使用新的经验数据和更高层次的理论见解有优势，但不一定用新模型替换现有模型。任何模型的实现都需要付出相当大的努力，简单地抛弃现有模型是对科学能量的浪费。此外，我们注意到某些混合建模方法由于假设不一致而根本不兼容。它们的比较是富有成果的，但它们的整合却不是。

其次，只要外显和内隐学习的潜在机制不明确，就无法建立包含第二语言学习的模型。目前还没有一个详细的、有效的第二语言学习理论。尽管 DevLex-II 之类的模型很有前景，但仍然缺乏有关长期学习曲线或第二语言词典随时间变化的知识。因此，尚不完全清楚第二语言学习模型应该解释什么。

因此，对单语和双语语言表现和第二语言学习建模的最佳自上而下方法仍有待确定。出于几个原因，我们认为为第二语言学习现象开发 IA 帐户将是最富有成效的。首先，人类研究人员根据符号（IA 模型的基本单位）进行思考和互动。符号表示易于用于交流和理解目的。我们不否认“现实”具有更细粒度的大小，但我们会争辩说 IA 模型确实“在其关节处雕刻了自然”（Fodor，1983 年，第 127-128 页）。每个模型都是一种简化，但只要抓住了核心机制（即使实际上它们的基本性质是模糊的），该模型就可以实现我们的目的。

有成功的受 IA 启发的单语语言处理模型，例如空间编码模型 (Davis, 2010 ) 和 WEAVER++ (Roelofs, 1992 )。将这些模型扩展到第二语言学习是有用的，并且允许嵌套建模。像 Multilink (Dijkstra et al., 2019 ) 这样的模型解释了不同语言、参与者和任务中不同单词类型的单语和多语言单词检索。原则上，可以将学习机制添加到模型中。或者，因为它们共享基本假设，我们可以通过将 IA 模型视为并行分布式处理模型（如 BIA-d）的端点来处理第二语言学习。

总之，我们同意李和徐的观点，跨学科工作“不是奢侈品，而是成功的必要条件”。事实上，要达到捕捉双语加工和学习背后的基本认知机制的持久目标，涉及不同的研究领域是必要条件。在这里，我们指出了需要考虑的其他概念、领域和见解。重要的是，我们得出结论，一般来说，第二语言学习应该在与单语和双语处理的交互中进行研究。