Insufficient Task Description can Impair In-context Learning: A Study from Information Perspective

1. The most severe problem is the unreasonable theorem in Section 3.

   • Flawed Equation 1. The correct objective to maximize the log-likelihood of the transformer $q_\theta(r|d,c,q)$ using the given data should be $E_{p(d,c,q)} E_{p(r|d,c,q)} [\log q_\theta(r|d,c,q)].$ However, Equation 1 states $E_{p(d,c,q)} E_{q_{\theta}(r|d,c,q)} [\log p(r|d,c,q)].$ This term is definitely not the log-likelihood of the data as it mistakenly utilizes the ground truth distribution $p(r|d,c,q)$ within the objective function. I suggest that the authors provide a step-by-step derivation of their objective function, explaining their reasoning at each step.
   • Problematic interpretation of Equation 3. The authors derive Equation 3 and state that the KL divergence term on the right side contributes to maximizing log-likelihood. However, unlike the typical Evidence Lower Bound (ELBO), where the left side includes an optimizable distribution, here, $\log p(r|d,c,q)$ on the left of Equation 3 is a fixed ground truth distribution. This raises the question: how does optimizing the KL divergence term on the right improve a fixed distribution on the left? I recommend the authors elaborate on this interpretation and explicitly connect the logic from Equation 3 to their claims. In addition, I suggest the authors compare Equation 3 with the standard ELBO and discuss any key differences.
   • An intuitive example of logical flaws. I use one example to highlight the theorem's absurdity after all the logical flaws have accumulated. If we replace the variable $t$ with a random variable $z$ indicating "whether tomorrow will be sunny in my hometown," and use the same logits from Equation 1 to 3, we absurdly conclude that forecasting the weather in my hometown contributes to the log-likelihood maximization for their transformers. This contradiction stems from the accumulated logical flaws, including the previous two. I thus suggest the authors carefully examine their theorem and justify why the task label ($t$) prediction is meaningful in the context of their problem.

2. Inappropriate Experimental Design: In the real-world experiments, some "insufficient" task descriptions are actually incorrect. For instance, in the spelling task, the full task info is "extract the second letter of the input word," while the partial task info is "extract letter of the input word." The latter implies extracting each letter, which is a different task. Ideally, answers given the full task info should be a subset of those given the partial task info. A more appropriate partial task description would be "extract a certain letter of the input word" in the previous case. I suggest that the authors revise their partial task descriptions to ensure they are truly subsets of the full task descriptions. Additionally, I recommend them discuss their criteria for determining "insufficient" task descriptions and analyze how their choices might impact their results and conclusions.

The reviewer's primary concern with this paper is that the analysis heavily relies on the synthetic tasks which may not accurately reflect real-world applications.

• Limited Practical Impact of Theoretical Formulation: Section 3 introduces a theoretical framework with equations involving KL divergence and mutual information to motivate the role of task descriptions. However, these equations, especially Equation (5), are not integrated into the experiments and thus do not guide the empirical work in any meaningful way. The formulation could be streamlined or more directly connected to the paper’s practical findings.

• Restricted Applicability of Mutual Information Calculation (Equation 6): The authors quantify task description information in Equation (6) by defining bounds on task parameters. This works well for their synthetic dataset, where parameters are precisely controlled. However, the method lacks applicability to real-world datasets, where task definitions are more complex and less structured. The authors do not demonstrate how to extend this metric to real datasets like CoFE, which limits the study’s relevance beyond synthetic setups. Neither the theoretical analysis nor the form of synthetic data make sense to CoFE.

• Limited Generalizability of Synthetic Data to Real-World Tasks: The synthetic data structure, based on simple arithmetic equations, does not represent the complexity found in most real-world datasets. Real tasks, such as those in natural language processing, often require interpreting nuanced instructions rather than solving modular arithmetic problems. Consequently, the insights gained from these synthetic tasks may not fully transfer to more realistic settings.

• Unclear Notations and Words: The paper contains many abbreviations and notations for readers to guess. For example, no ex, 1 ex, 3 ex in Figure 1. Hq(t) in equation (5). Not Pred Task in Figure 5.