Originality The topic is highly relevant and aligns with current research trends, yet it still offers an intriguing and fresh perspective.

Quality A more detailed discussion of the limitations and assumptions would enrich the paper. Additionally, delving deeper into the comparison with capacity theory could provide further insights (see question below).

Clarity Suggestion: Including a small diagram of the model would improve readability, especially considering its compact size. Could the results be validated in a more step-by-step manner? This would clarify that the approximations are sound and the rationale behind them, potentially expanding on this in the appendix. Providing full derivations in the appendix would enhance completeness and transparency.

Significance While the authors have noted the need for validation with larger models, doing so would strengthen the paper, despite the acknowledged material constraints.

(more important points first)

• While the model qualitatively explains the literature as stated above, quantitative connections are missing. I understand that some quantitative predictions may be contingent on the one-layer-one-head architecture and task, but others may be transferable, such as the two predictions mentioned in the Summary. I would find it interesting to evaluate these on a naturalistic task. Two examples come to mind: The path-finding task introduces in (Brinkmann et al., 2024) and possibly also a lightweight NLP setting.
• It is unclear to me how strong the dependence is in terms of data statistics. In particular, is there an intuition why the edge case of exactly $N/2$ positive $\ell=\+1$ tokens is so different?
• It took me a while to understand the relation between the two losses at the end of Section 3.7. It would help the reader to find details, possibly in the Appendix.
• Why does $\\beta=\\infty$ (or even just a large value) in Eq. (12) signify ICL dominance? I see this for $w$, but not for $\\beta$.
• The claim that $c\_1(t)$ has a power-law up to $K=10^5$ is not supported by Fig. A.3. The claim needs to be weakened or additional simulations are required.
• The title of the paper, “differential learning kinetics”, that also is used to label the distinction in Fig. 1, is not picked up much in the main text, and in my opinion also not very descriptive overall. I feel the paper would benefit from connecting the theory to this intuition that the authors developed.
• In Fig. 1 and 2: At what time is $K^*$ evaluated?
• No code is published, limiting transparency and reproduciblity.

Minor

• The paper states in line 376

While previous work has shown that such skewed data distributions favor ICL acquisition (Chan et al. (2022)), our theory suggests that such data dependencies can be examined by simply measuring $I\_K$.

As I understand these findings are compatible, the wording here to me however makes it unclear whether they are or not.

• It is not clear how good of a proxy $K$ is for data diversity, generally, so this caveat should be mentioned.
• Sometimes $\rangle\_{\\phi\_+}$ and sometimes $\rangle\_{\\phi\_+ \\sim P\_+}$ are used, that was slightly confusing to me. Also, $P_\+$ and $P(n_+)$ could be differentiated more clearly notationally.
• In line 413 it says

Equation 16 implies that $w$ after ICL acquisition tracks $w_{tr}$...

I assume $w_{tr}$ stems from gradient descent on Eq. (15), but this and why it bears this particular name is not clear.

• Data diversity is modelled by $K$, I would indicate this in Fig. 1 on the y-axis
• In line 361, the case $-\beta\_0 \gg 1$ is discussed, and then a conclusion is being made on long-tailedness. I believe that the results show that long-tailedness should hold for both $-\beta\_0 \\gg 1$ and $-\\beta\_0 \\ll 1$, but the wording here made it seem like it only applies to the former.
• Just before Section 3.3, the paper states

…three phenomena of interest, the transition from memorization to generalization, abrupt ICL learning and ICL transience,...

of which the first and second seem identical, and the (Reddy 2023) long-tailedness property does not appear.

• The Gaussian on the y-axis s Fig. 6c is not referenced.

Quality

The work is vague and lacks the necessary degree of rigor. The fact that no full derivations are presented even in the appendix is already grounds for rejection in my opinion. I recommend the authors provide a more thorough presentation of the derivations in this work.

This somewhat casual approach to the mathematics means that some very important simplify assumptions are not described accurately and in some case the work changes assumptions or conditions to suit whatever point it is currently trying to make. The most clear example of this is the dimension of the input D. It is foundational to the analysis here that D is large enough that the key-query matrix will be diagonal. This appears to me to be a huge simplification, worthy of clear mention. But the work fails to even acknowledge this in Section 3.2 when describing the model, instead referencing the fact indirectly and terming it an ``independence ansatz''. This fact of needing infinite D is only brought up in Section 3.3. This lack of clear assumptions and formal definition results in the jump from Equation 3 to Equation 4 being unclear. A similar case can be made for the implicit simplicity of the setup of binary classification itself - which is necessary for the analysis which relies of a single variable specifying the probability of the MLP being correct ($P^+$). Thus, the jump from Equation 4 to the equation after the sentence "since the two labels are symmetric the average loss $\mathcal{L}$ can be written as" (which again is not actually shown) is also unclear and missing multiple steps. Another example is the treatment of $N$ right before Equation 5, where it is never mentioned that N follows a distribution before this point, but then it is just defined as being approximated by a normal distribution and the loss equation updated again without derivation or explanation. This happens throughout the work and needs to be correct, for example before Equation 6 it is merely stated "From Equation 5 a few steps of simplification leads to...". I think I make my point but for clarity I will point out some quicker examples:

• Lines 297 to 302: The conclusion of the loss from the MLP separating from the in-context pathway seems true by construction and if I am not mistaken is essentially the independence ansatz. I'm not certain why here it is being phrased as an emergent phenomenon.
• Figure 4: The landscape depends on the probability of the MLP being correct but this is omitted entirely.
• Lines 329 to 330: it says "if the MLP is unable to perfectly memorize the K item-label pairs" but on lines 225 and 226 it is said that "all the information required by the MLP to memorize the label of the target is present in $t_{N+1}$". These are contradictory statements. It seems the second sentence is an assumption which is used in the derivation (or else you cannot summarize the MLP contribution just with $P^+$ - it is difficult to tell without the derivation). This would mean that you cannot interpret the model in the case of the MLP not being able to learn.
• Lines 336 to 338: The ultimate conclusion of this section is that the model behaviour depends on the initial values of $\omega$ and $\beta$ (less the MLP cannot learn the dataset in which case in-context learn will clean up the remaining loss as best it can). Given this conclusion I am confused what the point of this section is given that the condition of $\omega, \beta >> 1$ resulting in ICL is already noted from Equation 3. It's possible I am missing some nuance around this point but without derivations it is difficult to say.
• Two Taylor expansions are used in this work with almost no mention of what sorts of terms or information is lost but this approximation.
• Lines 355 and 356: It is not clear at all that $c_1(t),c_2(t) \approx 1/2$ here. This is likely due to the information treatment and lack of explanation of $I_k(t)$.
• Lines 369 to 372: The relationship between $c_1$ and time is not clearly discussed and $c_1$ in it's own right is not clear explained. Why is the mean of the sigmoid of the negative of the MLP output for the positive class useful? Why would it's integral over time diverge? Surely for a fixed dataset the MLP output stabilises? Is this integral then just a repeated sum of this stable mean value? Why does the divergence of $I_K(t)$ then imply ICL will occur?
• For Section 3.7: How standard is it to regularize only the in-context pathway? Seems like a fairly trivial result that if only this pathway is regularized then it will disappear.
• For Section 3.7: Since the dynamics are only considered once ICL is acquired, are the results of this section only valid if L2 regularization is applied once ICL is acquired? Since Equation 5 is not derived with L2 regularization I don't see how it can be just dropped in here and claimed that it ``applies throughout training'' and then the regularization term is just appended. I find it hard to believe that if the regularization term is present throughout training then ICL will emerge in the same manner as the model which is used to option Equation 5.
• Line 402: it is mentioned that the added regularization may be explicit or implicit. What justifies the conclusion that any sort of regularization will hold in a similar manner (or is that not the implication of this statement?). What sort of implicit regularization will only apply a weight normalization to t he in-context pathway?

Unfortunately, given my confusion with the derivation due to the lack of rigor and derivations it is difficult to even assess Section 4. Many of the phenomena which are considered in this section are either due to fairly vague conclusions drawn on equations without clear meaning or seem to be true by construction (again having sufficiently large D that the key-query matrix is diagonal is a large simplification not given sufficient attention). Thus, the conclusions and insights of this section seem premature.

It is possible I am missing something in the research - indeed it is possible this research is very impressive. I also appreciate that theory is difficult and requires simplifying assumptions, especially to get to grips with something as complex as in-context learning in transformers. But I am certain that the presentation of this research is significantly lacking for the current version.

Because the model used for the empirical validation is stripped down to a one layer transformer model the authors note that they cannot be sure that the dynamics are the same for much larger models. The authors could consider supplementing the one-layer analysis with tests on a deeper transformer model. Even if constrained by computational resources, experiments on a 2 or 3 layer transformer would help assess the applicability of their findings to larger networks.

The paper does not recommend methods to facilitate generalization. If possible, a discussion of how the ideas in the paper may be used to develop initialization and regularization techniques would make the submission even stronger.