The pseudo-code of plugging our method into the vanilla BO is summarised in Algorithm 1. Therefore, our method is applicable to any other variants of BO in a plug-in manner. In this section, we present the proofs associated with the theoretical assertions from Section 2. To Lemma 1. Assume the GP employs a stationary kernel Lemma 2. Given Lemma 1, determining Proposition 2. Leveraging Lemma 2, suppose Lemma 3. As per Srinivas et al., the optimization process in BO can be conceptualized as a sampling Pr null |f ( x) µ(x) | ωσ ( x) null > δ, (24) where δ > 0 signifies the confidence level adhered to by the UCB. This lemma is directly from Srinivas et al. . The proof can be found therein. Theorem 1. Leveraging Corollary 1, when employing the termination method proposed in this paper, As discussed in Remark 2 of Section 2.2 in the main manuscript, we suggest initializing L-BFGS Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's Different subplots are (a) our proposed method, (b) Naïve method, (c) Nguyen's method, (d) Lorenz's

Modularity is a compelling solution to continual learning (CL), the problem of modeling sequences of related tasks.

Prior to the close of the 2025 ARC Prize competition, the leading open source approach - known as TRM, or Tiny Recursive Models - involved training a 7M parameter recursive neural network on augmented variants of ARC tasks. That approach scored approximately 7.8% on the public ARC AGI II evaluation set, but required a level of compute far in excess of what is allowed during the competition. This paper shows that, by starting from a tiny recursive model that has been pre-trained on public ARC tasks, one can efficiently fine-tune on competition tasks within the allowed compute limits. Specifically, a model was pre-trained on 1,280 public tasks for 700k+ optimizer steps over 48 hours on 4xH100 SXM GPUs to obtain a ~10% score on the public evaluation set. That model was then post-trained in just 12,500 gradient steps during the competition to reach a score of 6.67% on semi-private evaluation tasks. Notably, such post-training performance is achieved by full-fine tuning of the tiny model, not LoRA fine-tuning or fine-tuning of task embeddings alone.

Weaknesses: * The dataset choice seems arbitrary. Since authors are defining a new setting, they should elaborate why specifically FEMNIST and FCelebA are used to create similar and dissimilar pairs. NeurIPS'19 also propose a similar masking based approach to learn non-overlapping paths for dissimilar tasks. These papers should be cited and disucssed (preferably compared against) in this manuscript. E.g., the prior works on task incremental learning have both sets of similar and dissimilar tasks.