A-IC3: Learning-Guided Adaptive Inductive Generalization for Hardware Model Checking

In-context learning (ICL) has attracted increasing attention for enabling models to perform new tasks using only a few ``input--output'' prompt examples. However, existing approaches suffer from \textbf{shallow task adaptation}, where prompts are primarily used as contextual cues to implicitly infer task intent through semantic representations, while the underlying computational process remains unchanged. This limitation restricts task-specific adaptation and compromises inference interpretability. We argue that prompts should not only condition feature representations but also dynamically regulate the model's computation pathways. To this end, we propose \textbf{PromptPath}, an adaptive ICL framework that enables computation-level adaptation through prompt-conditioned dynamic pathways. Specifically, PromptPath introduces a prompt-driven routing mechanism to selectively activate and compose lightweight low-rank experts, forming task-specific computational pathways tailored to different prompts. By integrating prompt information directly into the inference process, PromptPath dynamically reconfigures model computation to enhance task specialization and interpretability. Extensive experiments on 3D point cloud and 2D visual recognition benchmarks demonstrate that PromptPath consistently outperforms state-of-the-art ICL baselines while exhibiting strong cross-domain and cross-task generalization.

Whether large language models perform genuine algorithmic reasoning or mere pattern completion is hard to test, because most benchmarks lack a ground truth for correct inductive inference. We introduce F-ICL, an in-context-learning benchmark that supplies one exactly. Using the Turing-complete machine F, complement-symmetrised into sF to remove output-polarity bias, we exhaustively enumerate all 1.5 billion programs of length $L\le13$ and compute the Bayes-optimal posterior in closed form under a bounded universal (Levin--Solomonoff) prior; models are scored by how closely their served distributions approach it at matched evidence. Each task is paired with its bitwise complement, on which the optimum scores identically, so an original-twin gap isolates the model's inductive bias. Across 105 serving configurations spanning 37 open models (0.8B--675B) and frontier systems from four laboratories, models answer up to 92% of queries correctly, yet 45 of 46 models yield distributions farther from the optimum than a keystroke reference, and their behaviour is bracketed by low-order prefix statistics fitted only on visible evidence. That reference is itself an algorithmic mixture, induced by a print-only machine with no loops, so the panel's implied measure sits closer to a loop-free mixture than to the loop-bearing optimum, independently of the reference machine. Updating is also non-monotone, which no prior explains: a Bayes-rational solved set can only grow in this realisable, noiseless setting, yet added examples produce $6{,}545$ solved-to-unsolved transitions against $13{,}702$ gains. The gap is not predicted by accuracy (Spearman $ρ=-0.19$, $p=0.21$), does not close with scale or across frontier generations in the serving modes that expose distributions, and is widened by instruction and reasoning post-training. F-ICL is released as an open, reproducible benchmark and toolkit.

Large language models achieve strong reasoning performance by scaling inference-time compute, yet remain fundamentally stateless, discarding the rich, self-produced reasoning traces generated during this process. We investigate whether models can instead learn online from this experience, converting transient computation (reasoning traces) into persistent reusable knowledge, and without external supervision or access to future data. We show that In-Context Learning (ICL) over raw reasoning traces fails to generalize, reflecting a fundamental limitation of token-level reuse: individual traces lack the abstraction needed for transfer, even after refinement (e.g. self-reflection). In contrast, drawing inspiration from recent works on unsupervised reinforcement learning, we find that lightweight per-instance training with self-generated test-time signals (majority voting) as rewards yields substantial gains, often surpassing full-dataset offline training, motivating a shift from raw traces to learned latent representations. Building on this insight, we propose an online method that distills inference-time compute spent on encountered problems into compact modular latent memories capturing the underlying reasoning structure. These memories are stored and retrieved for future inputs, enabling continual improvement while avoiding catastrophic forgetting through modular design. Importantly, our method is highly efficient, parametrized as extremely lightweight soft prompt memories (~0.001% of model parameters) and trained with only a few gradient steps, yet achieving performance competitive with full parametric updates and offline training. Across challenging mathematical reasoning benchmarks, our approach significantly outperforms zero-shot and raw data ICL baselines, while transferring effectively across datasets.