#01Nov 5, 2026
cs.LG
When, Where, How: Active In-Context Learning for Tabular Foundation Models
Christian M. M. Frey
Tabular Foundation Models (TFMs) adapt to a new task only through the labeled rows in their context. However, labels are expensive to acquire in real-world scenarios due to the need for highly specific domain knowledge to ensure high-quality data. Active in-context learning transfers classical acquisition rules to this setting, in which the model that guides acquisition changes with every label added. We ask how the value of diversity, predictive uncertainty and target-aware information gain changes as a frozen TFM acquires more context. For that, we study Target-Aware Nearest Neighbor (TANN) acquisition and the Expected Predictive Information Gain in Context (EPIC) and evaluate them against classical rules. Our study across twenty benchmarks with two well-established TFMs and classical GBDTs highlights three findings: (i) When: diversity-based acquisition is best during the first acquisition iterations; (ii) Where: labeling pool rows that serve the target inputs via a simple target-aware nearest-neighbor rule matters substantially; (iii) How: EPIC yields the best models at the label budget, retains on average 80--87% of the chance-corrected full-data performance with only 5-10% of the pool labeled on the eight benchmarks with the largest pools, and selects labels that also improve the predictive performance of gradient-boosted decision trees.
#02Nov 5, 2026
cs.AI
How Finite Brains Generalize Without Bound: Spatial Memory as a Universal Computer
Yuhang He, Si Wu
A child who learns to add small numbers adds numbers of any length. LSTMs and Transformers trained on short sequences fail on longer ones. We trace the difference to what a learner reads when it decides. A position, a count or a time keeps taking new values as the input grows: it is a coordinate, and a learner that reads one meets in every long input values its experience never covered. Whether two things are the same has the same two answers at every size: it is a coincidence, and a learner that reads only coincidences finds in a long input nothing that short inputs lacked, so finite experience fixes its rule for every size. The memory carries the size of the input and the rule stays finite, and this determines the memory a generalizing brain can have: a memory that grows while what the learner reads of it stays finite has to look the same from every place, so it is made of cycles, and the past is reached by asking what happened when the cycles last stood where they stand now. The cycles are the grid modules, the cells that detect their return the place cells, the records the hippocampal index; a prefrontal controller moves the cycles and never sees them. Reading only coincidences costs no power: what finite experience fixes in such a learner is what Turing machines compute in step with their input, which is why a circuit that evolved to find the way home can learn arithmetic and grammar. In a network of neurons this machine of cycles is the dynamics seen through its symmetry, and symbols are its invariants. Trained on strings up to 40 symbols, the machine is at least 99% correct, on average over lengths 41 to 500, on nine of fifteen benchmark tasks, five of them tasks that no LSTM or Transformer solves; given new cycles after training it reverses strings of 15,015 symbols without error and fails beyond that on the curve the theory predicts; and its controllers run unchanged on neurons.
#03Nov 5, 2026
cs.LG
QRAE: Query-Relevant Attention Entropy for Context Compression in DeepSearch Agents
Yingjie Tan, Haiquan Qiu, Quanming Yao and 3 more
DeepSearch LLM agents repeatedly search and carry retrieved sources into subsequent reasoning steps. This expanding context increases token consumption and latency, although many results do not contribute to later reasoning. We propose Query-Relevant Attention Entropy (QRAE), an online context compression method that uses sparse evidence-assessment heads to decide which intact retrieved chunks should persist across reasoning steps. It scores bounded candidate batches through paired prefills: a query-free control suppresses shared attention responses, while normalized entropy measures the breadth of the positive response within each chunk. High-scoring chunks enter a persistent evidence whitelist and are included in the reasoning context. Uncertain chunks remain outside the reasoning context but are retained in a candidate cache, where they can be retrieved for later reevaluation. QRAE requires neither an additional generative compression pass nor modification of the attention operator. Across multiple DeepSearch benchmarks and reasoning models, QRAE improves task success by an average of 2.35 percentage points and reduces end-to-end latency and reported token usage by an average of 30% and 45%, respectively. These benefits generalize to a model with nearly 100B parameters.
#04Nov 5, 2026
cs.LG
Invariance before structure: two modes of emergent compression in representation learning
Hardik Rajpal, Dan Goodman
Learned representations show striking invariance across biological and artificial neural networks, with different substrates and variations driven by drift, heterogeneity and initialisation. To understand this invariance, we propose Emergent Adaptive Representation Learning (EARL), a framework that distinguishes two modes of emergence in learned representations: state-space compression, where a learned representation gains predictive power over its own future beyond what the network's units can predict individually, and parameter-space compression, where networks with different micro-level parameters converge to the same representation. We formalise both as Fisher sensitivities and introduce ensemble-level information-theoretic measures for each. In a recurrent reservoir with a trained bottleneck, parameter-space compression rises within the first few epochs of training and partly independently of the task, whereas state-space compression rises about 30 epochs later and only when the network begins to learn the temporal structure of the task. These results suggest that invariance to the substrate and task-specific emergent structure are acquired in distinct phases of learning.
#05Nov 5, 2026
cs.LG
Tight Asymptotic Bounds on the Maximum Number of Linear Regions of Piecewise-Linear Kolmogorov--Arnold networks
Ye Su, Yong Liu
Schoots et al.~\citep{schoots2025relating} (AISTATS 2025) established a generally loose upper bound on the number of linear regions of continuous piecewise-linear (CPWL) Kolmogorov--Arnold networks (KANs), without providing a lower bound. We consider a $T$-layer network with width vector $\mathbf n=(n_0,\ldots,n_T)$, input dimension $n_0=d$, output width $n_T=1$, and at most $k\geq2$ affine segments per edge. Our matching upper and lower bounds determine the tight growth order $Θ_{\mathbf n}(k^{\sum_{\ell=1}^{T}ρ_{\ell-1}})$ in $k$, where $ρ_{\ell-1}:=\min_{0\leq s\leq\ell-1}n_s$. When every hidden width is at least $d$, the tight order simplifies to $Θ_{\mathbf n}(k^{dT})$. The upper bound of \citep{schoots2025relating} is $k^{\sum_{\ell=1}^{T}n_{\ell-1}n_\ell}$. Our upper bound improves it by a factor of $Θ_{\mathbf n}\!\left(k^{\sum_{\ell=1}^{T}n_{\ell-1}n_\ell-\sum_{\ell=1}^{T}ρ_{\ell-1}} \right)$, with strict asymptotic improvement whenever a hidden layer has width greater than one. We further compare CPWL KANs with rectified linear unit (ReLU) networks using dense parameterizations with at most $Λ$ parameters per model and the same fixed nonlinear depth $T$. Counting trainable knot locations and optimizing the widths and $k$, we prove that the maximum region count of CPWL KANs divided by that of ReLU networks is $Θ_{d,T}(Λ^{d\lfloor T/2\rfloor})$ as $Λ\to\infty$, yielding a polynomial advantage for KANs when $T\geq2$. These tight bounds characterize the attainable geometric complexity of CPWL KANs, providing a foundation for understanding their expressive power and guiding architectural design.