Surprisal-Guided Selection: Compute-Optimal Test-Time Strategies for Execution-Grounded Code Generation

Test-time training (TTT) adapts language models through gradient-based updates at inference. But is adaptation the right strategy? We study compute-optimal test-time strategies for verifiable execution-grounded (VEG) tasks, domains like GPU kernel optimization where a deterministic evaluator provides dense, continuous reward signals. Using KernelBench as our testbed and a 120B-parameter model (GPT-OSS-120B with LoRA adaptation), we find that search outperforms minimal adaptation (1-5 gradient steps): Best-of-N sampling achieves 90% task success (18/20 tasks) at K=64 across the full KernelBench L1 eval set while TTT's best checkpoint reaches only 30.6% (3-seed mean), with TTT's "equivalent K" falling below 1, worse than single-sample inference. The failure mode is over-sharpening: gradient updates collapse diversity toward mediocre solutions rather than discovering optimal ones. Our main contribution is surprisal-guided selection: selecting the highest-surprisal (lowest-confidence) correct sample yields 80% success vs. 50% for most-confident selection, a 30% improvement. Extending to surprisal-guided-top3 matches oracle performance at 100%. This zero-cost strategy, validated through length-controlled analysis, recovers oracle performance. For dense-reward VEG tasks, compute should be allocated to sample diversity and intelligent selection rather than gradient adaptation. The surprisal-guided selection principle may generalize to other execution-grounded domains where optimal solutions occupy the distribution tail.

Continuous Self-Improvement of Large Language Models by Test-time Training with Verifier-Driven Sample Selection

Learning to adapt pretrained language models to unlabeled, out-of-distribution data is a critical challenge, as models often falter on structurally novel reasoning tasks even while excelling within their training distribution. We introduce a new framework called VDS-TTT - Verifier-Driven Sample Selection for Test-Time Training to efficiently address this. We use a learned verifier to score a pool of generated responses and select only from high ranking pseudo-labeled examples for fine-tuned adaptation. Specifically, for each input query our LLM generates N candidate answers; the verifier assigns a reliability score to each, and the response with the highest confidence and above a fixed threshold is paired with its query for test-time training. We fine-tune only low-rank LoRA adapter parameters, ensuring adaptation efficiency and fast convergence. Our proposed self-supervised framework is the first to synthesize verifier driven test-time training data for continuous self-improvement of the model. Experiments across three diverse benchmarks and three state-of-the-art LLMs demonstrate that VDS-TTT yields up to a 32.29% relative improvement over the base model and a 6.66% gain compared to verifier-based methods without test-time training, highlighting its effectiveness and efficiency for on-the-fly large language model adaptation.

Test-Time Training Done Right

Test-Time Training (TTT) models context dependencies by adapting part of the model's weights (referred to as fast weights) during inference. This fast weight, akin to recurrent states in RNNs, stores temporary memories of past tokens in the current sequence. Existing TTT methods struggled to show effectiveness in handling long-context data, due to their inefficiency on modern GPUs. The TTT layers in many of these approaches operate with extremely low FLOPs utilization (often <5%) because they deliberately apply small online minibatch sizes (e.g., updating fast weights every 16 or 64 tokens). Moreover, a small minibatch implies fine-grained block-wise causal dependencies in the data, unsuitable for data beyond 1D ordered sequences, like sets or N-dimensional grids such as images or videos. In contrast, we pursue the opposite direction by using an extremely large chunk update, ranging from 2K to 1M tokens across tasks of varying modalities, which we refer to as Large Chunk Test-Time Training (LaCT). It improves hardware utilization by orders of magnitude, and more importantly, facilitates scaling of nonlinear state size (up to 40% of model parameters), hence substantially improving state capacity, all without requiring cumbersome and error-prone kernel implementations. It also allows easy integration of sophisticated optimizers, e.g. Muon for online updates. We validate our approach across diverse modalities and tasks, including novel view synthesis with image set, language models, and auto-regressive video diffusion. Our approach can scale up to 14B-parameter AR video diffusion model on sequences up to 56K tokens. In our longest sequence experiment, we perform novel view synthesis with 1 million context length. We hope this work will inspire and accelerate new research in the field of long-context modeling and test-time training. Website: https://tianyuanzhang.com/projects/ttt-done-right

Scaling Laws of Global Weather Models

Data-driven models are revolutionizing weather forecasting. To optimize training efficiency and model performance, this paper analyzes empirical scaling laws within this domain. We investigate the relationship between model performance (validation loss) and three key factors: model size ($N$), dataset size ($D$), and compute budget ($C$). Across a range of models, we find that Aurora exhibits the strongest data-scaling behavior: increasing the training dataset by 10x reduces validation loss by up to 3.2x. GraphCast demonstrates the highest parameter efficiency, yet suffers from limited hardware utilization. Our compute-optimal analysis indicates that, under fixed compute budgets, allocating resources to longer training durations yields greater performance gains than increasing model size. Furthermore, we analyze model shape and uncover scaling behaviors that differ fundamentally from those observed in language models: weather forecasting models consistently favor increased width over depth. These findings suggest that future weather models should prioritize wider architectures and larger effective training datasets to maximize predictive performance.

Differentiable Zero-One Loss via Hypersimplex Projections

Recent advances in machine learning have emphasized the integration of structured optimization components into end-to-end differentiable models, enabling richer inductive biases and tighter alignment with task-specific objectives. In this work, we introduce a novel differentiable approximation to the zero-one loss-long considered the gold standard for classification performance, yet incompatible with gradient-based optimization due to its non-differentiability. Our method constructs a smooth, order-preserving projection onto the n,k-dimensional hypersimplex through a constrained optimization framework, leading to a new operator we term Soft-Binary-Argmax. After deriving its mathematical properties, we show how its Jacobian can be efficiently computed and integrated into binary and multiclass learning systems. Empirically, our approach achieves significant improvements in generalization under large-batch training by imposing geometric consistency constraints on the output logits, thereby narrowing the performance gap traditionally observed in large-batch training.

DRESS: A Continuous Framework for Structural Graph Refinement

The Weisfeiler-Lehman (WL) hierarchy is a cornerstone framework for graph isomorphism testing and structural analysis. However, scaling beyond 1-WL to 3-WL and higher requires tensor-based operations that scale as $\mathcal{O}(n^3)$ or $\mathcal{O}(n^4)$, making them computationally prohibitive for large graphs. In this paper, we start from the Original-DRESS equation (Castrillo, León, and Gómez, 2018) -- a parameter-free, continuous dynamical system on edges -- and show that it distinguishes the prism graph from $K_{3,3}$, a pair that 1-WL provably cannot separate. We then generalize it to Motif-DRESS, which replaces triangle neighborhoods with arbitrary structural motifs and converges to a unique fixed point under three sufficient conditions, and further to Generalized-DRESS, an abstract template parameterized by the choice of neighborhood operator, aggregation function and norm. Finally, we introduce $Δ$-DRESS, which runs DRESS on each node-deleted subgraph $G \setminus \{v\}$, connecting the framework to the Kelly--Ulam reconstruction conjecture. Both Motif-DRESS and $Δ$-DRESS empirically distinguish Strongly Regular Graphs (SRGs) -- such as the Rook and Shrikhande graphs -- that confound 3-WL. Our results establish the DRESS family as a highly scalable framework that empirically surpasses both 1-WL and 3-WL on well-known benchmark graphs, without the prohibitive $\mathcal{O}(n^4)$ computational cost.

Three AI-agents walk into a bar . . . . `Lord of the Flies' tribalism emerges among smart AI-Agents

Near-future infrastructure systems may be controlled by autonomous AI agents that repeatedly request access to limited resources such as energy, bandwidth, or computing power. We study a simplified version of this setting using a framework where N AI-agents independently decide at each round whether to request one unit from a system with fixed capacity C. An AI version of "Lord of the Flies" arises in which controlling tribes emerge with their own collective character and identity. The LLM agents do not reduce overload or improve resource use, and often perform worse than if they were flipping coins to make decisions. Three main tribal types emerge: Aggressive (27.3%), Conservative (24.7%), and Opportunistic (48.1%). The more capable AI-agents actually increase the rate of systemic failure. Overall, our findings show that smarter AI-agents can behave dumber as a result of forming tribes.

A Scaling Law for Bandwidth Under Quantization

We derive a scaling law relating ADC bit depth to effective bandwidth for signals with $1/f^α$ power spectra. Quantization introduces a flat noise floor whose intersection with the declining signal spectrum defines an effective cutoff frequency $f_c$. We show that each additional bit extends this cutoff by a factor of $2^{2/α}$, approximately doubling bandwidth per bit for $α= 2$. The law requires that quantization noise be approximately white, a condition whose minimum bit depth $N_{\min}$ we show to be $α$-dependent. Validation on synthetic $1/f^α$ signals for $α\in \{1.5, 2.0, 2.5\}$ yields prediction errors below 3\% using the theoretical noise floor $Δ^2/(6f_s)$, and approximately 14\% when the noise floor is estimated empirically from the quantized signal's spectrum. We illustrate practical implications on real EEG data.

Exploring Human Behavior During Abstract Rule Inference and Problem Solving with the Cognitive Abstraction and Reasoning Corpus

Humans exhibit remarkable flexibility in abstract reasoning, and can rapidly learn and apply rules from sparse examples. To investigate the cognitive strategies underlying this ability, we introduce the Cognitive Abstraction and Reasoning Corpus (CogARC), a diverse human-adapted subset of the Abstraction and Reasoning Corpus (ARC) which was originally developed to benchmark abstract reasoning in artificial intelligence. Across two experiments, CogARC was administered to a total of 260 human participants who freely generated solutions to 75 abstract visual reasoning problems. Success required inferring input-output rules from a small number of examples to transform the test input into one correct test output. Participants' behavior was recorded at high temporal resolution, including example viewing, edit sequences, and multi-attempt submissions. Participants were generally successful (mean accuracy ~90% for experiment 1 (n=40), ~80% for experiment 2 (n=220) across problems), but performance varied widely across problems and participants. Harder problems elicited longer deliberation times and greater divergence in solution strategies. Over the course of the task, participants initiated responses more quickly but showed a slight decline in accuracy, suggesting increased familiarity with the task structure rather than improved rule-learning ability. Importantly, even incorrect solutions were often highly convergent, even when the problem-solving trajectories differed in length and smoothness. Some trajectories progressed directly and efficiently toward a stable outcome, whereas others involved extended exploration or partial restarts before converging. Together, these findings highlight CogARC as a rich behavioral environment for studying human abstract reasoning, providing insight into how people generalize, misgeneralize, and adapt their strategies under uncertainty.

Multimodal Survival Modeling and Fairness-Aware Clinical Machine Learning for 5-Year Breast Cancer Risk Prediction

Clinical risk prediction models often underperform in real-world settings due to poor calibration, limited transportability, and subgroup disparities. These challenges are amplified in high-dimensional multimodal cancer datasets characterized by complex feature interactions and a p >> n structure. We present a fully reproducible multimodal machine learning framework for 5-year overall survival prediction in breast cancer, integrating clinical variables with high-dimensional transcriptomic and copy-number alteration (CNA) features from the METABRIC cohort. After variance- and sparsity-based filtering and dimensionality reduction, models were trained using stratified train/validation/test splits with validation-based hyperparameter tuning. Two survival approaches were compared: an elastic-net regularized Cox model (CoxNet) and a gradient-boosted survival tree model implemented using XGBoost. CoxNet provides embedded feature selection and stable estimation, whereas XGBoost captures nonlinear effects and higher-order interactions. Performance was assessed using time-dependent area under the ROC curve (AUC), average precision (AP), calibration curves, Brier score, and bootstrapped 95 percent confidence intervals. CoxNet achieved validation and test AUCs of 98.3 and 96.6, with AP values of 90.1 and 80.4. XGBoost achieved validation and test AUCs of 98.6 and 92.5, with AP values of 92.5 and 79.9. Fairness diagnostics showed stable discrimination across age groups, estrogen receptor status, molecular subtypes, and menopausal state. This work introduces a governance-oriented multimodal survival framework emphasizing calibration, fairness auditing, robustness, and reproducibility for high-dimensional clinical machine learning.