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Constitutional Midtraining: Content Presence Drives Alignment Gains
Post-training alignment is often shallow, eroding under fine-tuning. It remains untested as to whether constitutional midtraining interventions can produce durable alignment when cleanly isolated from post-training. We build a 394M-token constitutional corpus from Anthropic's Constitution and apply constitutional midtraining at 120B scale, where principled, values-based content is inserted into midtraining. A 2x2 design (curriculum ordering x deliberative reasoning) was used to produce four constitutionally midtrained conditions, plus a control, which were evaluated on self-generated and established benchmarks including alignment under pressure, value conflict resolution, blackmail, and emergent misalignment. All models were evaluated across three stages: post-midtraining, post-SFT, and post-benign fine-tuning. Constitutionally midtrained models outperformed the control on alignment generalization and durability, notably on blackmail: SFT instilled a blackmail propensity in all models, but constitutional midtraining blunted it, with the advantage surviving benign fine-tuning (-17.5pp). This durability did not extend to settings that required active resistance to in-context pressure or conflict, where the advantage attenuates after SFT. The presence of constitutional content at midtraining also mattered more than its structure, and constitutional midtraining incurred no capability cost, on average, at any stage (MMLU, ARC-Easy, piqa, GSM8K). A modest amount of constitutional content at midtraining could therefore yield broad, persistent alignment gains, offering a cheap, complementary addition to SFT-centered pipelines. Code, data, and models are available.
Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification
Nearest neighbor classification relies fundamentally on how locality is defined, yet conventional $k$-NN imposes the same neighborhood cardinality throughout the feature space. This assumption can be inadequate for data whose local geometry varies substantially across the underlying manifold. We introduce Curvature-Aware Radius Shrinkage for Adaptive Nearest Neighbor Classification (CARSANN), a geometry-driven framework that adapts the spatial support of each neighborhood according to local geometric complexity. CARSANN first estimates intrinsic dimensionality using TwoNN and constructs an intrinsic representation through principal component analysis. Local mean curvature is then estimated using a shape-operator-based formulation and controls neighborhood scale: highly curved regions receive stronger radius shrinkage, whereas approximately flat regions retain broader spatial support. Unlike methods that modify only the number of neighbors or the local metric, CARSANN explicitly adapts the spatial extent of local evidence. Experiments on more than 70 real-world OpenML datasets show that CARSANN consistently improves upon standard $k$-NN and is competitive with adaptive nearest-neighbor methods. In a controlled comparison using the same base neighborhood size, CARSANN achieves higher balanced accuracy on 40 of 45 datasets, increasing mean balanced accuracy from 0.6506 to 0.7528. The advantage also persists against $k$-NN with fixed $k=5$. Friedman and Nemenyi tests confirm that the improvements are statistically significant. These results indicate that local manifold curvature can serve as an effective geometric control variable for adapting neighborhood support, providing a complementary paradigm to cardinality-based nearest-neighbor adaptation.
Conformal Risk-Averse Decision Making with Optimized Certainty Equivalent Risk Control
We study risk-averse decision making, in which an agent selects actions while being uncertain about the true system state. The risk is measured via optimized certainty equivalent (OCE) metrics, which generalize popular criteria such as mean-variance risk and conditional value-at-risk (CVaR). We characterize the optimal policy under known distributions, and show that it reduces to a prediction set-based solution for the CVaR. This provides an operational interpretation of conformal prediction-type prediction sets. For unknown distributions, we develop a data-driven calibration strategy, based on a synthetic model for the likelihood and held-out calibration data, yielding high-probability control of the OCE risk. The approach is evaluated on two wireless beamforming settings.
Performative Privacy: When Differential Privacy Maximizes Utility
Privacy-preserving learning is often motivated by the idea that protecting users' data can preserve trust and thus participation, improving utility in the long term. However, this claim has not been formalized so far. In parallel, performative learning provides a framework for studying learning systems whose deployment affects the data they later observe. In this work, we bring these two perspectives together and introduce \emph{performative privacy}, where data leakage reduces future participation. We study a simple model where agents repeatedly contribute data for mean estimation but may leave the system when their data is leaked. Privacy is implemented through differentially private mechanisms, creating a trade-off between estimation noise and future participation. We show, through a theoretical study of the dynamics and numerical experiments, that a finite privacy budget can outperform non-private estimation in the long term when the feedback loop between leakage and participation is sufficiently strong. This provides first evidence that differential privacy can be optimal not only as a protection mechanism, but also from the perspective of long-term utility.