#01Nov 5, 2026
cs.LG
When Scores Conflict with Preferences: Pre-Alignment Diagnosis and Adaptive Correction of Constraint Drift in DPO
Ping Liu, Yan Yan
Direct Preference Optimization (DPO) is increasingly used in settings where pairwise preferences coexist with pointwise criteria such as response length, answer correctness, or safety scores. When the two disagree, standard DPO treats pairs whose preferred output scores worse on the pointwise criterion (conflict pairs) in the same way as the remaining (matching) pairs. We characterize a systematic failure mode, constraint drift: for sufficiently small updates, conflict pairs tend to increase constraint cost while matching pairs tend to repair it, and the net change depends on their balance. This balance yields a closed-form pre-alignment diagnostic, $ρ^{*}_{\mathrm{eq}}$, computable from dataset statistics, that indicates whether a dataset is self-correcting or requires intervention. Building on this diagnostic, we propose Conflict-aware DPO (CoDPO), which down-weights conflict pairs with a strength set from $ρ^{*}_{\mathrm{eq}}$ rather than tuned, and adds an adaptive margin shift that addresses residual drift during training. Empirically, drift grows monotonically with conflict exposure on the conflict-dominated domains, and the intervention decision given by $ρ^{*}_{\mathrm{eq}}$ matches the observed drift on every domain, including one that it identifies as self-correcting. On all four domains of the main comparison, CoDPO reduces drift while largely preserving the preference learning of vanilla DPO. Compared with hard filtering and recent constrained and multi-objective baselines, CoDPO also achieves a more favorable drift-preference trade-off.
#02Nov 5, 2026
cs.LO
Typed Knowledge over Constructive Institutions
Hans-Martin Will
Type theories designed for mathematics or program verification need only that a proposition holds; proof irrelevance in conversion erases, at the kernel level, how a claim was established. A persistent knowledge store, by contrast, must retain that record: who established a claim, by which derivation or external tool, and under which assumptions. This volume presents the theory of Eigenius---a store of typed knowledge over constructive institutions---and develops its metatheory from that requirement. The kernel theory is a dependent type theory with cumulative universes, an impredicative universe of propositions, inductive families, and an intensional identity type. Proof irrelevance is an axiom with an explicit witness rather than a conversion rule, so proofs of a proposition are provably equal yet remain distinct terms. Definitional equality is joinability under an orthogonal rewriting system---confluent, injective on type formers, and decidable by a type-free test---while a separate subsumption judgment covers universe cumulativity, codomain-covariant function types, and declared class inclusions. We prove consistency via a set-theoretic model; develop a justification logic over the kernel's propositions to track evidence and support; organize environments as an institution so that store extensions are signature morphisms and external verdicts enter via comorphisms; formulate a typed knowledge-graph theory with records, classes, and refinements; and prove the correctness of conversion, normalization by evaluation, and bidirectional type checking relative to termination. A Lean 4 formalization accompanies the volume.
#03Nov 5, 2026
cs.LG
Spectral symmetry fingerprints in equivariant representations
Jiacheng Cen, Anyi Li, Ning Lin and 3 more
Symmetry governs the organization of physical structures, while symmetry breaking reveals their transformations. In geometric deep learning, symmetry imposes rank constraints on equivariant representations, limiting the expressive capacity of equivariant graph neural networks (GNNs). Here we show that these constraints can instead be exploited: the singular-value spectra of equivariant representations provide a unified fingerprint of structural symmetry. We introduce spectral symmetry fingerprints (SymFP), which enable discrete point-group identification through rank-template matching and continuous symmetry analysis by quantifying spectral energy beyond target rank constraints. SymFP is orientation invariant and architecture agnostic, enabling a parameter-free GNN implementation. Its spectra can be reused across multiple target groups, and the resulting leakage scores satisfy subgroup monotonicity. Across synthetic structures, molecules, coordination complexes and large biological assemblies, SymFP accurately identifies point groups, tracks controlled symmetry breaking and reveals local and degree-resolved symmetry changes that can be obscured by global geometric measures. These results establish the spectral structure of equivariant representations as a general framework for characterizing symmetry across physical systems.
#04Nov 5, 2026
cs.LG
Two-stage residual learning for calibrated uncertainty in solar irradiance forecasts
RR Flanagan, E Kasha, PW Talbot and 2 more
Accurate forecasting of renewable generation requires not only point predictions but also reliable estimates of the uncertainty attached to them, particularly at extended horizons. Machine learning models are increasingly used to predict solar output, but they typically report a single value and capture the associated uncertainty poorly. The standard remedy is to train a model to predict the parameters of an assumed probability distribution directly. Here we develop an alternative two-stage method, motivated by synthetic solar signal generation, in which the forecast error is modeled separately from the expected irradiance. A first long short-term memory (LSTM) network predicts the expected global horizontal irradiance, and a second network models the distribution of the forecast error, which is added back to the mean to give both the forecast and its uncertainty. Using historical weather data from the National Solar Radiation Database and a probability integral transform evaluation, we show that explicitly modeling the error brings the predicted standard deviation markedly closer to the historical value, reducing the deviation between the two by 34.6 percent for a standalone LSTM and by 56.5 percent when the LSTM is coupled to Gaussian process regression, the most reliable of the configurations tested. Because the method models the total forecast error directly, it captures the full predictive uncertainty that matters for decisions, rather than only the model contribution that dropout-based approaches estimate.
#05Nov 5, 2026
cs.LG
Permanent and Transient Representations for Continual Reinforcement Learning
Nishanth Anand, Doina Precup
Continual Reinforcement Learning (CRL) agents struggle to adapt to new situations while retaining prior knowledge, leading to a stability-plasticity trade-off. One approach to solving this problem is by using complementary learning systems: one for slow, long-term learning and another for quick, transient adaptation. Anand & Precup (2023) instantiated this idea using permanent and transient value functions, but used the same features in both systems. Intuitively, long-term learning should rely more on parametric representations for broad generalization, while transient learning would be best served by non-parametric representations for situation-specific adaptation. In this paper, we explore this idea both theoretically and empirically. By introducing a novel non-parametric approximation for estimating the transient value function in complex tasks, we demonstrate that our method enables online learning and outperforms competitive baselines on image-based tasks and Craftax-Classic, underscoring the effectiveness of our system-level decomposition.