#01Oct 23, 2026
cs.CL
Measure Before You Train: Typed Decision Models vs. a Classical Baseline vs. a Generative LLM for Routing a Personal Multilingual Inbox
Federico Lucca
Personal email agents decide, for every message, what it is, whether it is urgent, whether to draft a reply, create a task, or ignore it. Their error rate is rarely measured: the stored labels were written by the system itself. We present Foyer, a self-hosted personal inbox agent in daily use, and a measurement protocol (stratified sampling, frozen snapshots, thread-grouped splits, pre-registered hypotheses, human labels in the agent's review loop) that yields ground truth before any training. On 739 real Italian/English emails labelled by the owner (231 unbiased, 500 adversarially sampled), we compare nine systems under thread-grouped cross-validation: the production keyword rules, a TF-IDF + logistic-regression baseline, local typed decision models (Tev1, Nimble), a hosted decision model (Nimble v4-max), and hosted generative LLMs (Qwen2.5-7B, Gemma 4 26B/31B). Four results. The production rules score 28% on message type against a 58% majority class: the field shown most prominently carried no information. With ~200 labels, logistic regression has the highest accuracy on every field (type 0.79, urgency 0.74, needs-reply 0.83, is-noise 0.90), though it never predicts the two rarest classes and is statistically tied with Gemma 4 on type; few-shot prompting does not close the gap. The sender's relationship (client, supplier, service) is recovered from other emails of the same contact with 98.6% accuracy where the contact has been seen, and is not inferable from a single message by any model: it belongs in the contact graph, not the prompt. Finally, accuracy is not the product metric: composed into actions, the most accurate system most often ignores emails needing action (18% vs 4% for the best LLM); a cost-chosen threshold on its noise probability halves that rate and makes it the cheapest system.
#02Oct 23, 2026
cs.AI
SemantEq: Faithful Bidirectional Equivalence of Formal Statements
Xinrui Li, Pawan Sasanka Ammanamanchi, Siddharth Bhat and 3 more
Statement autoformalization translates mathematics from natural language into a proof assistant such as Lean 4, and models now do it at scale. As provers get stronger, the burden of correctness shifts from the proof to the statement, that is, to whether the formal statement faithfully translates its source. Given a trusted reference formalization, the natural test is logical equivalence, and it proves too much. $P \leftrightarrow Q$ holds trivially for any two statements $P$ and $Q$ that the library proves, because a prover can prove each separately and pass through $P \leftrightarrow \mathrm{True} \leftrightarrow Q$. The stronger the prover, the more unrelated pairs pass. Earlier methods restrict the prover and check that each proof names the other statement. We introduce SemantEq, a more principled relation that instead requires each statement to turn into the other only through a chain of allowed steps, such as logical rearrangement and rewriting with the library's own equations. Our programs judge a proof by the proof term Lean checks, not by its tactic script. SemantEq-Eval, a search without a model, reaches 100% precision and 65.6% recall on the ProofNetVerif test split under our adjudicated labels, against 95.8% and 61.8% for BEq+, and an 8.9-fold increase in its CPU time adds at most three pairs. A language model finds more proofs, but under two of four prompts it proves both directions of about two in five of the non-equivalent pairs. SemantEq-ProofAudit audits each model-written proof under a policy derived from the relation and accepts none of the 104 non-equivalent pairs, and it raises recall on 407 equivalent pairs from 65.4% to 81.1% under the best prompt. Separating the generation of equivalence proofs from their acceptance lets a stronger prover raise recall without changing what an acceptance means. We release code and data at: https://github.com/hlxr89/SemantEq
#03Oct 23, 2026
cs.CV
Flownomaly: Single-Step Conditional-Mean Recovery for Few-Shot Anomaly Detection
Bernardo Perrone Ribeiro, Erkut Akdag, Egor Bondarev
Few-shot industrial anomaly detection requires modeling category-specific normality from only a handful of defect-free images. Common approaches tie inference to stored exemplars, impose rigid linear structure, or risk reproducing anomalous content. Flownomaly instead casts the problem as normal-counterpart recovery in frozen DINOv2 feature space. Given normal supports, a velocity field is learned through conditional flow matching over frozen patch tokens to transport Gaussian noise toward normal features. Along straight paths, a single recovery step using one evaluation of the optimal field yields the posterior mean of the clean normal token without trajectory integration. The operating time governs how strongly recovery modifies a query token. With no anomalous validation samples available for tuning, a normal-only Jacobian gain-to-noise criterion selects this time from the supports alone. Squared residuals between query tokens and their recovered counterparts yield anomaly signals for both dense localization and image-level detection. Across 1-, 2-, and 4-shot benchmarks on MVTec-AD and VisA, together with sample-shot evaluations on Real-IAD, Flownomaly achieves state-of-the-art performance against recent category-specific methods. In the 1-shot setting, image- and pixel-level AUROC reach 97.8% and 98.0% on MVTec-AD and 95.3% and 98.7% on VisA, with a 2.1-point image-level AUROC improvement over the strongest baseline on VisA. Code is available at https://github.com/b-rbmp/Flownomaly.
#04Oct 23, 2026
stat.ML
Singular Geometry of Low-Rank Adaptation
Kamillo Ferry, Anthea Monod, Keisuke Yano
Low-rank adaptation (LoRA) is now a standard approach to parameter-efficient fine-tuning of large neural networks. Its low-rank factorization is inherently non-identifiable, making LoRA a singular statistical model whose learning complexity cannot be described by parameter dimension alone. We study this complexity using the real log canonical threshold (RLCT) from singular learning theory and how it depends on both the low-rank parameterization and the pretrained network. Under a local linearization, LoRA induces a low-rank trace regression model whose Kullback--Leibler geometry is controlled by a forward-backward covariance, constructed from activations and backpropagated sensitivities at the adapted layer. This covariance determines which low-rank perturbations are statistically observable. When it is nondegenerate along the relevant low-rank directions, we recover the classical learning complexity of reduced-rank regression; when its kernel meets these directions, additional statistically indistinguishable parameters change the singular geometry. We characterize this geometry locally through observable tangent directions and a residual singularity, and globally through affine linear sections of determinantal varieties. The global learning complexity need not be determined at a ground-truth parameter, as singularities on another rank stratum can dominate. We also introduce a curvature-corrected multi-temperature estimator of the RLCT. Experiments on multilayer perceptron and transformer architectures reveal strongly layer-dependent forward-backward geometry and show that ambient covariance degeneracy does not imply degeneracy along the low-rank directions relevant to adaptation.
#05Oct 23, 2026
cs.DS
Learning Positive Linear Combinations of ReLUs in Fully Polynomial Time
Ilias Diakonikolas, Jelena Diakonikolas, Puqian Wang and 1 more
We study the fundamental problem of PAC learning positive linear combinations of $k$ arbitrary ReLU activations on $\mathbb{R}^d$ with respect to the Gaussian distribution, in $L_2$ loss. We give the first fully-polynomial time algorithm for this learning task. Specifically, our algorithm draws $\mathrm{poly}(d, k, 1/ε)$ samples, runs in $\mathrm{poly}(d, k, 1/ε)$ time, and outputs a hypothesis that is $ε$-close to the target concept with high probability. All prior algorithms for this problem require super-polynomial time in $k$ or $1/ε$, or leverage strong well-conditioned assumptions on the weight matrix. On a technical level, our approach develops a novel boosting procedure of a ``weak'' learner that recovers the hidden weight vectors to constant error, in a list-decodable manner. To develop this ``weak'' learning procedure, we leverage implicit tensor computation techniques to construct a low-degree filtering procedure based on Hermite tensors of the target function. This procedure amplifies separation among (clusters of) weight vectors to learn each of them to constant error. We then argue that the same procedure can be used for improving the estimation of hidden weight vectors, using gradient descent-like updates on the Euclidean sphere. A crucial ingredient of our algorithm is a pruning approach that ensures only relevant vectors that approximate the hidden weight vectors at target accuracy are maintained by the algorithm.