machine learning developers

Abstract: Identifiability of tensor decompositions is often established through linear-algebraic conditions on the factor families. For nonnegative decompositions, however, positivity provides additional information that is not captured by dimension and independence alone: nonnegative terms cannot cancel, and their supports constrain competing decompositions. We introduce a positive scattering term that quantifies this additional source of identifiability and combine it with the dimension budget underlying the Lovitz--Petrov generalization of Kruskal's theorem. For every subset of components, we obtain two sufficient conditions: a threshold of $2|S|-2$ guarantees minimality and nonnegative rank, while the stronger threshold $2|S|-1$ guarantees uniqueness among nonnegative decompositions of the same length. The key result is a positive splitting inequality for irreducible exchanges of nonnegative rank-one tensors, which combines the dimension constraint with support-induced geometric rigidity. Although the scattering term is defined through an optimization over intermediate factor spaces, we show that its mode costs are exactly $0$, $1$, or $+\infty$, yielding an exact activation characterization in terms of graph connectivity. The resulting criterion can strictly certify sparse nonnegative tensor decompositions beyond the reach of Kruskal and Lovitz--Petrov conditions, including examples for which those conditions fail even after reshaping. In the matrix case, the two criteria reduce respectively to full-rank factorization and two-sided separability.

Abstract: Hard symmetry constraints reduce model complexity, but can also erase label information. Statistical symmetry release determines when finite data and quantum measurements justify relaxing such a constraint, which directions to open, and how far to move. We connect global signal detection to local, loss-dependent improvement. A two-copy twirl--swap gate estimates task information in the symmetry-breaking complement with a dimension-independent copy count under paired-state and group-unitary access; reweighting the same records resolves representation sectors. An exact duality distinguishes this Hilbert--Schmidt signal from the larger signal accessible to bounded-outcome readouts. Local improvement is governed by the release gradient and a loss-corrected double-commutator matrix. Simultaneous confidence bounds convert empirical direction selection into certified descent, using either shared Pauli measurements or scalar probes with state-independent truncation bounds. Gaussian testing lower bounds quantify the cost of searching over unknown directions in the calibrated local experiment. Independent validation controls adaptively generated models, and a fast squared-loss bound preserves the approximation--estimation rate of a nested release path. On an eight-qubit Ising model, shared measurements certify release with 6300 times fewer shots than the specified scalar estimator on the tested budget grids. Quotient quantum natural gradient then controls parameter redundancy during training. Together, these results turn symmetry relaxation into a statistically justified model-selection decision.

Abstract: A wrong answer does not show whether the model lacked the needed information or held it and failed to use it. On an entity-obligation binding task, a language model can emit an incorrect prompt-supplied binding while a linear probe can recover the correct one from its frozen hidden state. We measure how often this occurs across 16 public checkpoints, each evaluated with three seeds. We fit a probe on a training fold, select its layer on a validation fold, and report results on a disjoint test fold. On the trials each model gets wrong, probe accuracy exceeds the strict present-obligation baseline, 1/K = 0.125, by +0.196 (95% CI [+0.101, +0.296], bootstrapped over models). A query-entity counterfactual rules out token presence and recency. A score built from the sign of probe-output disagreement improves failure detection over the model's own confidence by +0.079 AUROC (95% CI [+0.036, +0.126]). Raw probe confidence gives no measurable improvement over model confidence. Steering the residual stream toward the probe-decoded binding, with no gold label, raises accuracy on all eight models tested by a mean of +0.168 (95% CI [+0.066, +0.280]). Where recent studies report that probe-detected errors are resistant to interventions, we find that in-context binding is a setting in which probes are actionable.

Abstract: Motivated by data produced by generative systems, \cite{LZ26b} formulates similarity-aware statistics via a weighted similarity graph, replacing equality with similarity in classical frequency-based statistics. Although this framework captures semantic relationships between nonidentical items, under general similarity functions even coarse one-pass approximation can require linear space. We therefore ask whether the geometric structure present in natural vector similarities can overcome this barrier. We answer this question affirmatively for the Gaussian kernel. For fixed-dimensional Euclidean vector streams, we study similarity-aware analogues of classical frequency statistics, including the number of distinct elements and frequency moments, through the diversity index and Gaussian density moments. We give one-pass sublinear-space approximation algorithms that exploit the geometric and analytic properties of the Gaussian kernel, and complement them with lower bounds. Our results show that geometric structure can fundamentally change the streaming complexity of similarity-aware statistical analysis.

Abstract: Simulatability is an evaluation protocol for explanations that quantifies their usefulness by how well they help a user predict a task model's outputs. Since human evaluation is costly, automated simulatability replaces human explainees with LLM simulators, as proposed in ConSim (Poché et al., 2025) for large-scale experiments. We qualitatively replicate and extend ConSim's ranking of explanation methods across the tested datasets, explanation families, and simulator LLMs, and identify two limitations. First, when class names are meaningful, simulators can obtain high simulatability by solving the classification task directly, without relying on the explanations. Second, class anonymization can reward explanations for leaking the hidden label mapping, a limitation we expose with a new classes-as-concepts baseline. These results are consistent with a shortcut hypothesis: in the tested settings, simulator predictions mainly rely on task priors, while explanations produce small changes. We derive recommendations for more robust automated simulatability evaluations.

Abstract: Robotic manipulation often requires acting on information that is no longer visible, yet Vision-Language-Action policies are usually evaluated when the current observation largely determines the next action. Existing robotic memory benchmarks expose this gap, but they still rely mainly on final task success and therefore conflate forgetting with manipulation failure. We present \textbf{MEMOBench}, a benchmark for process level memory evaluation in robotic manipulation. MEMOBench includes 30 history dependent tasks, 1{,}500 expert demonstrations, and 4{,}200 executable checkpoint instances from 84 templates. Each checkpoint pairs coarse to fine language with a simulator predicate and labels one memory operation: Storage, Update, or Compression. These annotations define Memory Storage Rate, Memory Update Rate, and Memory Compression Rate, which measure memory fidelity alongside task success. Across standard and memory augmented VLA policies, the strongest memory module baseline reaches only 31.9\% average success rate, and high storage often coexists with weak update and compression. Checkpoint language also supervises semantic, contrastive, and framewise memory alignment objectives, yielding modest gains across different memory operations. MEMOBench provides a diagnostic evaluation suite and training supervision for memory grounded robotic policies. The project page is available at https://github.com/Collab-Gen/MEMOBench.