Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2508.07395

Parity Requires Unified Input Dependence and Negative Eigenvalues in SSMs

Behnoush Khavari·Mehran Shakerinava·Jayesh Khullar·Jerry Huang·François Rivest·Siamak Ravanbakhsh·Sarath Chandar
View original source ↗Read source document ↗Export metadata ↓

Abstract

Recent work has shown that LRNN models such as S4D, Mamba, and DeltaNet lack state-tracking capability due to either time-invariant transition matrices or restricted eigenvalue ranges. To address this, input-dependent transition matrices, particularly those that are complex or non-triangular, have been proposed to enhance SSM performance on such tasks. While existing theorems demonstrate that both input-independent and non-negative SSMs are incapable of solving simple state-tracking tasks, such as parity, regardless of depth, they do not explore whether combining these two types in a multilayer SSM could help. We investigate this question for efficient SSMs with diagonal transition matrices and show that such combinations still fail to solve parity. This implies that a recurrence layer must both be input-dependent and include negative eigenvalues. Our experiments support this conclusion by analyzing an SSM model that combines S4D and Mamba layers.

Explore related subjects

cs.LG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Behnoush Khavari, Mehran Shakerinava, Jayesh Khullar, Jerry Huang, François Rivest, Siamak Ravanbakhsh, Sarath Chandar. 2025-08-10. Parity Requires Unified Input Dependence and Negative Eigenvalues in SSMs. https://arxiv.org/abs/2508.07395

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

AUC Maximization from Biased Positive-unlabeled Data with Confidence

Maximizing the area under the receiver operating characteristic curve (AUC) is a standard approach to imbalanced binary classification. Although positive and negative data are required for maximizing the AUC, negative data are often difficult to collect in some real-world applications due to privacy concerns or the need for specialized expertise to annotate them. Thus, AUC maximization from positive and unlabeled (PU) data has been attracting attention. Existing methods assume that labeled positive data are unbiased samples from the true positive distribution. However, this ideal assumption is often violated in practice. In this paper, we propose a method to maximize the AUC from biased PU data. To address the bias, our key idea is to exploit {\it confidence}, i.e., the probability that an instance is positive, associated with the small number of labeled positive data. We derive an estimator of the AUC risk using biased PU data with confidence, enabling AUC maximization under such bias. We further show that the rewritten AUC risk induces a Bayes-optimal AUC ranking even when the available confidence is any strictly increasing transformation of the true posterior probability. We experimentally show the effectiveness of our method on eight real-world datasets.

cs.LG↗
arXiv2026

Measuring the Value of World-Model Updates: A Counterfactual Utility Protocol for Continual Adaptation

Continual world models must decide whether new data justify changing the model. Fixed replay schedules and prediction-error triggers specify when to update, but neither reveals the value of an individual update: one deployment run cannot show how the same model would have performed at that moment had it held its parameters. We introduce the fork ledger, which branches a deployment stream at pre-registered decision points into matched update and hold continuations under common random numbers. It evaluates both continuations on the same episodes and records $\Delta R = R_{\mathrm{update}} - R_{\mathrm{hold}}$. Always applying one fixed update mechanism lowers return on all three simulated control tasks: CartPole ($-144.0$; checkpoint-bootstrap $95\%$ CI $[-185.4,-116.1]$, against a converged return near $650$), Walker ($-82.8$; $[-101.1,-61.7]$) and Cheetah ($-18.6$; $[-29.0,-6.6]$). Divergence is an outcome of applying the update, so the estimand counts every attempted fork; restricted to the $693$ of $720$ that did not collapse, CartPole and Walker are unchanged in sign ($-113.4$ and $-82.1$) and Cheetah becomes unresolved ($-3.9$; $[-17.5,+13.0]$). The task is the unit of inference: each contributes $240$ attempted forks over five pretrained checkpoints crossed with two drift directions. The ledger makes counterfactual utility observable for a fixed mechanism, allowing triggers to be judged by the updates they select rather than by surprise detection alone.

cs.LG↗
arXiv2026

When More Is Not Better: Component Anti-Synergy in a P300 Speller

P300 brain-computer interface (BCI) spellers can provide hands-free communication for people with severe motor impairments. Modern pipelines combine multiple individually promising components, often assuming that 'more-is-better'. We tested this assumption using a four-component full-factorial experiment varying the inclusion of Euclidean Alignment (EA), xDAWN spatial filtering, subject calibration, and language model priors on a public P300 dataset. Performance was evaluated using accuracy, repetitions, and information transfer rate (ITR) with mixed-effects models. Results show that the value of components is conditional rather than additive. Calibration was the strongest singular contributor, while EA compensated for its absence in zero-calibration settings. Adding independently useful components could also reduce performance, revealing component anti-synergy. Contrary to conventional wisdom, LM support was not universally beneficial: its effect depends strongly on the strength of the underlying EEG pipeline, while results from a larger LM showed a similar pattern. Together, these findings challenge maximal 'all-on' pipeline design and highlight the value of selecting spatial and language-support components according to the quality of available EEG evidence.

cs.LG↗