arXiv:2609. 12259v1 Announce Type: new Abstract: Matrix-valued memories make rank the natural budget of a learned representation: the number of independent directions a state spans bounds what it can bind, compose, and track.
arXiv:2609.17594v1 Announce Type: new Abstract: Can gradient-based training learn the rank needed to store and compose associations in a matrix memory? In our earlier study, we used a matrix-augmente...
arXiv:2609.16183v1 Announce Type: new Abstract: Fixed-state recurrences--linear attention and state-space models--are reported to lag behind attention on associative recall, but whole-architecture co...
The paper proposes a new dimension‑reduction strategy for transfer‑operator models of dynamical systems that focuses on scoring the σ‑algebra generated by coordinates rather than the operator’s spectral span. By using a χ²‑divergence criterion between embedded present and future states, the method guarantees that twice the intrinsic system dimension suffices to capture the full operator spectrum, even for systems with weakly interacting components that would otherwise require exponentially many modes. Experiments on benchmark systems show that this algebraic approach recovers masked components missed by rank‑based methods and enables accurate prediction of those components from few labels.
arXiv:2605. 05189v2 Announce Type: replace-cross Abstract: How many key-value associations can a $d\times d$ linear memory store?
The paper investigates whether the rank of latent matrices in matrix‑chain‑of‑thought (Matrix‑CODI) models influences performance on reasoning tasks. Across multiple training regimes on ProsQA and GSM8K‑Aug, rank‑k projection ablations show flat accuracy curves, indicating that truncating the latent matrix to low rank does not hurt performance. Experiments with various readout architectures—bilinear, bilinear‑plus‑GELU, SVD‑augmented, and quadratic—confirm that rank‑indifference persists even for nonlinear readouts, and a linear probe on the latent matrix underperforms a raw pretrained hidden state.
arXiv:2607. 16524v1 Announce Type: new Abstract: Cooperative multi-agent RL systems routinely use team-averaged rewards, a feedback-attribution choice that gives each agent the team outcome regardless of its individual contribution.
arXiv:2606. 07596v1 Announce Type: new Abstract: Fine-tuning often introduces spurious correlations alongside task knowledge, causing systematic failures on underrepresented groups.
arXiv:2609. 16391v1 Announce Type: cross Abstract: Weight-only post-training quantization is the cheapest way to shrink a retrieval embedder, and the received advice for applying it -- protect the embedding table, allocate bits by module sensitivity, prefer a ranking-aware objective over weight reconstruction -- was carried into LLM quantization largely intact.
The paper investigates whether the rank of matrix-valued latent representations in continuous chain‑of‑thought models influences task accuracy. Experiments on ProsQA and GSM8K‑Aug show that truncating the latent matrix to low rank has negligible effect (within 0.6 pp), and this flatness persists across various readout designs and even in a vanilla GPT‑2 baseline. The results suggest that rank is not a useful structural signal for these models’ reasoning paths.
The paper addresses the limitations of spectral dimension reduction for dynamical systems composed of weakly interacting components, where standard rank‑based methods either require exponentially many modes or omit entire components (a phenomenon termed linear masking). It proposes scoring the σ‑algebra generated by coordinates instead of individual modes, using a χ²‑divergence criterion that guarantees an embedding with twice the intrinsic dimension captures the full operator spectrum. Experiments on benchmark systems show that this algebraic approach recovers masked components and enables accurate prediction from few labels, outperforming traditional rank‑based and VAMP methods.
How many directions does a neural representation use to encode a concept? A common answer repeatedly erases probe directions and reports the stopping count or cumulative removed rank.
arXiv:2608. 10566v1 Announce Type: cross Abstract: How many directions does a neural representation use to encode a concept?