#01Nov 12, 2026
cs.LG
Symmetry in Time: A Representation Theory of Linear Recurrent Memory
Anif N. Shikder, Ramit Dey, Jan Minac and 1 more
State space models (SSMs) are an emerging alternative to Transformers. SSMs offer linear-time inference and parallel training, but most implementations make the parallel scan efficient by making the recurrence diagonal: each channel of the hidden state is multiplied by an input-dependent real or complex number. These numbers commute, so the state records which inputs occurred but not their order. We formalize this with representation theory, which explains and fixes the state-tracking failures previously reported for SSMs. The state update defines a linear representation of the monoid of input sequences, and we show that an SSM tracks a group at every sequence length exactly when that group is a quotient of the group generated by its transition matrices. Two consequences follow. Diagonal real- and complex-valued SSMs can track only commutative groups, while the transition matrices of any SSM that can track a group must split into independent blocks over the real, complex, and quaternion numbers. We then introduce HyperSSM, which adds quaternion channels while keeping linear-time inference and parallel training. Trained only on final answers, HyperSSM solves the group tasks of recent state-tracking benchmarks exactly with at most five state numbers. This includes $S_5$ with 32 generators, where previous SSMs are at chance, and HyperSSM generalizes to sequences 25 times longer than those seen in training. Because the theory says what the transitions must encode, the learned weights of the linear recurrence can be interpreted directly. We demonstrate this by recovering the calibration of a real gyroscope, the rotations of imperfect qubit gates and the geometry of protein backbones.
#02Nov 12, 2026
cs.CL
Parsed, Plausible, Wrong: Output Format Controls Silent Errors in Small-Model Semantic Parsing
Umar Ahmed, Maxim Dunaev, Mohammad Nour Al Awad and 2 more
A small fine-tuned parser that emits a well-formed but wrong tree fails silently: nothing downstream can tell. We ask whether the output format, a free design choice, controls how often this happens. On the PIZZA ordering benchmark we fine-tune two sub-billion models (Qwen3.5-0.8B and LFM2.5-350M) with LoRA on six lossless encodings of the same target tree, from 44.3 down to 10.9 tokens per order, including two matched-length pairs that vary surface form at fixed length. Across 300 runs (5 training pool sizes, 5 seeds) with a hierarchical bootstrap and Holm correction fixed before the results were read, shortening alone never helps, but writing the target in ordinary words does. The word encoding is the most accurate format on both models (87.5% vs. 85.8% exact match for the native s-expression on Qwen) while emitting 4.1x fewer tokens, and it cuts the silent error rate by 2.3x on Qwen and 1.8x on LFM2, separating at every pool size. Error analysis locates much of the gain in negation. All runs also learn to refuse off-menu input (held out: 95.9-99.0% handled) and to apply in-utterance self-corrections. Strict refusal has a measured price: 2.1-10.1% of real, mostly polite, orders are refused.
#03Nov 12, 2026
cs.LG
ISLA: A Coordinate-Free, Measure-Weighted Transformer for Boundary-Driven PDEs
Peter Sharpe
A foundational principle of physics is that all coordinate systems are equally valid: the behavior of a PDE-governed system does not depend on the origin or orientation of the frame, nor on the units or mesh used to write it down, and neither should a surrogate model. Yet the neural surrogates with the lowest errors on today's aerodynamics benchmarks lack these invariances and fail under simple transformations of the same problem: for models trained on PDEs of cars in one pose (i.e., translation and rotation) and from one mesher, rotating the full PDE raises the surface-pressure error from 4% to more than 100%, and re-sampling its boundary raises it to about 30%. We introduce ISLA (Invariant Slice Attention), a slice-attention transformer for steady, boundary-driven PDEs in which no learned operation receives a coordinate and every sum over the boundary is a quadrature. Positions enter only as distances and relative angles to learned slice anchors, lengths are measured in a unit computed from the boundary, and interior points query the boundary through a tree-accelerated learned kernel without influencing one another. With every boundary cell a token and an exact boundary read, ISLA is equivariant to rigid motions and reflections, invariant to the units of its declared data, and consistent under mesh refinement, while at every setting each query is independent of all other queries. On AeroZoo, 2,816 flows that vary in shape, size, speed, and boundary conditions, its mean reference-scaled velocity and pressure errors are at least 3.1 and 3.3 times lower than any baseline's. On AirfRANS its errors are second only to those of a boundary-integral model (GLOBE) and at least 1.6 times lower than those of Transolver and GeoTransolver.
#04Nov 12, 2026
cs.AI
AgentSSL: Can MLE Agents Leverage Unlabeled Data?
Ethan Lin, Akanksha Sarkar, Ziang Liu and 2 more
Applying machine learning systems to new domains introduces bottlenecks in both labeled data acquisition and manual pipeline engineering. While recent MLE agents show promise in automating pipeline design, they have been studied almost exclusively in fully supervised settings, leaving them untested in realistic regimes where labeled data is scarce but unlabeled data is abundant. In this work, we introduce Agentic Semi-Supervised Learning (AgentSSL), framing SSL as a program search problem and studying how agents navigate this space under limited supervision. We find that even under weak feedback and matched compute, agents can synthesize code that combines and adapts established SSL techniques, exceeding the strongest human-engineered baselines in 8 of 12 settings by up to +21.8%. However, our results identify program selection as a critical bottleneck in AgentSSL, where performance drops by as much as 47% when selecting based on the agent's feedback metric. To systematically study this bottleneck, we introduce ProgramSelectBench, a large-scale benchmark with a combined total of 16,977 agent-generated and human-engineered SSL programs, and evaluate both unsupervised and active program selection methods. We further evaluate AgentSSL on real-world ecology detection tasks, highlighting the opportunities and challenges of transferring agent-discovered strategies beyond controlled benchmarks.
#05Nov 12, 2026
cs.LG
Maximizing Capacity Utilization of LoRA Adapters for Mitigating the Learning-Forgetting Trade-off
Tomohiro Sawada, Kartik Goyal
Low-Rank Adaptation (LoRA) often underperforms full fine-tuning, especially in heterogeneous and continual-learning settings in which substantial forgetting occurs. In general, it suffers from an undesirable learning-forgetting trade-off across diverse fine-tuning settings. We identify a potential contributor: LoRA adapters, especially high-rank ones, frequently fail to realize the available capacity afforded by the configured rank. Specifically, we find that standard LoRA updates have effective rank far below their configured rank, limiting how broadly the update energy is distributed. Therefore, we propose training mechanisms that optimize the original objective while maximizing adapter effective rank. Our main method adds a simple, stable, differentiable, and SVD-free Rényi-2 effective-rank regularizer to the language-modeling loss. We also connect capacity maximization to norm-bounded updates. In mixed-domain rank sweeps on three models evaluated with multiple random seeds, a penalty weight of $λ=0.01$ lowers mean Wiki perplexity at every tested rank of at least $16$ relative to unpenalized LoRA. Mean training perplexity improves or increases by at most $0.02$ in all but one model-rank comparison. Single-task and scheduling experiments further show that the balance between learning and retention depends on the configuration. We also observe that several LoRA variants in the literature also suffer from the identified capacity issue, and our approach provides a complementary axis of improvement to LoRA-based parameter-efficient fine-tuning. These results suggest that effective rank is not only a post-hoc diagnostic of adapter quality, but a trainable objective for improving the learning-forgetting frontier. Our code is available at https://github.com/tomohiro-sawada/lora-capacity-utilization