Elies Seguí-Mas

Hector Borobia, Elies Seguí-Mas, Guillermina Tormo-Carbó

Two recent approaches to computation in superposition reach different recursive capacity regimes: Hänni et al. certify $\tilde{O}(d^{3/2})$ computable features in width $d$ via an approximate-linear recursive template, while Adler and Shavit reach near-quadratic capacity (up to logarithmic factors) using thresholded Boolean recovery. The main contribution of this paper is conceptual: we argue these results are not contradictory because they maintain different interface invariants, and we formalize the distinction. As a tool, we record a rank-trace Welch-type lower bound for biorthogonal linear readouts: for $F \gg d$, the worst-case off-diagonal cross-talk of any unit-diagonal linear readout is $Ω(d^{-1/2})$, and the bound is tight on average for unit-norm tight frames. At quadratic feature load $F=d^2$, random-support threshold recovery succeeds for sparsities $s=O(d/\log d)$, while linear readouts still incur $Ω(s/d)$ average per-coordinate squared error on Bernoulli sparse states. Matching the Welch floor against the published tolerance of the Hänni correction layer explains the $d^{3/2}$ scale as a compatibility threshold for that template, not a universal upper bound. Robust nonlinear reset beyond the Hänni template is left open.

Hector Borobia, Elies Seguí-Mas, Guillermina Tormo-Carbó

Speculative decoding accelerates autoregressive inference by drafting candidate tokens with a fast model and verifying them in parallel with the target. Self-speculative methods avoid the need for an external drafter but have been studied exclusively in homogeneous Transformer architectures. We introduce component-aware self-speculative decoding, the first method to exploit the internal architectural heterogeneity of hybrid language models, isolating the SSM/linear-attention subgraph as a zero-cost internal draft. We evaluate this on two architecturally distinct hybrid families: Falcon-H1 (parallel: Mamba-2 + attention per layer) and Qwen3.5 (sequential: interleaved linear and attention layers), with a pure Transformer control (Qwen2.5). Parallel hybrids achieve acceptance rates of alpha = 0.68 at draft length k=2 under greedy decoding, while sequential hybrids yield only alpha = 0.038 -- an 18x gap attributable to how each architecture integrates its components. The property is scale-invariant: Falcon-H1 at 3B reproduces the rates observed at 0.5B. We further show that perplexity degradation from a companion ablation study predicts speculative viability without running speculative decoding: a 3.15x ratio (Falcon) maps to alpha = 0.37 at k=4, while 81.96x (Qwen) maps to alpha = 0.019. For sequential hybrids, generic LayerSkip achieves 12x higher acceptance rates than the component-aware strategy. The composition pattern of hybrid models -- not merely the presence of alternative components -- determines whether component-level self-speculation is viable.

Hector Borobia, Elies Seguí-Mas, Guillermina Tormo-Carbó

Hybrid language models that interleave attention with recurrent components are increasingly competitive with pure Transformers, yet standard LoRA practice applies adapters uniformly without considering the distinct functional roles of each component type. We systematically study component-type LoRA placement across two hybrid architectures -- Qwen3.5-0.8B (sequential, GatedDeltaNet + softmax attention) and Falcon-H1-0.5B (parallel, Mamba-2 SSM + attention) -- fine-tuned on three domains and evaluated on five benchmarks. We find that the attention pathway -- despite being the minority component -- consistently outperforms full-model adaptation with 5-10x fewer trainable parameters. Crucially, adapting the recurrent backbone is destructive in sequential hybrids (-14.8 pp on GSM8K) but constructive in parallel ones (+8.6 pp). We further document a transfer asymmetry: parallel hybrids exhibit positive cross-task transfer while sequential hybrids suffer catastrophic forgetting. These results establish that hybrid topology fundamentally determines adaptation response, and that component-aware LoRA placement is a necessary design dimension for hybrid architectures.