Martin Takáč

Soham Bhattacharjee, Dushyant Singh Chauhan, Salem Lahlou et al.

Inference-time scaling has become the dominant lever for improving language-model reasoning, but existing methods derive rollout diversity from a single source: stochastic token-level sampling. We argue that this single-axis sampling space is fundamentally limiting, and identify a second, fully deterministic and complementary axis: the layer span $L$ at which a frozen model's top decoder layers are recursively re-applied at high-uncertainty tokens. Different choices of $L$ produce distinct rollouts that solve different subsets of problems, with no stochasticity. We instantiate this axis through Entropy-Gated Latent Recursion (EGLR), a training-free decoding procedure that re-applies the top-$L$ layers for at most $K_{\max}$ iterations until the next-token distribution converges. Combined with $T$ temperature samples, EGLR turns a single-axis stochastic rollout pool into an $L\times T$ Cartesian sampling space at almost the same per-rollout cost. We characterize this space across $8$ instruction-tuned models and $6$ math reasoning benchmarks, and show that the $L$-axis is genuinely complementary to temperature: on MATH-500 with Qwen2.5-3B-Instruct, the joint $L\times T$ oracle reaches $91.6\%$, $+8.2$ percentage points beyond the temperature-only oracle ($83.4\%$) and $+10.4$ points beyond the layer-only oracle ($81.2\%$), confirming that the two axes capture genuinely complementary problems. The expanded rollout pool provides richer per-prompt candidates for any downstream procedure that consumes rollouts, including self-consistency, best-of-$N$ with verifiers, and group-relative RL training (GRPO), opening a new direction for inference-time scaling that does not rely on stochastic noise.

Dmitry Pasechnyuk-Vilensky, Martin Takáč

We study finite-horizon one-gradient realizations with the Chebyshev minimax terminal residual on $[μ,L]$. Under time-dependent Hessian perturbations, the terminal first variation is governed by a time-ordered spectral kernel $K_s(λ,ν)$; its sharp $\ell_2$ gain is $A_N$. For the prefix-exact Chebyshev recurrence, $$ A_N^{\rm pref} =\frac{ε_N^\star}{L-μ} \left(4N^2+16\sum_{m=1}^{N-1}m^2\right)^{1/2} =\frac4{\sqrt3}\frac{N^{3/2}}{L-μ}ε_N^\star(1+o(1)), $$ and this is sharp in the causal two-term class with Chebyshev exactness at every prefix. For terminal-only exactness, Jacobi coordinates give $P_N=2^{1-N}T_N$: the spectrum is fixed at the midpoint Chebyshev nodes, while the spectral weights parametrize the realizations. The sine weights give a final-exact Jacobi method with the same terminal residual and $$ A_N(J_N^{\sin}) =2\sqrt{c_{\sin}}\frac{N^{3/2}}{L-μ}ε_N^\star(1+o(1)), \; 2\sqrt{c_{\sin}}\approx2.137936<4/\sqrt3. $$ Thus the Chebyshev terminal polynomial does not determine the first-order Hessian-drift gain. The experiments show the finite-horizon effect: lower stochastic curvature overhead, larger admissible-block frontiers, accurate time-varying quadratic predictions, and lower restart cost on an endpoint-coupled smooth strongly convex GLM.

Alexander Yukhimchuk, Andrey Shulga, Mladen Kolar et al.

Running large language models locally is often impractical, pushing inference on sensitive text to third-party providers. Split inference partially mitigates this by keeping tokens on the client and sending only hidden representations, but these representations can still be recovered via nearest-neighbor search against the public embedding table. We propose an orthogonal obfuscation procedure in which the client multiplies embeddings by a secret orthogonal matrix before transmission. To enable correct inference under arbitrary rotations, we introduce ConjFormer, a transformer variant that is exactly $\mathrm{O}(d)$-equivariant via a lightweight normalization change (scalar RMSNorm) together with blockwise orthogonal conjugation of all linear weights. As a result, the server performs the full forward pass entirely in the rotated basis and never observes unrotated hidden states. Experiments on GPT-2 and Llama 3.2 1B models fine-tuned on PubMed show that orthogonal obfuscation eliminates direct cosine nearest-neighbor inversion and reduces token recovery from over 35% top-10 to at most 1.3%, while increasing perplexity by only 0.4% after fine-tuning. These results indicate that enforcing symmetry at the architectural level can provide a practical defense for privacy-preserving LLM inference without noise injection or heavy cryptographic machinery.