When researchers compare multilingual models for probing, interpretability, or cross-lingual transfer, they often align embedding spaces and assume that shared-language representations are comparable. We show that this assumption can be premature for decoder-only models. We pretrain paired 310M-parameter models (one English-only, one bilingual) across eight typologically diverse languages, separately controlling for English exposure, total compute, and document overlap. After aligning on shared English vocabulary, we test held-out words and find that token embeddings look similar after alignment, but the deeper hidden states that the model uses for prediction do not. This gap holds for all eight languages and survives controls for document overlap and alternative alignment methods. This hidden-state mismatch grows through middle transformer layers, suggesting that it arises from contextual processing rather than the input representations where alignment is performed. Embedding alignment can mask real differences in how models internally represent a shared language, which matters for any downstream study that treats aligned models as interchangeable.
Multilingual large language models often produce inconsistent reasoning and answers for semantically equivalent prompts in different languages. Prior work suggests that intermediate representations can be relatively language-agnostic, but generation becomes increasingly language-specific as models commit to discrete output tokens. This is problematic because language-specific lexical choices can cause semantically equivalent reasoning paths to diverge across languages. These divergences motivate searching for a cross-lingual alignment signal that is less tied to any single vocabulary item or script. We propose SOLAR, an auxiliary objective for supervised fine-tuning that aligns soft-token representations across languages, using English as a pivot. Soft tokens are probability-weighted mixtures over the vocabulary embeddings, yielding continuous representations that can aggregate information from semantically related tokens across languages. We then align each non-English soft-token summary to its English counterpart in the shared embedding space. Across four multilingual reasoning benchmarks, SOLAR improves accuracy by up to +17.7 points over the base model and +3.8 over standard supervised fine-tuning, with the largest gains on low-resource languages. SOLAR also strengthens final-layer cross-lingual similarity and substantially reduces language-cluster separability, suggesting that aligning soft-token representations helps preserve shared semantic structure during multilingual reasoning.
Do different LLM architectures encode high-level concepts in structurally compatible ways? We systematically characterize a geometric-functional universality dissociation: across multiple concept domains and architectural families, moderate geometric convergence coexists with near-perfect functional transfer. Using contrastive-difference CKA (CKA_Delta), a training-free diagnostic that computes kernel alignment on per-sample contrastive differences, we isolate concept-specific convergence from generic similarity -- achieving significant discrimination where standard CKA cannot. The dissociation replicates across all six concept domains we test (five with p <= 0.017 geometric discrimination and safety as a converging-functional trend, p = 0.08), including two non-instruction concepts (code-vs-NL, reasoning-vs-recall) validated without system prompts; a single 70B--70B pair provides an observational note that universality may strengthen with scale, requiring replication with additional >=70B models. We position CKA_Delta as a practical regime classifier and architectural outlier detector (Gemma: d = 1.08, AUC = 0.79) rather than an absolute transfer-accuracy predictor, providing a training-free diagnostic for cross-architecture concept monitoring.
Large language model (LLM)-based Socratic tutors increasingly guide students through multi-turn questioning, but they can suffer from scaffolding collapse: under sustained student pressure, a tutor gradually abandons guided inquiry and reveals solutions directly. Prior defenses primarily constrain observable responses through prompting, preference optimization, or filtering, leaving the internal representation drift that precedes trajectory-level collapse largely unaddressed. We propose Scaffold-Preserving Representation Alignment, a two-stage framework that first warms up a Socratic tutor with supervised fine-tuning, then combines trajectory-weighted direct preference optimization with a margin-preserving representation loss anchored to frozen reference states. Our method is designed to maintain separation between scaffold-preserving and collapse-inducing hidden states across dialogue turns. We evaluate our method across five STEM disciplines and five red-teaming attack strategies. On Qwen3-8B, our method lowers Collapse Rate to 32%, delays average collapse onset beyond nine turns, and keeps over-refusal low, suggesting that representation-level alignment can improve the robustness of long-horizon Socratic tutoring under our red-teaming protocol.
Instruction-tuned language models can answer the same causal-reasoning question differently after its English variable names are replaced by type-preserving placeholders, although the structural causal model and the gold answer are unchanged. We ask whether this lexical gap reflects information loss in the placeholder view or a misaligned read-out from a representation that still carries answer-relevant content. Vernier uses a paired-view weight update as an instrument and then inspects the mechanism left after the gap closes. In the working regimes, the evidence favours representational misalignment. A variable-name probe becomes more accurate on the placeholder view, and activation patching on Qwen-7B, Qwen-14B, and Llama-3.1-8B shows that the decision-token representation can transfer answer identity between views. The update that realigns the views is counterfactual augmentation over original and placeholder prompts, while the answer-subspace KL mainly sharpens intermediate answer-belief agreement. Success is bounded by model family, scale, and task. CRASS transfer is reliable across Qwen scales and Llama, e-CARE remains weak, and preliminary non-causal rename tasks show a similar qualitative pattern.