Evaluating task-oriented dialogue agents requires judging not merely whether a reply reads well but whether each turn advances the underlying workflow state correctly--a distinction conventional holistic LLM judges can miss because they evaluate the available context as a single unit and require one or more full-model calls per turn. We propose SAGE (State-Grounded Abstention-Aware Evaluation), which compiles a workflow specification and per-turn state diff into atomic, schema-grounded criteria and routes each through a cascade of symbolic and encoder/NLI verifiers that abstain rather than guess, aggregating criterion verdicts into a turn-level decision with an evidence trace. Its recommended operating point, SAGE-Core, decides 81--91% of criteria with only the compiler, symbolic rules, and on-device encoders--at zero paid LLM cost--while SAGE-LLM adds an optional focused-LLM fallback for open-class criteria. Across four slices spanning MultiWOZ, Schema-Guided Dialogue, and ABCD, no evaluated LLM-as-a-judge baseline--including a state-aware GPT-4.1 judge and cheaper GPT-4.1-mini variants--significantly exceeds SAGE-Core on any slice, even though the GPT-4.1 G-Eval judge costs $4.7--8.0 per 1,000 turns to SAGE-Core's $0. A two-annotator human audit (n=200, $κ$=0.94) confirms strong label fidelity on the transcript-visible failure classes--where, excluding the weak-salience IUV class, SAGE-Core is statistically tied with the strongest LLM judge--and honestly scopes ignored-user-value as a state-consistency signal with weak broad-human salience. We analyze construct-validity limits from injected failures and partial symbolic circularity.
In this paper, we propose \textbf{Mahalanobis-Based Multi-Head Attention} (MHA-CSP), a novel attention mechanism that replaces the standard dot-product with a \textbf{Mahalanobis distance-based RBF kernel}, which effectively computes attention in an infinite-dimensional feature space without increasing the parameter count. Crucially, the positive definiteness of the Mahalanobis distance enables a \textbf{direct construction of Tree Attention}: attention scores are built directly from accumulated distances, with a LogSumExp correction that rectifies the raw distance by subtracting the log-sum of edge exponentials. Moreover, the multi-head Mahalanobis distance matrices are themselves repurposed to construct an \textbf{attention meshing mechanism}, enabling cross-head kernel collaboration that simultaneously boosts accuracy and training efficiency. Extensive experiments demonstrate that MHA-CSP, with only 119K parameters and \textbf{teacher forcing applied exclusively at the final hidden state}, consistently outperforms Transformer and GCN baselines trained from scratch under identical conditions on long-sequence state tracking tasks. While these baselines rely on dense attention or graph propagation, MHA-CSP achieves robust structured reasoning via synthetic distance rectification---powered by Mahalanobis-based attention---and efficient information bypass inherited from the CSP backbone. This result highlights the effectiveness of complex-valued state propagation with collaborative multi-head rectification in capturing symbolic structures, establishing a new efficiency-performance trade-off for structured reasoning.
Transformer-based architectures have dominated sequence modeling, largely due to the expressive power of attention mechanisms. However, for a class of deterministic state tracking tasks---such as parity checking, modular counting, and parenthesis matching---attention may be overkill. In this paper, we show that \textbf{state propagation alone is sufficient}. We propose the \textbf{Complex State Propagator (CSP)}, a minimalistic recurrent architecture that \textbf{only propagates hidden states} across layers without output projections at intermediate steps. The state is represented as a complex-valued vector, updated via input-dependent rotations in the complex domain. To enable deep propagation without gradient vanishing or degradation, we introduce a \textbf{block-level skip connection} alongside element-wise complex normalization and SiLU activation at sequence boundaries. Applied with Focal Loss, CSP achieves \textbf{100\% accuracy} with perfect F1 scores across canonical tasks.
Hybrid language models that mix attention and recurrent layers have shown promise: theoretically, recurrent layers ameliorate the limitations of pure transformers on state tracking, and empirically, hybrids can outperform pure transformers in loss and downstream evaluations \citep{waleffe2024empirical,merrill2026olmohybrid}. Yet it remains unclear which data or capabilities drive these gains, and to what degree they reflect the theoretical advantages motivating hybrid models. We address this question using the open weights from Olmo 3 \citep{olmo2025olmo3} and Olmo Hybrid \citep{merrill2026olmohybrid}: we compare the loss of a matched transformer and hybrid at the same target tokens under the same prefixes, stratifying the results by natural token tags, copy features, delimiter structure, and controlled synthetic probes. The hybrid has lower loss on most tag families, but the gains are not uniform: they are largest for open-class content words and smaller for many closed-class function words. Across prose, code, and markup, the hybrid's loss advantage is larger on opening delimiters than on the corresponding closing delimiters, and nearly vanishes on repeated $n$-grams. Synthetic probes show the same split: the hybrid is favored on pronoun-memory and entity-tracking tasks, whereas the transformer is favored on bracket-matching tasks that require choosing closing delimiters. These patterns suggest that the recurrent layers in hybrids improve predictions that leverage the semantic state of a document, whereas attention helps on tokens predictable by $n$-gram copying or syntactic bracket matching. We conclude with proof-of-concept filtered evaluations showing how token-level decompositions can sharpen pretraining diagnostics for hybrid architectures.
Linear attention replaces softmax attention's growing KV cache with a fixed recurrent state, but this compression limits exact state tracking and long-context memory. We introduce \emph{Semidirect Fourier Delta Attention} (SFDA), a phase-controlled generalization of Kimi Delta Attention that replaces real diagonal decay with block-rotational Fourier control: \[ S_t=(I-β_t k_tk_t^*)Λ_tS_{t-1}+β_tk_tv_t^*, \qquad Λ_t=\diag(α_t\odot e^{iθ_t}). \] Our main result is a constructive chunk-WY factorization for products \(A_t=Λ_t-u_tr_t^*\), giving \[ A_t\cdots A_1=Γ_t-Y_tM_tW_t^* \] with rank growth bounded inside fixed chunks. This yields an exact affine chunk transfer, formal stability and complexity bounds, and a compact characterization of phase-plus-low-rank memory. We verify the algebra numerically and show in toy state-tracking experiments that SFDA learns cyclic memory where the phase-disabled KDA baseline remains near chance. Fused kernels and large-scale language-model comparisons are left to future work.
Anamaria-Roberta Hartl, Levente Zólyomi, David Stap +6cs.LG
Transformers dominate modern sequence modeling, but their quadratic attention incurs substantial computational cost. Subquadratic architectures offer a scalable alternative. However, it remains unclear which designs yield the most effective sequence models. We compare three leading approaches: xLSTM, Mamba-2, and Gated DeltaNet. We evaluate these models on tasks with complex dependencies: (1) code-model pre-training, (2) distillation of code models from large language models, and (3) pre-training of time-series foundation models. Across these settings, xLSTM delivers the strongest overall performance. To explain xLSTM's advantage, we present a unified formulation and analyze the underlying architectural mechanisms, focusing on state tracking and memory dynamics. Our results show that xLSTM enables more flexible and stable memory correction via its gating scheme. We corroborate these findings on controlled synthetic length-generalization tasks. Overall, our findings indicate that xLSTM's gains on complex tasks stem from robust state tracking and accumulation.
To interpret context correctly and retrieve relevant information, large language models must bind entities to their attributes and update these bindings as state changes. We analyze how LLMs implement this binding process in a dynamic state tracking. Using causal interventions, we identify a retrieval conditioned rebinding mechanism, a compact attention head circuit that encodes swap relevant binding information and reinstates it at readout. Across Gemma and Llama models, this circuit supports rebinding behavior, but the representational signature of the mechanism differs across model families. In Gemma models, the binding signature is clearly expressed in the query/key subspaces of the relevant attention heads, whereas in Llama models, the binding information is carried primarily in key vectors. Overall, our results reveal an interpretable mechanism for context dependent state tracking in LLMs.