Lost-in-the-Middle Effect

We develop an adjoint-sensitivity framework for positional influence in causal residual Transformers and separate unconditional analytic results from conditional boundary-shape conclusions. The principal unconditional theorem is the residual-to-depth-flow estimate for layer controls converging in $L^1$, complemented by a finite-token-to-Volterra attention estimate that explicitly controls the first cells near the causal endpoint. We define a normalized adjoint-energy influence density and derive its exact evolution along full-batch gradient flow. The adjoint admits an exact generator-term decomposition into residual transmission, nonlocal Volterra, and local channels, including all covariance cross terms. Causal masking can amplify early-position sensitivity and residual identity paths can transmit a right-localized terminal bias, but neither mechanism alone forces a U-shaped profile. We therefore state boundary advantages under independently checkable energy, correlation, and local-channel bounds; these conditions are sufficient rather than necessary. Finite-token influence balancing, positional reweighting, and task-aligned observability are presented as diagnostics or regularizers with explicit differentiation requirements, computational costs, and limitations. Controlled simulations illustrate that each intervention controls its designated surrogate, while observability balance or outer-loop reweighting need not monotonically reduce the influence-based Lost-in-the-Middle diagnostic.

Synthesizing long-context supervised fine-tuning (SFT) data is a scalable way to enhance the long-context understanding of large language models (LLMs), yet existing approaches share three limitations: narrow task coverage, insufficient instruction difficulty, and a lack of faithfulness supervision. We propose LongCrafter, a structured synthesis framework that couples a hierarchical task taxonomy with an evidence-grounded pipeline. The taxonomy organizes long-context understanding into local/shallow and global/deep levels and yields 32 fine-grained task types that serve as a global generative prior. Guided by this taxonomy, LongCrafter constructs task-aligned long contexts, decomposes them into explicit evidence graphs that model cross-paragraph dependencies, and generates instruction--response pairs strictly grounded in the located evidence spans, ensuring both controllable difficulty and faithful, traceable reasoning. Models fine-tuned on LongCrafter data outperform all SFT baselines and even the official post-trained models on LongBench, LongBench~v2, and LooGLE across both Qwen2.5-7B and LLaMA-3.1-8B, with the largest gains on high-difficulty tasks. Further analysis shows that LongCrafter data is more diverse and better spread across difficulty levels, and that the trained models locate evidence robustly regardless of position, effectively mitigating the ``lost in the middle'' problem.

Diffusion large language models (dLLMs) re-encode the entire prefix at every denoising step, causing recomputation that scales quadratically with context length and becomes prohibitive for long-context scenarios. We propose Prefilling-dLLM, a training-free prefill-decode disaggregation framework for dLLMs that partitions the prefix into N chunks, caches their KV representations once, and selects the top-K most relevant chunks with intra-chunk token sparsity for decoding, showing that sparse prefilling can outperform dense attention while reducing per-step complexity from quadratic in the full sequence length to quadratic only in the decode length. On LongBench and InfiniteBench, Prefilling-dLLM achieves state-of-the-art quality among dLLM acceleration methods, and an attention kernel that parallelizes decoding over the non-contiguously cached chunk KV yields 9.1--28.0x speedup at 8K--32K contexts. We further show that beginning-of-sequence tokens prepended to each chunk act as periodic attention anchors that eliminate the lost-in-the-middle phenomenon. Code is available at https://github.com/menik1126/Prefilling-dLLM.

We study causal self-attention dynamics -- a toy model for decoder Transformers -- which we interpret as a non-exchangeable interacting particle system. Adapting cumulant expansions to the triangular causal dependency structure of the model, and appealing to non-hierarchical methods to estimate correlations using Glauber calculus, we prove a quantitative mean-field limit result and a next-order characterization of correlations. For iid uniformly distributed tokens, the limiting correlation equation can be solved in closed form and we obtain a rigorous explanation of the empirically observed lost-in-the-middle phenomenon: the token retrieval profile, as a function of the source position in the prompt, is $\mathsf{U}$-shaped, with primacy, recency, and a unique interior minimum under an explicit smallness condition.

A common approach to question answering with retrieval-augmented generation (RAG) is to concatenate documents into a single context and pass it to a language model to generate an answer. While simple, this strategy can obscure the contribution of individual documents, making attribution difficult and contributing to the lost-in-the-middle'' effect, where relevant information in long contexts is overlooked. Concatenation also scales poorly: computational cost grows quadratically with context length, a problem that becomes especially severe when the context includes visual data, as in visual question answering. Attempts to mitigate these issues by limiting context length can further restrict performance by preventing models from benefiting from the improved recall offered by deeper retrieval. We propose Bayesian Ensemble Retrieval-Augmented Generation (BERAG), along with Bayesian Ensemble Fine-Tuning (BEFT), as a RAG framework in which language models are conditioned on individual retrieved documents rather than a single combined context. BERAG treats document posterior probabilities as ensemble weights and updates them token by token using Bayes' rule during generation. This approach enables probabilistic re-ranking, parallel memory usage, and clear attribution of document contribution, making it well-suited for large document collections. We evaluate BERAG and BEFT primarily on knowledge-based visual question answering tasks, where models must reason over long, imperfect retrieval lists. The results show substantial improvements over standard RAG, including strong gains on Document Visual Question Answering and multimodal needle-in-a-haystack benchmarks. We also demonstrate that BERAG mitigates the lost-in-the-middle'' effect. The document posterior can be used to detect insufficient grounding and trigger deflection, while document pruning enables faster decoding than standard RAG.

Large Language Models (LLMs) struggle with long-horizon tasks due to the "context bottleneck" and the "lost-in-the-middle" phenomenon, where accumulated noise from verbose environments degrades reasoning over multi-turn interactions. To address this issue, we introduce a symbiotic framework that decouples context management from task execution. Our architecture pairs a lightweight, specialized policy model, ContextCurator, with a powerful frozen foundation model, TaskExecutor. Trained via reinforcement learning, ContextCurator actively reduces information entropy in the working memory. It aggressively prunes environmental noise while preserving reasoning anchors, that is, sparse data points that are critical for future deductions. On WebArena, our framework improves the success rate of Gemini-3.0-flash from 36.4% to 41.2% while reducing token consumption by 8.8% (from 47.4K to 43.3K). On DeepSearch, it achieves a 57.1% success rate, compared with 53.9%, while reducing token consumption by a factor of 8. Remarkably, a 7B ContextCurator matches the context management performance of GPT-4o, providing a scalable and computationally efficient paradigm for autonomous long-horizon agents.

Large Language Models (LLMs) exhibit a well-documented positional bias when processing long input contexts: information in the middle of a context window receives substantially less attention than content at the boundaries, a phenomenon termed the Lost-in-the-Middle effect (Liu et al., 2024). This limits knowledge-retrieval applications that embed large structured knowledge bases directly in the LLM context. Retrieval-Augmented Generation (RAG) addresses scalability by retrieving only relevant fragments, but introduces substantial infrastructure overhead and is ill-suited to libraries whose semantic boundaries are human-defined rather than statistically learned. We propose Self-Describing Structured Retrieval (SDSR), a lightweight framework in which structured data files embed human-authored navigational metadata at the file's primacy position, thereby exploiting rather than fighting the LLM's primacy bias. We further propose a Dual-Layer Guidance strategy combining in-file metadata with explicit routing rules in the system prompt. We validate SDSR through a four-round benchmark using a 190-skill library expanded from 36 to 119 categories via adversarial distractor injection. Four conditions are tested: (A) no guidance, (B) in-file summary only, (C) prompt hint only, (D) both combined. Version D achieves 100% primary routing accuracy (20/20) at 119 categories versus 65% for the no-guidance baseline. We identify a fundamental asymmetry: primary routing is solvable by explicit rules, while secondary cross-category routing requires architectural intent explicitly encoded in the data structure. We further extend SDSR to semi-structured corpora, showing how cross-reference encoding enables operation without vector databases in domains with recoverable document structure.

The ``Lost in the Middle'' phenomenon -- a U-shaped performance curve where LLMs retrieve well from the beginning and end of a context but fail in the middle -- is widely attributed to learned Softmax artifacts or the distance-decay of positional encodings like RoPE. This paper makes a single, precise claim: the U-shape is already present at initialization, before any training or positional encoding takes effect. It is an inherent geometric property of the causal decoder with residual connections. We model multi-layer causal attention as iterated powers of the Cesàro matrix and derive the exact closed-form influence density in the continuous limit. Causal masking forces a logarithmic divergence of gradient influence at the start of the prompt (the Primacy Tail), while residual connections create an isolated $\mathcal{O}(1)$ anchor at the final token (the Recency Delta). Between these extremes lies a factorial dead zone of order $\mathcal{O}(1/(H{-}1)!)$, where $H$ is the network depth, making middle-context retrieval and training structurally hostile. We validate empirically that untrained Qwen2 and GPT-2 architectures exhibit this U-shape at Step~0, and that it is identical with or without RoPE. Comparing initialized and pretrained networks, we show that standard training does not overcome the topological valley, confirming that the U-shape persists as an architectural baseline under standard pretraining objectives. We do not claim that this bias is insurmountable, nor that interventions such as RoPE modifications are useless. We establish what the baseline is and where it comes from, so that future efforts to overcome it can be precisely targeted.

Transformer models systematically favor certain token positions, yet the architectural origins of this position bias remain poorly understood. This bias is closely connected to the Lost-in-the-Middle phenomenon, where models underutilize information placed in the middle of the context. We show that causal Transformer architectures induce a systematic position-bias prior that can help explain the influence profiles associated with Lost-in-the-Middle. To characterize this prior, we develop a structural theory based on cumulative attention rollout with layerwise residual mixing. At finite depth, we isolate the competing positional drifts induced by causal masking, residual mixing, and positional encoding. Their interaction produces broad, often U-shaped profiles. At infinite depth, prior work predicts inevitable collapse under attention-only theory and identifies the discrepancy with observed Transformer behavior as an open problem. Under the stated boundedness assumptions, our residual-aware analysis replaces inevitable collapse with a dichotomy governed by cumulative attention mixing. Empirically, across 30 model-dataset settings, our adaptive residual-aware rollout closely matches measured input-token influence and reduces the average profile discrepancy by approximately 85% relative to both the attention-only and fixed-residual rollout baselines.