Title: Lost in Transmission: When and Why LLMs Fail to Reason Globally
Venue: NeurIPS 2025
Accepted: yes
Keywords: LLM limitations

chain of thought

reasoning

communication complexity
Abstract: Despite their many successes, transformer-based large language models (LLMs) continue to struggle with tasks that require complex reasoning over large parts of their input. We argue that these failures arise due to capacity limits on the accurate flow of information within LLMs. To formalize this issue, we introduce the bounded attention prefix oracle (BAPO) model, a new computational framework that models bandwidth constraints on attention heads, the mechanism for internal communication in LLMs. We show that several important reasoning problems like graph reachability require high communication bandwidth for BAPOs to solve; we call these problems BAPO-hard. Our experiments corroborate our theoretical predictions: GPT-4o, Claude, and Gemini succeed on BAPO-easy tasks and fail even on relatively small BAPO-hard tasks. BAPOs also reveal another benefit of chain of thought (CoT): we prove that breaking down a task using CoT can turn any BAPO-hard problem into a BAPO-easy one. Our results offer principled explanations for key LLM failures and suggest directions for architectures and inference methods that mitigate bandwidth limits.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nReasoning across the global input context is important to boosting accurate task performance. This paper introduces a theoretical model to bound the communication constraints due to causal attention in transformer-based large language models (LLMs): bounded attention prefix oracle (BAPO). The authors use the framework to outline 3 classes of problems: BAPO-easy, BAPO-hard, BAPO-$\\sum$-hard. They provide upper and lower bounds on the (prefix, attention) bandwidth. They then empirically show that these hardness classes are indicative of actual LLM performance on the analyzed problems. They further extend the empirical results to include real-world problems in the area of sentiment analysis and code tracing.\n\nSTRENGTHS AND WEAKNESSES:\n**Quality:**\n\nThe theoretical model proposed (BAPO) is both analyzed via proof and empirical experiments which support the authors main arguments.\n\n**Clarity:**\n\nThe paper is well organized, and the experiments are well motivated by the theoretical analysis.\n\nWeakness: \n- In figures 3, 4, and 5, the theoretical lower and upper bound should be included to allow for quick comparison. \n- When trying to compare figure 3 vs. 4 I found myself having to quickly flip between the two figures to compare w/ and w/o COT. It would be helpful if you could summarize the COT vs. no-COT results in a table side-by-side to allow for easier comparison.\n\n**Significance:**\nIt is interesting to study the theoretical bounds on if/how transformers are able to complete different types of problem formulations as this analysis can directly be applied to many real-world LLM problem formulations. It informs humans on the limits of LLM abilities and their failure modes. \n\n**Originality:**\nThis work builds on an area on a line of work which studied LLM communication complexity. They contribute a new framework (BAPO) for reasoning about communication problems which are bounded by causal attention.\n\nQUESTIONS:\n- Can you include the theoretical lower and upper limits of BAPOs with COT similar to what was provided in table 1 for BAPO with no COT?\n- You only consider production-grade language models in your empirical analysis. At what point during model training do LLMs become well trained enough to fit the BAPO framework. Presumably, randomly initialized LLMs would not perform well on any task.\n- I am curious to see if adding in-context examples to the real-world tasks, as is suggested in the discussion (lines 324-330), empirically improves performance?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-06-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper delves into the challenges LLMs face when handling tasks that require global reasoning, attributing these difficulties to bandwidth limitations in their internal information transmission. To formalize this issue, the research introduces the Bounded-Attention Prefix Oracle (BAPO) model, which simulates the communication constraints of an LLM's attention heads. This model classifies problems into \"BAPO-hard\" (requiring high bandwidth) and \"BAPO-easy.\" Experimental results validate that LLMs falter on BAPO-hard tasks. Furthermore, the study demonstrates that Chain of Thought (CoT) can effectively mitigate these bandwidth limitations by decomposing complex tasks into BAPO-easy steps.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n1. Novel Computational Framework (BAPO Model): The paper introduces the Bounded Attention Prefix Oracle (BAPO) model, a new computational framework that formalizes and quantifies communication bandwidth constraints within LLMs' attention heads. This model offers principled explanations for why LLMs struggle with complex global reasoning tasks, abstracting away lower-level transformer details to focus on information flow.\n2. Theoretical Explanation for Chain of Thought (CoT) Effectiveness: The research provides a strong theoretical basis for the success of Chain of Thought (CoT), proving that CoT can decompose BAPO-hard problems into a sequence of BAPO-easy steps. It further demonstrates that constant-bandwidth BAPOs become Turing-complete with CoT, theoretically enabling them to solve any decidable problem, albeit potentially requiring a large number of output tokens.\n3. Empirical Validation and Practical Implications: The paper's experiments consistently corroborate its theoretical predictions: LLMs perform well on BAPO-easy tasks but systematically fail on BAPO-hard ones, even for relatively small instances across various models like GPT-4o, Claude, and Gemini. This alignment provides practitioners with actionable insights into LLM limitations and suggests mitigation strategies, such as inference-time scaling or hybrid architectures, or even optimizing for low bandwidth requirements during training.\n\nWeaknesses:\n\n1. Simplifying Assumptions in BAPO Model (**Too simple to evaluate the validity**): The BAPO model incorporates several simplifying assumptions that do not fully capture the complexities of real transformer computation. For example, it assumes problems have **single-token** solutions for simplicity, posits unbounded computational power for prefix/suffix streams** (though tempered by the requirement to work for all splits), allows the attention function `g` to base decisions on the **entire suffix** (unlike real causal attention, which communicates across layers), and assumes **perfect positional encoding** and attention only on the token layer. These simplifications might limit its direct applicability to all nuances of LLM behavior.\n2. Unidentified Root Cause of Limited Effective Bandwidth: Although the paper hypothesizes that LLM failures stem from limited effective bandwidth, it explicitly states that the \"root causes of this severely limited bandwidth\" are not fully understood. The authors acknowledge this as a limitation, suggesting it might even be a beneficial feature for generalization rather than a flaw, indicating an incomplete understanding of the underlying mechanism.\n3. Loose Theoretical Lower Bounds and Unexplored Problem Space: The paper acknowledges that \"many of our lower bounds are loose\" and there are \"many important problems whose BAPO bandwidths have yet to be explored\". This implies that the theoretical characterization of problem hardness in terms of bandwidth is not yet fully refined or comprehensive, leaving gaps in precisely understanding the communication requirements for various computational problems.\n\nQUESTIONS:\n1. How would the BAPO model's theoretical framework and bandwidth requirements change if problems with multi-token, structured outputs were directly modeled, rather than just single-token solutions?\n2. How can the hypothesized trade-off between an LLM's \"generalization ability\" (for natural language tasks) and its \"effective bandwidth\" (for exact global reasoning tasks) be empirically isolated and quantified?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-06-25"}

comments: SUMMARY:
In this paper, the authors argue that failures in LLM on tasks requiring global reasoning are due to capacity limits on their internal information flow. They introduce the Bounded Attention Prefix Oracle (BAPO) model, a new computational framework that models these communication bandwidth constraints. The authors use this framework to classify problems as "BAPO-hard" if they require high bandwidth . Their experiments show that major LLMs succeed on BAPO-easy tasks but fail on BAPO-hard ones, corroborating their theoretical predictions.

STRENGTHS AND WEAKNESSES:
Strengths:
1. The development of a novel and principled theoretical framework (BAPO) is a valuable contribution, and the BAPO-hardness classification serves as a practical diagnostic tool.
2. The paper successfully bridges the gap between theory and practice by aligning with the actual performance of state-of-the-art models.

Weaknesses:
1. The BAPO model is a significant abstraction of a real transformer as the authors acknowledge.

QUESTIONS:
Suggestion:
The paper compellingly identifies that a key unanswered question is why modern LLMs, despite their immense scale, exhibit such a limited effective bandwidth. I suggest training small transformer models from scratch specifically on BAPO-hard problems. By systematically varying the models' depth and width during this process, it might be possible to isolate the specific architectural factors that contribute to these communication limits and gain crucial insights into this fundamental issue.

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 4
IMPACT: 4
ORIGINALITY: 3
DATE: 2025-06-29

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work introduces BAPO, a framework to reason about when LLMs can solve decision problems. BAPO is centered around communication bandwidth which is used to differentiate between BAPO easy and hard problems. The BAPO framework is able to predict if Transformers will successfully solve problems based on if they require constant or super-constant bandwidths.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths.** I find the framework to be simple yet elegant for predicting how Transformers perform on certain decision problems. While the idea of using communication complexity / bandwidth has been explored in prior works, the new contribution of this work is to split up the input into a prefix and suffix in order to reason about decision problems.\n\n**Weaknesses.** While the authors have presented the results in 6 different problems, I think this set is very limited. For example, it would be interesting to see if the predictions still hold if we consider problems where the communications bandwidth isn't just 0 or 1. Also, some of the results of CoT also don't seem to hold in practice, i.e., experiments in figure 4 do not show a significant benefit from using chain-of-thought.\n\nI worry that some of the assumption are too strong to clearly make predictions about problems beyond the ones considered in this work. By assuming that the prefix and suffix have infinite computational power, the predictive power of this theory may be a lot weaker.\n\nQUESTIONS:\nAn experiment that I think would be very interesting: Consider the problem of finding the kth larger element in an array and the problem of sorting. If I understand correctly, the former is BAPO-easy (for constant k) while the latter if BAPO-hard. How well do you perform on these problems for different values of k, and different sequence lengths. Do the LLMs successfully solve this problem for different values of k?\n\nLIMITATIONS:\nYes, the authors have clearly listed out assumptions but could expand a bit more on how these assumptions directly translate to limitations on their theory.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}