Is the Reversal Curse a Binding Problem? Uncovering Limitations of Transformers from a Basic Generalization Failure — part 1/4
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# Is the Reversal Curse a Binding Problem? Uncovering Limitations of Transformers from a Basic Generalization Failure
###### Abstract
Despite their impressive capabilities, LLMs exhibit a basic generalization failure known as the Reversal Curse , where they struggle to learn reversible factual associations. Understanding why this occurs could help identify weaknesses in current models and advance their generalization and robustness. In this paper, we conjecture that the Reversal Curse in LLMs is a manifestation of the long-standing binding problem in cognitive science, neuroscience and AI. Specifically, we hypothesize two primary causes of the Reversal Curse stemming from transformers’ limitations in conceptual binding: the inconsistency and entanglements of concept representations. We perform a series of experiments that support these conjectures. Our exploration leads to a model design based on JEPA (Joint-Embedding Predictive Architecture) that for the first time breaks the Reversal Curse without side-stepping it with specialized data augmentation or non-causal masking, and moreover, generalization could be further improved by incorporating special memory layers that support disentangled concept representations. Our research opens up the broader fundamental challenge of designing models capable of learning systematic conceptual binding with less human scaffolding. 1 1 1 Code and data: https://github.com/OSU-NLP-Group/reversal-curse-binding .
## 1 Introduction
Current large language models (LLMs) exhibit a notable failure of basic generalization known as the Reversal Curse ( Berglund et al., 2024 ) , where they struggle to learn rules of inversion over parametric knowledge and form reversible factual associations. For instance, after internalizing the fact “Tom Smith’s wife is Mary Stone” , LLMs fail badly at recalling “Tom Smith” when asked “Mary Stone’s husband is __” . 2 2 2 A special case is when the involved relations are symmetric, which leads to examples like “A is B” then “B is A” , a popular reference to the Reversal Curse. Reversal is not confined to natural language; it represents a class of basic operations across various domains such as mathematics/logic and numerous scientific disciplines, where inverse relationships are commonplace. Given that LLMs are trained on web-scale corpora containing data more than enough for inducing these rules, it is clear that there are missing inductive biases in current transformer-based language models ( Vaswani et al., 2017 ; Brown et al., 2020 ; Chowdhery et al., 2023 ; Touvron et al., 2023 ) that hinder this kind of generalization. The simplicity of the rules also suggests their limitations in learning more complex skills and principles, which could hurt both their general abilities and potential to specialize into domain experts.
There are several pieces of work trying to understand or mitigate the Reversal Curse. Zhu et al. (2024) theoretically shows that reversal cannot be learned for transformers under special settings and assumptions. Lin et al. (2024) shows that the issue may be related to inherent biases in LLMs’ factual recall. Golovneva et al. (2024) ; Guo et al. (2024) ; Lu et al. (2024) ; Lv et al. (2024) ; Kitouni et al. (2024) propose specialized data augmentation strategies (e.g., reversing/permuting sentence segments) or non-causal training objectives, which circumvent the problem and reduce generalization demands on models. Overall, existing solutions are ad-hoc and fall short of uncovering the potentially more foundational issues behind such a curse—in fact, the very first question still remains a mystery:
Are conventional (autoregressive) transformers fundamentally doomed for learning reversal?
Surprisingly, the answer is “No” . Our first major finding is that standard transformers can learn reversal without any specialized data augmentation or modifications to the architecture or objective , when the inputs are represented and perceived at the abstract concept level (Figure 1 (a)). We then focus on the gap between abstract and real settings, where inputs are instead at the surface form level. Our investigations lead us to hypothesize that the Reversal Curse is fundamentally a manifestation of the long-standing binding problem in cognitive science, neuroscience and AI, which is concerned with the mechanisms for natural or artificial neural networks to combine information distributed throughout the network to form integrated percepts and knowledge ( Roskies, 1999 ; Engel and Singer, 2001 ; Zimmer et al., 2006 ; Greff et al., 2020 ) . Specifically, we conjecture that the Reversal Curse is primarily caused by two limitations of conceptual binding in transformers, the inconsistency and entanglements of concept representations: • Inconsistency. While many existing studies show that LLMs could form internal concepts and even “world models” from surface-level predictions ( Meng et al., 2022 ; Geva et al., 2023 ; Lad et al., 2024 ; Kaplan et al., 2025 ; Li et al., 2023 ; Gurnee and Tegmark, 2024 ) , we hypothesize that they are still unable to adequately learn consistent concept representations across various places within the network under different contexts. Specific to reversal, we conjecture that transformers fail to bind representations of the same underlying entity when it switches roles between perceived subjects and predicted objects (Figure 1 (b), Left), which makes the model’s acquired knowledge fragmented and impedes the learning of reversal.
• Entanglements. Since concepts are activations in transformers, their representations can only be indirectly updated by altering the lower-level weights in the recognition module mapping surface-form names to concepts. We conjecture that transformers with gradient-based optimizations face difficulties in maintaining the separation of distinct concepts during learning due to representational entanglements (Figure 1 (b), Right), which impacts the training dynamics and hinders generalization.
A series of quantitative experiments support our hypotheses, and inform two novel designs for mitigating the Reversal Curse: 1) performing autoregressive prediction at the concept level, akin to Joint-Embedding Predictive Architectures (JEPA) ( LeCun, 2022 ) and concept models ( Barrault et al., 2024 ) , and 2) building dedicated recognition modules which support disentangled concept representations. We show that 1) a model design based on JEPA and in-batch contrastive learning could, for the first time to our knowledge, break the Reversal Curse with non-trivial performance without circumventing the problem, but suffers from entanglements that scale with model depth; 2) incorporating special memory layers ( Sukhbaatar et al., 2015 ; Berges et al., 2024 ) into the recognition module could further boost generalization. We also demonstrate that the reversal skill unlocks a new kind of parametric memory integration, which allows models to perform parametric forward-chaining during information internalization to solve large-scale arithmetic reasoning problems with impressive performance, outperforming frontier LLMs based on non-parametric memory.
To summarize, our work 1) contributes towards understanding and addressing the Reversal Curse, and more importantly, 2) connects the Reversal Curse with the more foundational problem of improving conceptual binding and generalization in AI models, rigorously establishing the concrete challenges for the broader research community.
## 2 Learning Reversal at the Concept Level
Humans think and learn at the concept level. When reading a sentence, we (usually subconsciously) parse and map the words into concepts, and update the concept representations and associations upon encountering new information ( Collins and Loftus, 1975 ; Jackendoff, 1995 ) . While transformers fail to learn reversal in real settings, do they first have appropriate inductive biases to learn reversal at the abstract concept level?
Concepts in reversal. Reversal is a simple and clean task involved with some of the most basic low-level concepts: entities and relations. Take “Tom Smith’s wife is Mary Stone” as an example: each fact consists of the subject entity ( “Tom Smith” ), relation ( “’s wife” ), and the object entity ( “Mary Stone” ). At the concept level, each fact is hence ( e 1 , r , e 2 ) (e_{1},r,e_{2}) , and its reverse is ( e 2 , r − 1 , e 1 ) (e_{2},r^{-1},e_{1}) which contains the same piece of information. If a model acquires reversal, then after internalizing a certain fact in one direction, i.e., its parameters are changed s.t. p ( e 2 | e 1 , r , ? ) p(e_{2}|e_{1},r,\textit{?}) is large, the model should also assign a high probability p ( e 1 | e 2 , r − 1 , ? ) p(e_{1}|e_{2},r^{-1},\textit{?}) to its reverse direction.
Setup. We prepare a set of relation pairs { ( r i , r i − 1 ) ∣ i = 1 , … , N } \{(r_{i},r_{i}^{-1})\mid i=1,\dots,N\} , and two disjoint sets of entities ℰ A \mathcal{E}_{A} (for learning) and ℰ B \mathcal{E}_{B} (for testing). We focus on one-to-one relations that give a unique object entity for each fact. We synthesize facts separately over ℰ A \mathcal{E}_{A} and ℰ B \mathcal{E}_{B} by randomly pairing the entities for each ( r i , r i − 1 ) (r_{i},r_{i}^{-1}) , and form a pair of facts which are reverses of each other over each entity pair. Through this, we obtain two sets of facts D A D_{A} and D B D_{B} over ℰ A \mathcal{E}_{A} and ℰ B \mathcal{E}_{B} respectively. The training data contains all of D A D_{A} (for the model to induce the rules) and one random direction from each pair of facts in D B D_{B} , where its reverse goes into the test set. We set N = 6 N=6 , and vary | ℰ A | |\mathcal{E}_{A}| while keeping the ratio | ℰ A | : | ℰ B | = 5 : 3 |\mathcal{E}_{A}|:|\mathcal{E}_{B}|=5:3 . Importantly, each concept (entity/relation) is directly represented by its own learnable embedding , without attaching to surface-level names. We train standard decoder-only transformers as in GPT-2 ( Radford et al., 2019 ) (with 768 768 hidden dimensions and 12 12 attention heads) to predict the object entity in each fact, with cross-entropy loss over embeddings of all concepts. We train models for a large number of steps ( 3 e 6 3e6 ) and report the highest mean reciprocal rank (MRR) on the test examples achieved among different model checkpoints. More training details are included in Appendix A .
Transformers can learn reversal at the concept level. Results are in Table 1 . Surprisingly, in contrast with the negative results and views in previous studies, we find that transformers can learn reversal with high performance without any specialized training objectives or data augmentation. Models with different depths could all strongly generalize, where the performance overall increases with | ℰ A | |\mathcal{E}_{A}| . Despite being extremely straightforward, this positive result becomes one of the major findings in this work. The critical question then arises: If transformers can learn reversal at the abstract concept level, why do they fail in realistic settings?
## 3 The Binding Problem Underlying Surface-level Predictions
The main difference in realistic settings is that the model perceives surface-form names instead of processing concepts directly, where the “curse” somehow arises. In this section, we analyze the main challenges of learning reversal through surface-level predictions, accompanied with quantitative experiments supporting our conjectures.
The binding problem. Our central thesis is that the Reversal Curse is a manifestation of the long-standing binding problem in cognitive science, neuroscience and AI, which is concerned with the mechanisms for natural or artificial neural networks to bind information distributed throughout the network and form integrated percepts and knowledge ( Roskies, 1999 ; Engel and Singer, 2001 ; Zimmer et al., 2006 ; Greff et al., 2020 ) . The binding problem could be divided into two major types: perceptual binding and conceptual binding . Perceptual binding refers to the combination of features from raw inputs into cohesive concepts, typically occurring during low-level perception/recognition ( Von Der Malsburg, 1994 ; Tallon-Baudry and Bertrand, 1999 ; Singer, 2007 ; Palmigiano et al., 2017 ) . Conceptual binding is centered around forming unified and integrated long-term knowledge, which occurs during high-level semantic processing and memory consolidation ( McNorgan et al., 2011 ; Opitz, 2010 ; Murre et al., 2006 ; Patterson et al., 2007 ; Ralph et al., 2017 ) .
Numerous studies show that LLMs have no trouble learning perceptual binding through surface-level predictions. For instance, prior work finds that detokenization is typically carried out in a “recognition module” within the lower layers, where subword tokens are combined and mapped into cohesive concept representations at the end of surface names ( Meng et al., 2022 ; Geva et al., 2023 ; Lad et al., 2024 ; Yang et al., 2024 ; Kaplan et al., 2025 ) ; in upper layers, tokens of the output surface name beyond the immediate next token are also usually (often-times, linearly) encoded in the hidden states ( Pal et al., 2023 ; Belrose et al., 2023 ; Wu et al., 2024 ; Cai et al., 2024 ) . Complementary studies tracing the evolvement of LLMs’ internal states during inference suggest that, beyond perceptual binding, they also “think” in an abstract concept space within a “semantic module” in the middle layers ( Geva et al., 2022 ; Wendler et al., 2024 ; Lad et al., 2024 ; Sun et al., 2025 ) . An illustration is in Figure 1 (b). These findings indicate that the issues lie not in perceptual binding, but in the specific representations learned under surface-level prediction. Upon closer examination, we identify two key potential factors contributing to the failure in learning reversal, both stemming from transformers’ deficiency in conceptual binding: inconsistency and entanglements .
### 3.1 Inconsistency of Concept Representations
We conjecture that one major cause of the Reversal Curse is that transformers lack inductive biases to learn consistent concept representations when they emerge across different contexts. This skill is performed seamlessly by humans; for example, when separately reading “the city that held the 2024 Summer Olympics” and “the center of political change during the French Revolution” , despite activating from and carrying different contexts (sports and history), the representations formed in our mind are bound and connect to the same underlying concept “Paris” instead of being isolated from each other. 3 3 3 Consistency of concept representations is also the central thesis of the Hub-and-Spoke model, a prominent framework for human semantic memory ( Patterson et al., 2007 ; Ralph et al., 2017 ) supported by evidence from neuroanatomy and studies on memory-impaired patients, which proposes that different experiences bind through a shared central ‘hub’ storing core concept representations, allowing knowledge integration and conceptual generalization. Concretely for reversal, inconsistency instantiates into the failure of binding entity representations when they switch roles between the perceived subjects and the predicted objects , which emerge at the lower and upper layers within the model respectively (Figure 1 (b), Left). Due to this, facts that are reverses of each other cannot be well integrated as one piece, impeding the induction of reversal.