Nested Learning: The Illusion of Deep Learning Architectures (2512.24695v1)

Abstract: Despite the recent progresses, particularly in developing LLMs, there are fundamental challenges and unanswered questions about how such models can continually learn/memorize, self-improve, and find effective solutions. In this paper, we present a new learning paradigm, called Nested Learning (NL), that coherently represents a machine learning model with a set of nested, multi-level, and/or parallel optimization problems, each of which with its own context flow. Through the lenses of NL, existing deep learning methods learns from data through compressing their own context flow, and in-context learning naturally emerges in large models. NL suggests a philosophy to design more expressive learning algorithms with more levels, resulting in higher-order in-context learning and potentially unlocking effective continual learning capabilities. We advocate for NL by presenting three core contributions: (1) Expressive Optimizers: We show that known gradient-based optimizers, such as Adam, SGD with Momentum, etc., are in fact associative memory modules that aim to compress the gradients' information (by gradient descent). Building on this insight, we present other more expressive optimizers with deep memory and/or more powerful learning rules; (2) Self-Modifying Learning Module: Taking advantage of NL's insights on learning algorithms, we present a sequence model that learns how to modify itself by learning its own update algorithm; and (3) Continuum Memory System: We present a new formulation for memory system that generalizes the traditional viewpoint of long/short-term memory. Combining our self-modifying sequence model with the continuum memory system, we present a continual learning module, called Hope, showing promising results in language modeling, knowledge incorporation, and few-shot generalization tasks, continual learning, and long-context reasoning tasks.

• The paper introduces a paradigm that reformulates deep learning architectures as nested multi-level optimization systems, unifying memory, meta-learning, and continual adaptation.
• The methodology decomposes models into hierarchically organized modules with distinct update frequencies, enabling efficient in-context adaptation and improved memory consolidation.
• Empirical results from Hope-augmented architectures show enhanced long-context reasoning and resilience to catastrophic forgetting compared to traditional models.

Nested Learning: Reframing Deep Architectures as Systems of Multi-Level Optimization

The paper "Nested Learning: The Illusion of Deep Learning Architectures" (2512.24695) introduces Nested Learning (NL), a paradigm that reformulates modern machine learning architectures and their optimization as systems of nested, multi-level, and potentially parallel optimization problems, each with its own context flow and update frequency. This perspective provides a unified lens to view architectures, optimizers, in-context and continual learning, memory systems, and meta-learning, suggesting that both computation and memory in current machine learning models are artifacts of managing context at multiple temporal and structural scales.

Motivation: Biological Inspiration and Deficiencies of Deep Stacking

Despite the scaling of neural architectures powering state-of-the-art LMs, core deficiencies remain in continual learning, test-time adaptation, and memory consolidation. NL is motivated by neuroscientific theory: specifically, the human brain's capacity for continual learning, enabled by multi-timescale neural processes and a uniform, reusable structure. Unlike the static parameterization and update frequencies in deep networks, the brain organizes computation via nested oscillations—each operating at a distinct temporal frequency, supporting both fast adaptation and persistent memory.

Figure 1: Uniform, reusable structures and multi-timescale updates in the brain inspire NL's multi-level, frequency-aware decomposition of learning.

Transformers, for example, are argued to possess only two extreme update frequencies after pretraining: attention updates weights at every token ($f=\infty$) and MLP blocks remain static ($f=0$), rendering their long-term memory immutable post-deployment. This is analogized to anterograde amnesia, where only immediate (contextual) and long-past (pretraining) knowledge are accessible.

The Nested Learning Paradigm: Formalization

Nested Learning (NL) proposes representing a model and its training as multiple nested, hierarchically-organized (or parallel) optimization problems, each with an explicit level, update frequency ($f_A$), and context flow. The core primitive is the nested system of associative memories (NSAM), where each level $k$ comprises modules learning key-value associations from its own context, via (possibly distinct) objectives and update rules, often under gradient descent.

NL offers a formal framework for decomposing architectures and their training into multi-level optimization:

• Level Structure: Each component has an associated update frequency, dictating its position in the hierarchy.
• Knowledge Transfer: Across levels, information can be transferred via gradient flow, initialization (meta-learning), direct conditioning, hypernetworks, or value generation.

  Figure 2: NL depicts models as collections of nested optimization problems, each block with its internal gradient flow and context—contrasting with standard "flattened" deep learning diagrams.

Example: An MLP trained with momentum-based SGD can be decomposed into a 2-level system: the inner loop updates momentum (an associative memory over gradients), and the outer applies the momentum to parameters. More complex architectures, like Transformers with meta-learned initial states, instantiate deeper, more intricate nested systems.

Architectures and Optimizers as Learning Modules

NL reframes both neural architectures and their optimizers as instances of associative memory systems, each compressing their own context flow (tokens or gradients, respectively).

• Backpropagation as Memory: Standard gradient descent can be interpreted as a memory compressing input-output "surprises" (prediction errors) into internal states.
• Momentum/Adam/AdaGrad: Momentum terms are associative memories of past gradients; Adam is the optimal associative memory for minimizing elementwise $L_2$ regression. Preconditioners and more expressive optimizers (Muon, Shampoo) generalize this perspective to arbitrary mappings.
• Generalized Updates: Delta Gradient Descent (DGD) and Deep Momentum (DMGD) extend these concepts, utilizing more expressive, value-dependent, or nonlinear objectives and parameterizations to improve memory management and long-term retention during continual learning.

  Figure 3: Comparing MLP (stateless) and linear attention (with in-context adaptation) within a Transformer backbone—modifying the memory level depth enables in-context learning without architectural heterogeneity.

Memory Systems: Continuum Memory System (CMS)

NL generalizes the traditional split between long-term and short-term memory via the Continuum Memory System (CMS): a distributed ensemble of MLP (or memory) blocks at distinct frequencies, each handling different persistence horizons. Updates are chunked per frequency, and higher-frequency modules adapt quickly while lower-frequency modules maintain persistence.

Combining CMS with self-modifying, in-context adaptable modules yields models (notably, the Hope architecture) capable of robust continual learning, long-context reasoning, rapid knowledge incorporation, and resilience to catastrophic forgetting.

Figure 4: Structural comparison between Hope (with CMS and self-modifying memory modules) and traditional Transformers.

Experimentation: Empirical Findings

1. Continual Learning: In class-incremental tasks (CLINC, Banking, DBpedia), Hope-augmented models (using Llama3 backbones) outperform ICL-only models, Elastic Weight Consolidation, and external-learning methods. The improvement is attributed to multi-level memory and effective knowledge transfer between levels.

Figure 5: Hope's multi-level memory outperforms ICL and other continual learners in class-incremental text classification.

2. In-Context and Long-Context Learning: Increasing memory levels in Hope leads to better performance on benchmarks for in-context QA (LongHealth, QASPER), and multi-key NIAH tasks, with more frequent lowest-level updates (shorter timescale memory) trading adaptability for persistence.

Figure 6: Increasing the number of memory levels in CMS boosts in-context learning performance on varied long-text tasks.

1. Long-context Modeling: On benchmarks like RULER and BABILong, Hope outperforms strong recurrent and attention-free architectures (e.g., RetNet, Titans), particularly in tasks requiring recall and manipulation over contexts exceeding hundreds of thousands or millions of tokens.
2. Language Modeling and Reasoning: Across standard benchmarks, Hope matches or surpasses the best existing sequence models at comparable scale, excelling especially as model capacity increases.
3. Optimizers: The multi-level M3 optimizer demonstrates state-of-the-art loss minimization in ViT/ImageNet and language modeling, although computational scaling remains a challenge.
4. Formal Language Recognition: Hope achieves perfect accuracy where Transformers fail, leveraging non-parallelizable computation enabled by its nested, recurrent structure.

Theoretical and Practical Implications

Theoretical Consequences

• Unified View of Memory and Learning: NL abolishes the hard separation of memory, optimization, and architecture, viewing all as nested context-compression problems optimized at multiple timescales.
• Reinterpretation of Pretraining and In-Context Learning: Pretraining is "in-context learning at the largest scale"; all adaptation—in-context, continual, meta—is an emergent effect of explicit management of context at different hierarchy levels.
• Illusion of Heterogeneous Architectures: Standard architectures (e.g., Transformers, RNNs) appear heterogeneous only because we observe their solutions, not their underlying system of nested memory modules.

Practical Implications and Future Directions

• Design Axis: Level Stacking: Architectural improvement may be more productively sought by increasing the number/structure of memory levels and their knowledge transfer, rather than simple stacking of layers.
• Continual Learning: NL provides a roadmap for scalable, robust continual learning—designing memory and optimizer modules attuned to both frequent and persistent knowledge storage.
• Optimizer-Architecture Co-Design: The interplay between model gradients (architecture) and memory management (optimization) should motivate the design of architecture-specific, potentially self-modifying optimizers.
• Parallelism and Scalability: Despite incorporating recurrence, Hope and CMS designs enable highly parallel chunk-wise training, essential for practical scaling.
• Unaddressed Limitations: While Hope/CMS significantly reduce catastrophic forgetting in studied settings, NL clarifies that true immunity is only possible with unbounded memory—capacity-limited networks will always face tradeoffs.

Conclusion

Nested Learning offers a technically precise, biologically motivated paradigm that subsumes classical architectural, optimization, and memory distinctions under a generalized system of multi-level, context-driven optimization. This reframing not only unifies in-context learning, meta-learning, continual learning, and optimizer design, but also provides actionable axes along which future AI systems may achieve robust, data-efficient adaptability and memory consolidation. NL suggests that the path forward lies not in ever deeper static networks, but in the explicit orchestration of learning and memory across nested, interacting, and frequency-sensitive modules.