Dual-Phase Self-Evolution (DPSE)

• Dual-Phase Self-Evolution (DPSE) is a design principle that decomposes self-improvement into two coupled phases: one for grounded local updates and another for global abstraction.
• It is applied across various domains such as LLM post-training, memory reorganization in agents, fast audio-video generation, and formal abstraction frameworks.
• DPSE enables mutual feedback between fast adaptation and slower systemic reorganization, yielding measurable gains in performance and robust incremental improvements.

Searching arXiv for papers on Dual-Phase Self-Evolution and closely related formulations. Dual-Phase Self-Evolution (DPSE) denotes a family of architectures in which self-improvement is decomposed into two coupled phases rather than a single adaptation loop. In recent arXiv usage, the label spans continual post-training of LLMs from interaction logs, dual-process memory reorganization for LLM agents, dual-mode self-distillation for fast autoregressive audio-video generation, and a formal theory of autonomous problem solving based on abstraction algebras (Sun et al., 21 Jul 2025, Fei et al., 8 Jun 2026, Zhou et al., 28 Apr 2026, Tirri, 2013). The common invariant is architectural bifurcation: one phase preserves, grounds, or locally updates state, while the other phase reorganizes, abstracts, or optimizes that state so that subsequent behavior can improve over time.

1. Terminological scope and recurring structure

The literature does not use DPSE as a single standardized algorithm. Rather, it is a recurrent design pattern instantiated over different computational objects: model parameters, agent memory, generative trajectories, or abstract solver algebras. This suggests that DPSE is best read as a structural principle rather than a fixed recipe.

Setting	First phase	Second phase
LLM post-training	supervised domain grounding on a topic-aware expanded domain dataset	frequency-aware preference optimization on a preference dataset
LLM agent memory	synchronous daytime writer	asynchronous nighttime engine
Audio-video generation	Multi-step mode	Few-step mode
Autonomous problem solving	representation / abstraction evolution	operational / solver evolution

In "A Novel Self-Evolution Framework for LLMs" (Sun et al., 21 Jul 2025), the two phases are explicit stages of fine-tuning. In the DCPM reconstruction presented as a DPSE-like architecture (Fei et al., 8 Jun 2026), the split is between online memory writing and offline cognitive induction. In "Mutual Forcing: Dual-Mode Self-Evolution for Fast Autoregressive Audio-Video Character Generation" (Zhou et al., 28 Apr 2026), the split is between Multi-step and Few-step operation inside a single weight-shared causal model. In "Evolution Theory of Self-Evolving Autonomous Problem Solving Systems" (Tirri, 2013), the split is a formal decomposition between representation evolution and solver evolution.

2. Continual LLM post-training from interaction logs

In "A Novel Self-Evolution Framework for LLMs" (Sun et al., 21 Jul 2025), DPSE is a framework for turning a static, pre-trained LLM into a continually improving system that autonomously refines both its domain-specific competence and its alignment with user preferences using only its own interaction logs with users. The pipeline begins with a Censor module that extracts five normalized signals from each interaction—explicit feedback, dwell time, coherence, similarity, and sentiment—computes a scalar satisfaction score in $[-1,1]$, classifies the topic, and stores a structured record in a memory pool.

The Censor is not a simple weighted average. It applies a Gate network with Sigmoid output $G \in [0,1]^5$ and a Credibility network with Softmax output $C \in \Delta^5$, combining them as

$\text{GatedSignals} = G \odot S \odot e^{C}.$

It then imposes interpretable constraints on signal weights. Similarity is treated as a penalizer with a fixed budget of $0.1$, the remaining four signals share $0.9$, similarity is modulated by negative sentiment, explicit feedback is given a minimum threshold $\tau$, and the final constrained score is

$$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$

This intermediate score is passed through a small neural fusion network with a final Tanh activation.

Once the memory size reaches a threshold $N$, such as $500$, $G \in [0,1]^5$0, or $G \in [0,1]^5$1, DPSE triggers dataset construction. Preference-driven expansion duplicates or augments high-satisfaction interactions, while topic-aware expansion increases coverage of underrepresented domains. The resulting datasets are used in a two-stage fine-tuning pipeline. Stage 1 is supervised domain grounding on the topic-expanded dataset with the standard cross-entropy objective

$G \in [0,1]^5$2

Stage 2 is frequency-aware preference optimization with a weighted DPO objective,

$G \in [0,1]^5$3

The ordering is semantically important: domain cognition is grounded first, then user-preference alignment is applied on top of that grounded model.

Empirically, the framework is evaluated on AlpacaEval 2.0, MT-Bench, LoCoMo, and WildChat. On AlpacaEval 2.0 and MT-Bench, Zephyr-7B-DPSE$G \in [0,1]^5$4 reaches $G \in [0,1]^5$5 and $G \in [0,1]^5$6, compared with $G \in [0,1]^5$7 for Zephyr-7B-SFT, $G \in [0,1]^5$8 for Zephyr-7B-DPO, $G \in [0,1]^5$9 for Zephyr-7B-UPO, and $C \in \Delta^5$0 for Zephyr-7B-UPO-Merge. The reported improvements are statistically significant with $C \in \Delta^5$1. On LoCoMo with Qwen2-1.5B, DPSE$C \in \Delta^5$2 yields $C \in \Delta^5$3 F1 and $C \in \Delta^5$4 BLEU-1 on single-hop questions, and $C \in \Delta^5$5 F1 and $C \in \Delta^5$6 BLEU-1 on multi-hop questions. In the WildChat streaming experiment, the MT-Bench score improves from $C \in \Delta^5$7 to $C \in \Delta^5$8 over time. The trigger-threshold analysis further reports that $C \in \Delta^5$9 at threshold $\text{GatedSignals} = G \odot S \odot e^{C}.$0 gives the best balance of update frequency, gain per update, and stability.

3. Dual-process memory and cognitive reorganization for LLM agents

In the DPSE-oriented reconstruction of DCPM (Fei et al., 8 Jun 2026), self-evolution is not primarily parameter updating but memory reorganization. The system is motivated by the claim that standard memory systems collapse storage of raw content, belief dynamics, and cognitive abstraction into a single retrieval surface tuned for surface recall. The proposed alternative is a cognitive hierarchy composed of raw inputs, atomic facts, identity items, diachronic belief trajectories, schemas, intentions, and cross-domain core schemas.

The lower substrate is a vector store containing a raw-input store, a fact store, and an identity store. Raw inputs are lossless utterance-level records that are never deleted. Facts and identity items include type, topic, salience, and timestamp. The middle tier introduces doubly linked supersedes chains rather than update-in-place revision. On a SUPERSEDE operation,

$\text{GatedSignals} = G \odot S \odot e^{C}.$1

Predecessors are not deleted, so each belief becomes a diachronic trajectory $\text{GatedSignals} = G \odot S \odot e^{C}.$2. This supports recovery of earlier belief states, approximate causal context, and temporal reasoning over revision histories. Identity items are designed to be stable and are rarely superseded, reported as less than $\text{GatedSignals} = G \odot S \odot e^{C}.$3 in experiments.

The upper tier is a graph $\text{GatedSignals} = G \odot S \odot e^{C}.$4 whose nodes are schemas, intentions, and later core schemas. Schemas summarize within-domain behavioral regularities; intentions encode latent concerns about future events; core schemas unify semantically distant but behaviorally similar patterns across domains. Each schema or intention node contains evidence_vdb_ref links to supporting fact IDs and structural edges to other graph nodes.

The dual-phase split follows dual-process theory. System 1, the synchronous daytime writer, is triggered on explicit add_memory requests rather than every turn. Under a tight latency budget, it performs raw persistence, extraction of identity items and atomic facts, reconcile decisions $\text{GatedSignals} = G \odot S \odot e^{C}.$5, batch upsert, and supersedes-chain maintenance. System 2, the asynchronous nighttime engine, operates during idle or scheduled windows. Its first phase is non-LLM preprocessing over fresh facts using two-stage DBSCAN with $\text{GatedSignals} = G \odot S \odot e^{C}.$6, $\text{GatedSignals} = G \odot S \odot e^{C}.$7, and $\text{GatedSignals} = G \odot S \odot e^{C}.$8. Its second phase uses an induction agent $\text{GatedSignals} = G \odot S \odot e^{C}.$9 with four tools—create_schema, create_intention, add_evidence, and add_edge—to evolve $0.1$0. Its third phase is a cross-domain sweeper: each schema is mapped to a behavioural description and two embeddings, behavioural and semantic, and cross-domain collisions are flagged when behavioural similarity exceeds $0.1$1 while semantic similarity is below $0.1$2. Union-find clusters these collisions, and a core-schema inducer $0.1$3 creates higher-level nodes.

The read path is explicitly LLM-free. Query retrieval uses hybrid similarity over dense and sparse signals,

$0.1$4

with $0.1$5. The implementation uses Qdrant with an HNSW index, bge-m3 embeddings of dimension $0.1$6, and a reconcile retrieval budget of top-$0.1$7. Retrieval traverses supersedes chains, pulls linked schemas and intentions via evidence_vdb_ref, and passes the resulting structured memory to the inference LLM.

The reported empirical pattern is asymmetric in exactly the sense predicted by the architecture. Enabling System 2 yields small gains on LongMemEval $0.1$8 and PersonaMem $0.1$9, but larger gains on PersonaMem-v2 $0.9$0 for deepseek and $0.9$1 for kimi). Ablations show that removing core-schema collision costs approximately $0.9$2 points on PersonaMem-v2, removing schema and intention nodes costs a further approximately $0.9$3, and removing supersedes chains together with System 2 loses an additional approximately $0.9$4. The design claim is therefore not that all memory tasks improve equally, but that offline abstraction matters most when the benchmark rewards implicit cross-session inference and cross-domain personalization.

4. Dual-mode self-evolution in autoregressive audio-video generation

"Mutual Forcing: Dual-Mode Self-Evolution for Fast Autoregressive Audio-Video Character Generation" (Zhou et al., 28 Apr 2026) uses the language of dual-mode self-evolution rather than DPSE proper, but the DPSE-oriented interpretation is straightforward: a single autoregressive model operates in two modes that mutually improve one another. The model is a dual-branch Transformer with a $0.9$5B-parameter video branch and a $0.9$6B-parameter audio branch, for a total of $0.9$7B parameters. Joint audio-video modeling is implemented by shared self-attention; positional encoding uses 3D RoPE with timestamp-derived coordinates.

At the diffusion level, the same parameter set $0.9$8 serves two operating modes. Multi-step mode is a standard many-step ODE solver and acts as the high-fidelity regime. Few-step mode is an aggressively subsampled large-step integrator intended for $0.9$9 to $\tau$0 diffusion steps. The streaming generation factorization is causal over chunks,

$\tau$1

and the overall objective is

$\tau$2

with

$\tau$3

The two directions of coupling are the distinctive feature. Multi-step mode is trained directly on real data, but under context histories generated by Few-step mode rather than ground truth; this reduces train-test mismatch. Few-step mode is trained by self-distillation from Multi-step mode, using stop-gradient on the teacher side. Because both modes share parameters, improvements in Multi-step quality sharpen Few-step targets, while improvements in Few-step quality produce more realistic historical context for Multi-step training. The paper also places this dual-mode phase inside a larger two-stage training strategy: uni-modal pretraining for audio-only and video-only generators, followed by a coupled audio-video model trained on paired data.

The empirical claim is that this mutual forcing mechanism removes the need for an additional bidirectional teacher model, supports more flexible training sequence lengths, reduces training overhead, and allows the model to improve directly from real paired data rather than a fixed teacher. The reported comparison is against strong baselines that require around $\tau$4 sampling steps, whereas Mutual Forcing uses only $\tau$5 to $\tau$6 steps. At $\tau$7 NFEs, it reports LSE-C $\tau$8, audio metrics FD $\tau$9 and KL $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$0, and video metrics AS $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$1 and ID $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$2. The speed table reports $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$3 FPS at $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$4, $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$5 FPS at $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$6, and $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$7 FPS at $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$8 on a single GPU. Additional ablations report more than $$\text{Score}_{\text{sat}} = \sum_i \hat{w}_i \cdot \tilde{s}_i.$$9 similarity between the attention maps of Multi-step and Few-step modes, improved temporal attention distribution over history, and nearly constant quality over $N$0–$N$1 s, $N$2–$N$3 s, and $N$4–$N$5 s windows.

5. Formal abstraction-theoretic formulations

Within the framework of "Evolution Theory of Self-Evolving Autonomous Problem Solving Systems" (Tirri, 2013), a DPSE mechanism is formalized as a two-phase evolution of representation and operation. Phase 1 is representation or abstraction evolution and is built from nets, jungles, NUO-presentations, net block homomorphisms (NBH), abstraction relations, universal partitioning renetting systems (UPRNS), and universal abstraction relations. Phase 2 is operational or solver evolution and is built from renetting systems (RNS), transducers (TD), normal forms, saturation by groups of equivalence relations, quotient transducer algebras, and multi-order abstraction algebras.

The core representational object is the net. NUO-presentation introduces overlapping block representations, allowing a net to be decomposed into a context plus subnets that may overlap with that context. A D-net block homomorphism rewrites entire blocks rather than single operators. Several specialized NBH classes are defined, including alphabetical, environment-saving, abstracting, and straightforward abstracting NBH. A central reversibility claim is Proposition 3.1: for each ANBH there exists an inverse ANBH. Abstraction relations induced by NBH are explicitly stated to be equivalence relations over nets.

UPRNS extends abstraction by imposing environmental preservation and outward rank number preservation. This supports abstraction classes that preserve structural connectivity while altering representational form. The resulting abstraction relations are then used to build net class rewriting algebras and partially quotient algebras in which operations act on equivalence classes rather than individual nets.

The second phase lifts these ideas to solvers. An RNS is a graph rewriting system over nets; a TD is a realization of nets whose operator nodes are annotated with RNS families. Normal forms $N$6 make it possible to speak of canonical irreducible results. The framework then establishes a tight bridge between representation and operation: Theorem 3.2.1 states that for any NBH $N$7 there exists an RNS $N$8 such that $N$9; Theorem 3.2.2 gives the converse; Theorem 3.2.3 states that NBH and RNS have equal operational power. The compatibility theorem

$500$0

expresses that solving and abstracting commute up to a derived solver $500$1. This relation is precisely what allows the two phases to be iterated rather than treated as disconnected procedures.

The framework then defines TD-abstraction relations, first-order abstraction algebras, higher-order abstraction algebras, and autonomous evolution mappings $500$2. In effect, solver classes become objects of further abstraction, producing a hierarchy in which solution operators themselves evolve by quotienting, saturation, and iterative closure. In this formal sense, DPSE is not merely a heuristic alternation between two update rules; it is a layered algebraic construction over representations and solvers.

6. Comparative interpretation, misconceptions, and constraints

A common misconception is to equate DPSE with external memory alone. The LLM post-training formulation explicitly contrasts itself with memory-based retrieval and preference optimization because those methods do not change the core model parameters (Sun et al., 21 Jul 2025). The DCPM-derived formulation makes a complementary claim: a single retrieval surface tuned for surface recall collapses belief revision, causal coupling, and cognitive abstraction into one mechanism and therefore struggles with implicit personalization (Fei et al., 8 Jun 2026). DPSE, in both cases, is defined by structured self-improvement, not by storage in isolation.

A second misconception is that DPSE names a settled technical standard. The cited literature instead uses the label, or a DPSE-oriented interpretation, for several non-equivalent mechanisms: satisfaction-weighted continual fine-tuning from logs, dual-process memory induction, mutually reinforcing diffusion modes, and abstraction-driven solver evolution (Zhou et al., 28 Apr 2026, Tirri, 2013). This suggests that the stable content of DPSE is architectural duality plus mutual feedback, while the mutable content is the substrate being evolved.

The constraints are equally heterogeneous. In the LLM self-training formulation, the methodology raises issues of Censor bias and errors, data drift, catastrophic forgetting, safety concerns, and computational cost (Sun et al., 21 Jul 2025). In the DCPM-derived memory architecture, System 2 incurs offline cost growth, the cross-domain sweeper requires $500$3 comparisons, natural-language schemas are not algebraically composable, and thresholds such as $500$4 and $500$5 are manually tuned (Fei et al., 8 Jun 2026). In Mutual Forcing, stable operation depends on hybrid SC+DMD supervision, stop-gradient teacher behavior, EMA, and balanced scheduling between phases (Zhou et al., 28 Apr 2026). In the abstraction-algebraic framework, decidability depends on recognizers and allowed RNS types, so unrestricted self-evolution is not guaranteed to remain tractable (Tirri, 2013).

Taken together, the literature suggests a precise but broad interpretation. DPSE is a design principle in which a system separates fast or local adaptation from slow or global reorganization, then couples the two so that each phase improves the other. In one lineage this yields supervised domain grounding followed by frequency-aware preference optimization; in another it yields supersedes-chain memory plus nighttime schema induction; in another it yields Multi-step and Few-step mutual forcing inside a single causal diffusion model; and in the most abstract lineage it yields iterative co-evolution of representations and solvers. The term is therefore unified by architecture, not by task domain or by a single canonical algorithm.