SE(3)-Bi-equivariant Transformers (BITR)

• BITR is a transformer model that integrates bi-equivariance under the SE(3) group, ensuring consistent performance across 3D rotations and translations.
• It leverages geometric symmetry to reduce model complexity and enhance generalization for tasks in robotics, molecular simulation, and computer graphics.
• Empirical results indicate that BITR achieves superior efficiency in aligning spatial data and improves performance in applications requiring 3D invariant representations.

Tool-Memory Conflict (TMC) denotes a form of knowledge conflict unique to tool-augmented LLMs, where the model’s internal parametric (memory) knowledge produces an answer that disagrees with the output obtained via externally-invoked tools—such as calculators, symbolic solvers, or retrieval APIs. TMC is especially prevalent in STEM domains and presents both theoretical and practical challenges in knowledge integration, prioritization, and conflict-resolution within the inference pipelines of current LLM architectures (Cheng et al., 14 Jan 2026).

1. Formal Definition and Conceptual Foundations

Let $f(q)$ represent the answer a tool-augmented LLM $f$ generates for a query $q$ when restricted to parametric knowledge alone, and $f(q;\mathcal{T})$ the answer generated when the model is permitted to invoke any tool $t\in\mathcal{T}$. Tool-Memory Conflict arises precisely for those queries $q$ such that

$f(q) \neq f(q; \mathcal{T})$

Thus, TMC instances are characterized by explicit disagreement between the model’s parametric recall and the knowledge retrieved or computed by external tools (Cheng et al., 14 Jan 2026).

Unlike inter-context or context-memory conflicts, which are restricted to the model’s attention stream or its parameters, TMC is motivated by the unique status of tool knowledge: acquired “on demand” via function calls and typically more temporally up-to-date or numerically precise. The LLM must nontrivially arbitrate between static, pre-trained memory and authoritative but external tool knowledge. Causes of TMC include temporal data mismatch (knowledge cutoff vs. real-time tools), noise or misinformation in tool outputs, and incorrect tool invocation (misparsed queries, invalid arguments).

2. Metrics and Theoretical Framework

TMC prevalence is quantified for dataset $\mathcal{D}$ by the empirical conflict probability: $$\Pr_{q\sim\mathcal{D}}[f(q)\neq f(q;\mathcal{T})] = \frac{1}{|\mathcal{D}|} \sum_{q\in\mathcal{D}} \mathbf{1}[f(q)\neq f(q;\mathcal{T})]$$ Beyond frequency, critical assessment of source prioritization is captured by “Memory Bias” and “Tool Bias”—the probabilities, conditioned on conflict,

• Memory Bias: the model selects its internal answer even when the tool result is objectively correct.
• Tool Bias: the model selects the tool’s output even when its own memory-produced answer is correct.

These metrics enable systematic investigation of source preference and resolution dynamics within LLM-tool pipelines (Cheng et al., 14 Jan 2026).

3. Empirical Prevalence and Domain Analysis

Comprehensive evaluation across multiple architectures (GPT-4o, DeepSeek-V3, LLaMA-3, QWen-2.5, QwQ, Groq-LLaMA-3, Watt) and datasets (MMLU, GSM8K, MATH-500, AIME 2024, GPQA Diamond) reveals TMC rates that scale inversely with model capacity. High-capacity models (GPT-4o, LLaMA-3 70B) exhibit conflict on 14–15% of queries; mid-sized models such as QWen-2.5 72B show ~27%, while smaller models (QwQ 32B, Groq-LLaMA-3 8B) exceed 75% TMC rates.

Domain breakdown yields further insights:

• Math/Arithmetic and algorithmic tasks manifest the highest TMC (>70–80%).
• Multi-hop retrieval ~50–60%.
• Humanities and social sciences <10%.
• Long-tail factual queries ~20–30%.

The occurrence of TMC is reliably associated with a quantifiable performance penalty: ~4.5 pp accuracy loss on Math, 2–3 pp on STEM/Health, with negligible (<1 pp) impact on non-technical domains (Cheng et al., 14 Jan 2026).

Model	TMC Rate (%)
GPT-4o	14.1
DeepSeek-V3	15.3
LLaMA-3 70B	15.5
QWen-2.5 72B	26.9
QwQ 32B	75.4
Groq-LLaMA-3 8B	83.2
Watt 8B	48.6

4. Knowledge Prioritization: Tool vs. Memory Bias

Systematic assessment distinguishes models by their weighting of internal versus tool-derived knowledge under conflict. High-capacity models (GPT-4o, LLaMA-3 70B) display near-equilibrium between tool and memory bias (≈40–45% each), reflecting more nuanced arbitration. Mid-capacity models show weaker but balanced bias. In lower-capacity models, tool invocation is nearly absent (tool bias <1%), with memory bias dominating, and often simply reflecting memorized correctness (as in Watt 8B’s 51.4% memory bias matching its accuracy).

Model	Tool Bias (%)	Memory Bias (%)
GPT-4o	41.7	41.9
DeepSeek-V3	39.2	41.3
LLaMA-3 70B	44.3	40.2
QWen-2.5 72B	35.8	37.3
QwQ 32B	0.1	24.5
Groq-LLaMA-3 8B	0.2	16.4
Watt 8B	0.0	51.4

This suggests that model capacity and training influence both the likelihood and modality of knowledge-source selection during TMC (Cheng et al., 14 Jan 2026).

5. Empirical Evaluation of Conflict-Resolution Methods

Several classes of conflict-resolution strategies are empirically assessed:

• Prompting approaches: “Vigilant” prompts encourage explicit comparison of tool and memory outputs; “opinion” prompts bias towards pre-selected sources.
• Retrieval-Augmented Generation (RAG): External documents or computations are appended to the input, informing the model before answer generation.

Empirical results demonstrate only modest improvements from prompting (up to ~4 percentage points (pp) conflict reduction for “vigilant” prompts, with “opinion” strategies sometimes worsening TMC via over-filtering). RAG proves comparatively more effective, reducing TMC by 2–3 pp in large models and up to 15 pp in smaller models. No method entirely resolves TMC, especially on hard STEM tasks (Cheng et al., 14 Jan 2026).

6. Specialized Architectures for TMC Mitigation

Conflict-Aware REtrieval-Augmented Generation (CARE) explicitly addresses TMC by attaching a lightweight context assessor (with soft “memory” tokens and LoRA adapters) atop a frozen base LLM. CARE is trained under dual scenarios—grounded (helpful) and adversarial (misleading) context—using objective-specific soft prompting and scenario-adaptive knowledge distillation losses. At inference, the encoded memory embedding $E_{mem}$ acts as a soft prefix, gating the base LLM’s reliance on context or memory depending on learned reliability. CARE achieves 5–6% absolute improvement over vanilla RAG in open-domain QA and fact verification and demonstrably increases system resilience to misleading external context (Choi et al., 21 Aug 2025).

For instance, removing adversarial soft-prompting or eliminating pretraining leads to substantial resilience loss, underscoring the necessity of dual-scenario training. Efficient memory-token encoding ensures CARE incurs minimal latency penalty compared to standard RAG. Embedding separation analysis (t-SNE) demonstrates that positive and negative contexts become well-clustered under CARE, facilitating adaptive arbitration between knowledge sources at generation time (Choi et al., 21 Aug 2025).

7. Practical Guidelines and Prospective Directions

Effective mitigation of TMC depends on domain-aware tool integration and tailored training:

• Math/STEM: Embed symbolic or exact-arithmetic computation pipelines to minimize numeric drift.
• Long-tail knowledge tasks: Use multi-source retrieval and cross-validation to detect and override outdated or noisy memory.
• Prompting: Design vigilance-based meta-instructions, but avoid over-specific opinion-based frames which can entrench bias.
• Training: Inject contrastive parametric-tool conflicts during fine-tuning; jointly optimize tool-selection policy.
• System design: Expose tool provenance and confidence scores to downstream consumers for interpretability and reliability.
• Architectural innovations: Fusion of tool outputs into latent states and differentiable tool interfaces, along with real-time calibration of tool confidence, represent plausible future research avenues (Cheng et al., 14 Jan 2026).

TMC is a fundamental, capacity-dependent obstacle to robust, trustworthy reasoning in tool-augmented LLMs. While interventions such as RAG and prompting offer partial relief, only architectural and training-level methods targeting the underlying arbitration mechanisms—such as those instantiated in CARE—demonstrate consistent systematic mitigation of TMC (Cheng et al., 14 Jan 2026, Choi et al., 21 Aug 2025).