HANNA: Multifaceted Applications in Science and AI

• HANNA is a multi-context label used to denote a thermodynamic neural network, embodied AI simulator, story evaluation benchmark, hardware-aware NAS architecture, and a reference to the Hanna Neumann conjecture.
• In thermodynamics, HANNA employs hard constraints to ensure Gibbs-Duhem consistency, achieving lower mean absolute errors compared to traditional models like UNIFAC.
• Across domains, HANNA facilitates interactive navigation in embodied AI, evaluates automatic story generation against human criteria, and optimizes device-specific neural architectures while linking to mathematical group theory.

HANNA is a label used in several distinct arXiv research contexts. In recent machine-learning literature, it denotes a hard-constraint neural network for activity-coefficient and excess-Gibbs-energy prediction in liquid mixtures (Specht et al., 2024, Hoffmann et al., 8 Sep 2025). In embodied AI, it denotes “Help, Anna!”, an interactive photo-realistic simulator for navigation with natural multimodal assistance (Nguyen et al., 2019). In natural-language generation evaluation, it denotes a human-annotated benchmark for story assessment (Chhun et al., 2022). In hardware-aware model design, it denotes a neural architecture discovered by differentiable NAS (Srinivas et al., 2019). Separately, the proper name “Hanna” is central to the Hanna Neumann conjecture and its extensions in combinatorial and geometric group theory (Hunt, 2015).

1. Disambiguation across research domains

The uses represented in the cited literature are heterogeneous rather than terminologically unified. Some are acronyms for concrete systems or datasets, while another refers to Hanna Neumann through the Hanna Neumann conjecture. The following summary isolates the main referents appearing in arXiv-indexed work (Specht et al., 2024, Hoffmann et al., 8 Sep 2025, Nguyen et al., 2019, Chhun et al., 2022, Srinivas et al., 2019, Hunt, 2015).

Domain	Expansion or referent	Core role
Thermodynamics ML	Hard-constraint Neural Network for Consistent Activity Coefficient Prediction	Predicts activity coefficients and excess Gibbs energy
Embodied AI	“Help, Anna!”	Interactive simulator for help-seeking visual navigation
Story evaluation	Human-ANnotated NArratives	Benchmark for human and automatic evaluation of ASG
Hardware-aware NAS	Hardware Aware Neural Network Architecture	Device-optimized child architecture
Group theory	Hanna Neumann conjecture	Rank bound for subgroup intersections

This multiplicity matters because the same token, “HANNA,” can refer either to a thermodynamic surrogate model, a benchmark, a simulator, an architecture-search outcome, or a mathematical lineage associated with Hanna Neumann. In technical writing, the surrounding domain therefore determines the intended meaning.

2. HANNA in mixture thermodynamics: binary activity coefficients

The 2024 paper “HANNA: Hard-constraint Neural Network for Consistent Activity Coefficient Prediction” defines HANNA as a neural-network model for predicting activity coefficients in binary mixtures from SMILES, mole fractions, and temperature (Specht et al., 2024). Its central design choice is that thermodynamic consistency criteria are enforced by construction rather than imposed as soft penalties. The architecture combines ChemBERTa-2 molecular embeddings, a component embedding network, a deep-set mixture embedding network, and a property prediction network that outputs a preliminary estimate of the dimensionless molar excess Gibbs free energy.

The hard-constraint step is explicit. The model transforms the neural prediction according to

$$\frac{g^\mathrm{E}}{RT} = g^\mathrm{E}_{\rm NN}\cdot x_1(1-x_1)\cdot \left(1-\cos(\mathbf{f}_\theta(\mathbf{E}_1),\mathbf{f}_\theta(\mathbf{E}_2))\right),$$

so that $g^\mathrm{E}$ vanishes for pure components and for pseudo-binary mixtures of identical species (Specht et al., 2024). The activity coefficients are then derived by automatic differentiation: $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$ Because both $\ln \gamma_i$ are obtained from a single $g^\mathrm{E}$, the Gibbs-Duhem equation is automatically satisfied in the binary setting (Specht et al., 2024).

Permutation symmetry is handled through a deep-set aggregation: $$\mathbf{C}_{\rm mix}=\sum_{i=1}^2 \mathbf{f}_\alpha(\mathbf{C}_i).$$ This makes the model permutation invariant with respect to component order, which is a physical symmetry requirement for binary mixtures (Specht et al., 2024). The paper also states explicit guarantees for the activity coefficient of a pure component, pseudo-binary identity, and permutation equivariance.

The training corpus came from the Dortmund Data Bank. The reported dataset size was 317,421 data points over 35,012 binary systems and 2,677 unique components, using vapor–liquid equilibria data and activity coefficients at infinite dilution (Specht et al., 2024). The evaluation compared HANNA against modified UNIFAC Dortmund using system-wise mean absolute error. The reported results included a median MAE of 0.05 for HANNA versus 0.09 for UNIFAC, and 74% of test systems with MAE $<0.1$ for HANNA versus 54% for UNIFAC (Specht et al., 2024). The same study emphasized coverage advantages: HANNA requires only SMILES, mole fraction, and temperature as inputs.

3. HANNA in mixture thermodynamics: excess Gibbs energy and multi-component extrapolation

The 2025 paper “A machine-learned expression for the excess Gibbs energy” extends HANNA from a binary activity-coefficient predictor to a model that predicts the excess Gibbs energy of liquid mixtures directly from molecular structure and state point, across binary and multi-component systems (Hoffmann et al., 8 Sep 2025). The model is described as “Hard-constraint Neural Network for consistent Activity coefficient prediction,” but the operational emphasis shifts to $g^\mathrm{E}$ as the primary learned object.

In this formulation, molecular structures are again encoded from SMILES using ChemBERTa-2 embeddings, which are processed by an embedding network, a mixture network, and a pairwise property network that predicts binary interactions $q_{ij}$. Multi-component prediction is then assembled through the Muggianu geometric projection: $$\frac{g^\mathrm{E}}{RT} = \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} x_i x_j q_{ij}.$$ The paper states that this step is parameter-free and reduces exactly to the binary values in the binary limit (Hoffmann et al., 8 Sep 2025). A plausible implication is that HANNA treats multi-component prediction as a structured extrapolation from binary-trained interaction functions rather than as a separate parameterized model family.

The thermodynamic constraints are broader than in the 2024 binary-only formulation. The activity coefficients are computed from $g^\mathrm{E}$0 via automatic differentiation using

$g^\mathrm{E}$1

and

$g^\mathrm{E}$2

The paper explicitly associates this with Gibbs-Duhem compliance, permutation invariance, component lumping, pure-component and binary limits, and smoothness through Lipschitz regularization (Hoffmann et al., 8 Sep 2025).

A distinctive methodological contribution is the inclusion of liquid-liquid equilibrium data through a differentiable surrogate solver. The paper states that the surrogate solver was trained separately, using synthetic data generated from mod. UNIFAC, to emulate the Convex Envelope Method for extracting LLE phase compositions from a predicted discretized Gibbs energy profile (Hoffmann et al., 8 Sep 2025). This avoids embedding a non-differentiable nonlinear root-finding loop in end-to-end training.

The total loss is reported as

$g^\mathrm{E}$3

with a Gibbs stability loss and a Lipschitz regularization term

$g^\mathrm{E}$4

Training used system-wise data splits, AdamW with OneCycleLR, and ensembles of multiple models (Hoffmann et al., 8 Sep 2025).

The 2025 paper reports binary-mixture coverage of over 36,000 unique systems, more than 3000 unique components, and more than 330,000 data points, with temperatures mainly in the range 273–433 K (Hoffmann et al., 8 Sep 2025). It compares HANNA against mod. UNIFAC (Dortmund), mod. UNIFAC 2.0, and UNIFAC-LLE, and states that HANNA consistently outperforms these benchmark models in system-wise mean absolute error for VLE, ACI, and LLE phase compositions in both binary and ternary systems (Hoffmann et al., 8 Sep 2025).

4. Other acronymic uses of HANNA in AI and machine learning

Outside thermodynamics, HANNA labels several unrelated artifacts. In embodied AI, “Help, Anna!” is an interactive simulator in which an agent solving object-finding tasks can request assistance from Automatic Natural Navigation Assistants (ANNAs) that provide natural language instructions and a target image (Nguyen et al., 2019). The simulator is built atop Matterport3D and contains 68 residential buildings. The associated agent is memory-augmented and hierarchical, with separate navigation and help-request policies, text memory, inter-task and intra-task modules, and a retrospective curiosity-encouraging imitation-learning algorithm (Nguyen et al., 2019). Reported evaluation used success rate, SPL, navigation error, and requests per task; the paper gives results such as SR $g^\mathrm{E}$5, SPL $g^\mathrm{E}$6, and navigation error $g^\mathrm{E}$7 m on SeenEnv, and SR $g^\mathrm{E}$8, SPL $g^\mathrm{E}$9, and navigation error $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$0 m on UnseenAll (Nguyen et al., 2019).

In automatic story generation evaluation, HANNA denotes a benchmark dataset named Human-ANnotated NArratives (Chhun et al., 2022). It contains 1,056 stories produced by 10 ASG systems, using 96 prompts from WritingPrompts, with 3 annotations per story across six human criteria: relevance, coherence, empathy, surprise, engagement, and complexity. The resulting total is 19,008 human annotations, and each story is also associated with 72 automatic metrics (Chhun et al., 2022). The paper distinguishes story-level from system-level correlations and reports that most automatic metrics show weak to moderate correlation with human ratings at the story level, while system-level correlations can be substantially higher. It also reports top story-level absolute Pearson correlations such as 42.6 for relevance with BARTScore, 43.0 for engagement with BERTScore Recall, and 58.8 for complexity with chrF (Chhun et al., 2022).

In hardware-aware architecture search, HANNA stands for Hardware Aware Neural Network Architecture (Srinivas et al., 2019). That paper extends an FBNet-inspired differentiable NAS objective by adding an energy term: $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$1 The search space is a supernet with 24 layers, 22 of which are to-be-searched layers, each choosing one of 9 candidate blocks, for a search space of $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$2 possible architectures (Srinivas et al., 2019). Latency and energy are profiled on Raspberry Pi 3B and incorporated into the differentiable search. The reported benchmark on CIFAR-10 gives accuracy $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$3, latency $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$4 s, and energy $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$5 J for HANNA, versus $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$6, $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$7 s, and $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$8 J for MobileNetV2, and $$\ln \gamma_1 = \frac{g^\mathrm{E}}{RT} + (1-x_1)\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}, \qquad \ln \gamma_2 = \frac{g^\mathrm{E}}{RT} - x_1\left(\frac{\partial g^\mathrm{E}}{\partial x_1}\right)_{T,p}\frac{1}{RT}.$$9, $\ln \gamma_i$0 s, and $\ln \gamma_i$1 J for CondenseNet (Srinivas et al., 2019).

These uses share no common ontology beyond the name. In one case HANNA is a physics-constrained thermodynamic surrogate, in another a simulator, in another an evaluation benchmark, and in another a NAS-discovered architecture.

5. “Hanna” in mathematics: the Hanna Neumann conjecture and extensions

The mathematical use of “Hanna” is not acronymic. It refers to Hanna Neumann through the Hanna Neumann conjecture for finitely generated subgroups of a free group. With reduced rank

$\ln \gamma_i$2

the conjecture states

$\ln \gamma_i$3

and the strengthened form sums over double cosets $\ln \gamma_i$4 with nontrivial intersections $\ln \gamma_i$5 (Hunt, 2015). The 2015 paper “The Hanna Neumann Conjecture and the rank of the join” treats an inclusion–exclusion style extension involving the join $\ln \gamma_i$6,

$\ln \gamma_i$7

which it proves under a finite-index hypothesis and disproves in general by explicit counterexamples (Hunt, 2015). The same paper also gives a counterexample to Guzman’s conjecture for $\ln \gamma_i$8 and discusses graph-based random subgroup generation using Stallings graphs and random partial injections, following Bassino, Nicaud, and Weil (Hunt, 2015).

The strengthened Hanna Neumann conjecture was independently proved in 2011. Joel Friedman’s sheaf-theoretic proof develops sheaves of vector spaces on graphs, their homology, and the invariant called maximum excess, using Galois graph theory and $\ln \gamma_i$9-kernels to reduce the conjecture to a vanishing statement for maximum excess (Friedman, 2011). In a different extension, the reduced Kurosh rank of intersections of subgroups of free products of right-orderable groups is bounded above by the product of the reduced Kurosh ranks, recovering the strengthened Hanna Neumann inequality for free groups as a special case (Antolín et al., 2011).

Subsequent work generalizes Hanna-Neumann-type inequalities beyond free groups. Zakharov proves estimates for the reduced rank of the intersection of free subgroups in virtually free groups and, more generally, in fundamental groups of finite graphs of groups with finite edge groups, obtaining inequalities of the form

$g^\mathrm{E}$0

for free finitely generated subgroups in a virtually free group (Zakharov, 2013). A later paper establishes a strengthened analogue for arbitrary subgroups in virtually free groups, expressed via virtual reduced rank and total virtual reduced Kurosh rank (Klyachko et al., 2021). Another recent direction proves the $g^\mathrm{E}$1-Hall property for graphs of free groups with cyclic edge groups that are hyperbolic relative to virtually abelian subgroups, and deduces a strengthened geometric Hanna Neumann conjecture for those groups and for limit groups (Fisher et al., 2023).

There are also monoid-theoretic and probabilistic analogues. For submonoids of a free monoid generated by finite prefix sets, two 2011 papers study the Hanna Neumann property by means of deterministic semi-flower automata, branch points going in, product automata, and explicit rank formulas (Singh et al., 2011, Singh et al., 2011). The 2025 paper “Probabilistic Hanna Neumann Conjectures” develops polymatroids on Stallings core graphs, proves gap results for stable invariants, gives a unified proof of the “rank-1 Hanna Neumann conjecture” and its higher-rank analogue, and proposes a field-theoretic analogue of the Hanna Neumann conjecture (Shomroni, 31 Dec 2025).

6. Cross-domain patterns and conceptual significance

Despite the unrelated subject matter, the acronymic HANNA systems share a methodological tendency toward structural constraints. In the thermodynamic model, constraints are hard-coded so that Gibbs-Duhem compliance, pure-component limits, permutation invariance, and component lumping are enforced in the architecture (Specht et al., 2024, Hoffmann et al., 8 Sep 2025). In the navigation setting, the agent’s help-request behavior is organized hierarchically and trained with a retrospective teacher that identifies states where the agent will not make further progress on its own (Nguyen et al., 2019). In the story-evaluation benchmark, the framework is explicitly built around six orthogonal human criteria and a meta-evaluation protocol comparing 72 automatic metrics with those criteria (Chhun et al., 2022). In the hardware-aware NAS setting, the objective function itself encodes the multi-objective trade-off among accuracy, latency, and energy on a concrete device (Srinivas et al., 2019).

The mathematical “Hanna” literature exhibits a different but related kind of structuralism. The conjectural and proved inequalities are not merely empirical regularities; they are expressed in invariants such as reduced rank, reduced Euler characteristic, Kurosh rank, twisted homology, maximum excess, and virtual reduced rank, and they are transported across categories including free groups, free products, virtually free groups, graphs of groups, and submonoids (Hunt, 2015, Friedman, 2011, Antolín et al., 2011, Zakharov, 2013, Klyachko et al., 2021, Fisher et al., 2023, Singh et al., 2011, Singh et al., 2011, Shomroni, 31 Dec 2025).

This suggests a useful editorial distinction. “HANNA” in current applied arXiv usage usually denotes a named model, simulator, benchmark, or architecture. “Hanna” in the mathematical literature usually points to the legacy of Hanna Neumann and to intersection inequalities for algebraic objects. The overlap is lexical rather than conceptual, but both clusters are notable for making invariance, consistency, or exact structural bounds central to their formulation.